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GMAT

McGraw-Hill’s

2008 Edition
James Hasik Stacey Rudnick Ryan Hackney

New York | Chicago | San Francisco | Lisbon London | Madrid | Mexico City | Milan | New Delhi San Juan | Seoul | Singapore | Sydney | Toronto

Professional

Contents

Foreword..............................................................................................................................VII McGraw-Hill’s GMAT: Introduction .........................................................................IX
@Welcome to the GMAT @Attaining Your Competitive Edge: McGraw-Hill’s GMAT @Meet the GMAT @Achieving Your Goals on the GMAT @Registering for the GMAT @Additional Practice @Some Final Advice

PART ONE
CHAPTER 1

THE QUANTITATIVE SECTION

The Techniques of GMAT Problem Solving ..................................3

CHAPTER 2

Data Sufficiency ....................................................................................13

@Can You Answer the Question? @The Intent Behind the Question Type @Working Data Sufficiency Problems Efficiently @Practice Problems
CHAPTER 3

Basic Principles of Numbers ...........................................................27

@Introduction: Remembering Your High School Math @Number Systems @Algebraic Notation and the Order of Operations @Exponents and Roots @Factoring Numbers @Working with Nonintegers @Key Concepts to Remember @Practice Problems
CHAPTER 4

Algebraic Equations and Analytical Geometry ......................43

@The Importance of Algebra @Linear Equations @Quadratic Equations @Hyperbolic Equations @Application Problem: Depreciation @Practice Problems

III

CHAPTER 5

Probability and Statistics...............................................................................63

@Introduction: What Do Numbers Mean? @The Mean @The Median @The Mode @The Range @Calculating the Standard Deviation @What You Need to Remember @Application Problems—Statistics @Probability @Practice Problems
CHAPTER 6

GMAT Geometry ................................................................................................79

@Introduction @Parallel and Intersecting Lines @Types of Triangles and Their Attributes @Quadrilaterals @Circles @Volume of Boxes and Right Circular Cylinders @What You Need to Remember @Practice Problems
CHAPTER 7

Boolean Problems and Combinatorics ....................................................99

@Introduction @Boolean Problems on the GMAT @Combinatorics Problems: Two Approaches @Practice Problems

PART TWO
CHAPTER 8

THE VERBAL AND WRITING SECTIONS

Critical Reasoning ..........................................................................................115

@Introduction @Critical Reasoning Reading @What Is an Argument? @Assumption Questions @Weaken the Argument @Strengthen the Argument @Inference Questions @Less Common Question Types @The Art of Wrong Answers @Practice Arguments @Practice Problems
CHAPTER 9

Sentence Correction.......................................................................................137

@Introduction @Verbs: Where the Action Is @Pronouns: In Place of the Right Answer @Misplaced Modifiers @Parallelism @Idiomatic Expressions @False Comparisons: Apples and Oranges @Quantity @Rare Errors @The Most Common Type of Error @How to Approach a Hard Question @Further Study @Practice Sentences @Practice Problems
CHAPTER 10

CHAPTER 11

The Analytical Writing Assessment ......................................................175

@Introduction @How the Analytical Writing Assessment Is Used @How to Approach the AWA @How the Writing Assessment Is Scored @Factors That Can Help or Hurt Your Score @Maximizing Your Score @Analysis of an Issue @Analysis of an Argument @Practice Essays

IV#

CONTENTS

PART THREE
CHAPTER 12

BEYOND THE GMAT

Choosing the Right Program ...................................................................191

@Introduction @Choosing a School: Considering Your Objectives @A Brief Taxonomy of MBA Program Types @A Brief Bibliography of School Ratings Lists @Selecting a Portfolio of Schools
CHAPTER 13

@The Importance of the GMAT in Admissions @The Importance of Your Past University Transcripts @Researching the Programs @Preparing Your Résumé @Soliciting the Right Recommendations @Requesting an Interview @Writing Some Compelling Essays @Thinking About Your Career Plan During the Admission Process
CHAPTER 14

Getting Ready to Survive B-School ......................................................211

@Concepts to Remember from Your GMAT Preparation @Math Camp @Essential Tools for the MBA Student
CHAPTER 15

Recruiting and Career Management ...................................................215

@Introduction @The Importance of the GMAT to Recruiters @Planning Your Job Search @Tools for Career Management @Preparing Your Cover Letters @Thank-you Notes @Interviews @Finishing Up and Looking Back @Networking @Selecting the Right Offer @Will the GMAT Ever Haunt You Again?

PART FOUR

THE PRACTICE TESTS

Instructions for the GMAT Practice Tests .....................................................................................234

Practice Tests ........................................................................................................................235
@Practice Test 1 @Practice Test 2 @Practice Test 3 @Practice Test 4 @Practice Test 5 @Practice Test 6

@Practice Test 1 @Practice Test 2 @Practice Test 3 @Practice Test 4 @Practice Test 5 @Practice Test 6

CONTENTS

\$V

Foreword

VII

VIII# FOREWORD

McGraw-Hill’s GMAT: Introduction

WELCOME TO THE GMAT

ATTAINING YOUR COMPETITIVE EDGE: McGraw-Hill’s GMAT
Broadly speaking, success in business comes from effectively executing a strategy to attain a competitive edge. What you are looking for in your application to business school is a competitive edge; the GMAT is, after all, a competition between you and every other B-school candidate in the country. There can be a lot of winners in this competition, but you will be compared to each of them, so you must develop a strategy that will help you attain your competitive edge on this vital aspect of the application process. This book will help you develop two different strategies: first, a strategy of preparation for the days, weeks, or months before you take the test; and second, a strategy of execution for when you walk into the testing center and sit down at the keyboard.

IX

MEET THE GMAT
Please allow us to introduce you to your new friend, the GMAT. The GMAT is a three-and-a-half-hour writing and multiple-choice test. For many years GMAT test forms were created by Educational Testing Service (ETS), a private company based in Princeton, New Jersey. ETS is famous as the creator of the SAT. However, since January 2006, creating new GMAT test forms has been the job of ACT, Inc., an Iowa-based company that also develops a well-known college admission exam. ACT designs the GMAT in coordination with the Graduate Management Admission Council (GMAC), a consortium of business schools with its headquarters in McLean, Virginia. GMAC provides ACT with guidelines about the type of information business schools are looking for from the GMAT, and ACT turns these guidelines into the test you are going to encounter in the near future. Administering the test is the job of still another company, called Pearson VUE. This company is the electronic testing division of Pearson Education.

What You Will See
You will probably take the GMAT on a computer at a Pearson VUE test center. You’ll get the specifics about where and when that will be when you register for the test (more on registration at the end of this chapter). The parts of the test are as follows:
Section Analytical Writing Assessment Analytical Writing Assessment Optional Break Quantitative Number of Questions 1 “Analysis of an Issue” 1 “Analysis of an Argument” Number of Minutes 30 30 10 75

37 Multiple-Choice ~15 Data Sufficiency ~22 Problem-Solving

Continued
X# INTRODUCTION

Section Optional Break Verbal

Number of Questions 41 Multiple-Choice ~12 Critical Reasoning ~14 Reading Comprehension ~15 Sentence Correction

Number of Minutes 10 75

Each of these test sections is covered in detail in the chapters of this book. Add up the minutes and the number of different types of questions you’re going to face. When you take the test, you will spend about four hours in the testing center furiously analyzing, writing, computing, reading, scribbling, reasoning, and, almost certainly, guessing. It’s not an easy test—if it were, business schools wouldn’t use it. But with the proper preparation, you can handle it and make your score work for you.

How the GMAT Is Scored

The computer-adaptive GMAT is not the same test as the old paper-based GMAT. When you take the test on a computer, the computer gives you different questions based on how many of the previous questions you have answered correctly. It begins by giving you a question of medium difficulty— which means that ACT expects roughly half of the test takers to answer it correctly and half to get it wrong—and if you answer it correctly, the computer will give you a harder question; if you answer it incorrectly, the computer will give you an easier question. As you answer more questions, the computer will refine its picture of the level of difficulty you are capable of handling. By the end of the test, it should, theoretically, present you with questions at a level of difficulty where you get about half the questions right and half wrong (unless you’re heading for either a very high or a very low score). Obviously, the higher the level of difficulty at which you end a test section, the higher your score will be. You want to see hard questions.
INTRODUCTION

\$XI

1 2 3 4 5 6 7 A A A A A A A B B B B B B B C C C C C C C D D D D D D D E E E E E E E

4. You have to type the Analytical Writing Assessment essays. This could be an advantage for you if you are a good typist, but it could be a handicap if you don’t often type. See more in Chapter 11, “The Analytical Writing Assessment.”

XII#

INTRODUCTION

ACHIEVING YOUR GOALS ON THE GMAT

Preparation Strategy
Your GMAT preparation strategy can differ dramatically based on how much time you have to prepare. A two-month preparation plan will be significantly different from a two-week plan. We have attempted to make McGraw-Hill’s GMAT into a flexible tool that you can use in the way that works best for you. The one thing you can’t get around, though, is time. The more time and energy you devote to preparation, the better your odds are of achieving your goals.
INTRODUCTION \$XIII

Action Plan 1—If You Have Two Months
This is an adequate amount of study time for most people, but that depends on your work schedule and personal commitments. If you have a spouse and family, this is a good time to practice your skills at getting “buy-in” from your family members so that they will support your efforts to get a great score on the GMAT.
Two months until test day

\$ Examine your scores from the practice GMAT that you took. Since you have two months to prepare, you can probably focus on each area of the test in depth, but you should start with your weaknesses. Reading Comprehension in particular tends to require more long-term work, so it may be a good idea to start working on the Reading Comprehension chapter early. If there is any math content that consistently gives you trouble—geometry, perhaps, or quadratic equations—start brushing up on it as well. Similarly, certain question types may be problematic; Data Sufficiency questions are generally unfamiliar to most test-takers before taking the GMAT, so they may be a weakness. Identify three key areas to work on first.
XIV# INTRODUCTION

\$ Schedule time over the following month to work on the chapters in this book that correspond to those three key areas. Be sure you read and review each whole chapter, in addition to working the drills at the end of each chapter. For the best retention, read the chapter and work half of the practice problems in one study session, then review the chapter and work the remainder of the practice problems in the next study session. \$ Set aside time to take one of the practice tests in the book (or another if you have already taken one). Take the entire test in one sitting, if possible. If not, at least take a whole section at a time.
One month until test day

\$ Take another GMAT from the CD-ROM or from the tests in this book to check your progress. Chances are, you’ve improved in your weaker areas, but you still need to increase your overall speed. \$ Schedule time in the next three weeks to complete the chapters you have not worked and take two more practice tests in the book. For chapters that cover material with which you are adept, start with the drills at the end of the chapter. Do half of them and check your accuracy. If you’ve made any mistakes, review the explanations and use the chapter to brush up on your knowledge and skills; then complete the rest of the end-of-chapter drills.
Two weeks until test day

\$ Take another GMAT from the CD-ROM or from the tests in this book to check your progress. If needed, re-evaluate your study schedule for this week to accommodate any additional areas you need to review or practice.
One week until test day

\$ Take another GMAT from the CD or from the tests in this book. This test will give you the best idea of what score to expect on test day. \$ Call the test center if you have any final questions, make sure you have your required identification ready, and actually drive to the testing center so that you know exactly how to get there and how long it will take. \$ To keep your mind focused and ready, schedule some review work every day, but don’t cram. The idea is definitely not to get stressed out.

Action Plan 2—If You Have Two Weeks
Preparing for the GMAT in just a couple of weeks is ambitious, but it has been done. The more time and energy you can carve out for GMAT practice, the better.
Two weeks until test day

\$ Examine your scores from the practice GMAT you took from the CD or from the tests in this book. To make your preparation as efficient as possible, you really need to home in on your weaknesses at this point. You probably are not going to have time to study every area in depth, but you need to shore up your weak areas so that if one of those questions shows up in the first part of your verbal or quantitative section (which is likely), you can at least eliminate some
INTRODUCTION

\$XV

wrong answers and make an educated guess. Choose which areas you’re going to focus on first according to your primary weaknesses. \$ Schedule time over the next week to do the chapters that focus on those areas. If possible, do an entire chapter and all the practice problems that go with it in one sitting.
One week until test day

\$ Take another GMAT from the CD-ROM or from the tests in this book to check your progress. \$ Schedule time over the next week to address the remaining chapters that you need to cover. Try a few questions from the practice problems at the end of a chapter, then review what you need from the chapter to clear up any questions you might have, then do more practice problems. \$ Alternate your study of the chapters with doing whole sections from the practice tests at the end of this book. \$ Call the test center if you have any final questions, make sure you have your required identification ready, and actually drive to the testing center so that you know exactly how to get there and how long it will take.
Three or four days until test day

\$ If there is time, do another GMAT from the CD-ROM or from the tests in this book to check your progress and get more used to the testing procedure. By the time you take the actual test, you will know what to expect.

The Day Before the Test
No matter which preparation schedule you’ve chosen, your preparation on the day before the test should be the same. \$ If at all possible, schedule some relaxing activity that will get you focused on something other than the test. A full-body massage would be nice, but if that isn’t possible, a brisk walk is great for relieving stress too. The night before the test, watch your favorite comedy or action movie, play a video game, or even color in a coloring book to stay relaxed. Do things that do not tax your brain-power and choose activities that appeal to you. \$ Don’t cram, or stay up late, or don’t do anything to dehydrate yourself (and drinking a lot of alcohol falls into this category), and stress yourself out about the test and your future plans.

Test-Day Strategy
Someday soon—probably sooner than you’d like—the day for your face-to-face encounter with the GMAT will arrive. Your test-day strategy should include the following: \$ Stick to whatever routine will make you most comfortable when you walk into the test. For example, if you have coffee every morning, have it on the morning before you take the test; if you don’t usually drink coffee, don’t start on the day of the GMAT. It is a good idea to eat a light meal in the hours before the test. You don’t want to get hungry, but you don’t want to feel sluggish, either. You may want to bring a snack that you can eat during your two five-minute breaks.
XVI# INTRODUCTION

If Something Goes Wrong at the Test
Sometimes the test does not go according to plan. Most likely, everything will go fine, but it is worth devoting a little thought ahead of time to how you would handle the following scenarios: You freak out, your mind freezes up, or the test is way harder than you expected. \$ If you really are not at your best during the test, then you can cancel your score at the end and retake the test another day. It happens—something might have happened in your personal life, you could be sick, or you might just be having an off day. If this happens, you can cancel your score and walk away. It will cost you another \$250 to take the test again, and you will get your score a few weeks later. Before you cancel, though, be aware that on the day of the test, many people think that their performance was worse than it actually was. Remember, the test makers want to give you questions hard enough that you will miss some; difficult questions mean that
INTRODUCTION

\$XVII

you’re heading for a high score. Cancel only if you are certain that your performance really was below your capabilities. Something bizarre and distracting happens at the testing center. \$ The designated testing centers are usually very well run, so the risk of outside distractions or computer malfunctions is low. These things are possible, though. If something outside of your control happens that you feel may affect your score, you should notify the staff at the testing center immediately. If the problem cannot be remedied, you can file an official complaint with the staff at the testing center, and then immediately after you leave the center, you should file a report by e-mail to ACT. If the test administrators support your claim, they might cancel your score and let you take the test again without charge.

REGISTERING FOR THE GMAT
One advantage of the CAT is that the GMAT is now far easier to register for than it was in the past. Just grab a credit card or your checkbook and either call up 1-800-717-GMAT or go online at www.mba.com. The registration fee as of early 2007 was \$250. Call several weeks ahead of time in order to get the date and time of day you want. You can choose either a morning or an afternoon slot, so pick the time of day you think your mind will be at its best. GMAC will give you all the information you need to show up for your testing slot.

If you seek additional practice on the GMAT, the first place to look is the source itself. On the Web site www.mba.com, you’ll find some computer-based practice tests that use questions from old GMATs. These tests will provide you with a very authentic test experience.

\$ Read all questions carefully. \$ Give extra attention to the early questions. \$ Keep track of your pace (average about two minutes per question). \$ Use process of elimination to guess strategically if you run short on time. \$ Practice! \$ Keep calm! \$ Good luck!

ACKNOWLEDGMENT
The authors wish to thank Judy Unrein for her contributions to the 2008 Edition. James Hasik Austin, Texas Stacey Rudnick Austin, Texas Ryan Hackney Houston, Texas

XVIII#

INTRODUCTION

The Quantitative Section
PART ONE

f

CHAPTER 1

The Techniques of GMAT Problem Solving

d

Y

ou are going to see more Quantitative Problem Solving questions than any other type of question on the GMAT, around 22 out of the 37 Quantitative problems on the test.

These questions cover a wide range of mathematical concepts that you almost certainly encountered in high school, but that you might not have studied since. A very easy Problem Solving question could look like this:
1. A certain standardized test taken by business school applicants demands that the test

takers answer 37 quantitative questions within 75 minutes. Which of the following is closest to the average amount of time the test takers can spend on each question? A. 1 minute, 58 seconds B. 2 minutes, 2 seconds C. 2 minutes, 5 seconds D. 2 minutes, 12 seconds E. 121.6 minutes Word problems like this are common on the GMAT. The trick with any word problem is to work step-by-step, making sure you pay as much attention to the words as the numbers, because the words tell you how to do the problem. In this example, you can see from the answer choices that the answer will probably include seconds, so it might be a good idea to turn that 75 minutes into seconds from the start; the GMAT assumes that you know things like “there are 60 seconds in a minute.” So, you have 75 × 60 = 4,500 seconds in which to complete 37 questions. 4,500 divided by 37 equals 121.62 . . . seconds (you can tell from the answer choices that you don’t need to calculate any farther than that), which is closest to 2 minutes, 2 seconds, answer B. Most problems can be solved in a number of different ways. If, for example, you don’t like long division, you could approach this question in the following way: 75 minutes divided by 37 questions is 2 minutes per question with a remainder of 1 minute. That remainder means that you have 60 additional seconds divided up among 37 questions; you could divide 60 by 37, or you could reason that since 37 is close to 30, and 60 divided by 30 equals 2, then you have about 2 seconds more per question, which is answer choice B, 2 minutes, 2 seconds. Ponder that answer for a moment. A period of 2 minutes, 2 seconds is plenty of time to calculate a simple arithmetic problem like this one, but would it be enough to calculate the

3

volume of 2 right circular cylinders? Probably, if you dive right in and you remember that the volume of a right circular cylinder = πr2h, but almost certainly not if you need to scramble around in your head for an approach to the problem and a formula that may or may not be right. Your task, then, is to brush up on your math and work enough practice problems that when you see a question like the following, you’ll know how to answer it correctly in a short enough amount of time that you’ll be able to get to all 37 questions.
2. A certain barrel, which is a right circular cylinder, is filled to capacity with 100 gallons of oil. The

first barrel is poured into a second barrel, also a right circular cylinder, which is empty. The second barrel is twice as tall as the first barrel and has twice the diameter of the first barrel. If all of the oil in the first barrel is poured into the second barrel, how much empty capacity, in gallons, is left in the second barrel? A. There is no empty capacity B. 100 gallons C. 300 gallons D. 700 gallons E. 800 gallons The GMAT would consider this question medium difficult, so if you can solve it already, good for you. If not, don’t sweat it. Let’s walk through some time-tested steps for how to approach an unfamiliar problem.

THE ART OF PROBLEM SOLVING
In this chapter, we have followed the outline recommended in G. Polya’s How to Solve It (Princeton University Press, 1957). Polya was a mathematics professor at Stanford who wrote the book after a career of teaching math to frustrated students who had learned mostly by rote in elementary and secondary school. That is, they knew a great deal about how to solve the problems that they had seen before, but they were rather helpless as investigators of original issues. How to Solve It has a bit of a cult following, particularly among computer programmers. While we have followed the outline broadly, we have related its contents to issues typically encountered on the GMAT. While the information here is specifically tailored to solving quantitative problems, the general principles can be applied equally well to pretty much all GMAT problem types.

Understanding the Problem
In the first place, you must understand the nature of the problem. For each problem on the GMAT, you could ask the question, “What skill is the question writer testing here?” If you understand what is being asked, you’re a long way toward developing an approach to solve the problem. You may also be able to form an idea of what a correct answer might look like, and thereby eliminate one or two incorrect answer choices. In the question about the barrels of oil, the skill needed apparently has to do with finding the volume of right circular cylinders. So you’re going to need some geometry, and you’re also going to do some arithmetic comparing two volumes.
4# THE QUANTITATIVE SECTION

THE TECHNIQUES OF GMAT PROBLEM SOLVING

\$5

Devising a Plan
Your next task will be to find some connection between the information provided to you and the unknown for which you are trying to solve. Along the way, you may need to solve some subsidiary problems if an immediate connection between the question and one of the answer choices cannot be found. The goal here is to eventually obtain a plan for how you will go about solving the problem. That does not necessarily mean that from the start you will be able to identify each step in the process. We can draw an analogy between your eventual job search and baseball. As we will discuss in Chapter 15, successful job searches are often a matter of getting more at-bats—you’re not looking for a high batting average, just one long ball out of the park. With those “700-level” questions, you will be hoping to create situations in which you may encounter just the spark of brilliance you need to draw that one correct inference that will lead you to the answer. Breaking a complicated problem down into as many separable questions as possible improves your at-bat rate, and thus the likelihood that you will be able to solve the problem. Along the way, you will need to consider a number of questions related to your problem-solving approach: \$ Have you seen this problem before? One of the consequences of offering the same sort of standardized test year after year for over 50 years is that eventually some of the questions will start to resemble questions from earlier exams. It’s unlikely that you will face a question on the actual GMAT that you solved in practice, and it’s almost as unlikely that you will encounter no surprises on the test. Still, you will almost certainly see questions that require analytical techniques analogous to, that feature diagrams similar to, and that involve relationships comparable to some of those that you faced in trial exams. Increasing the probability that this

6#

THE QUANTITATIVE SECTION

will happen is, after all, the point of books like this. If you see something that looks familiar, good—you should know how to solve the problem. Make sure, however, that you are solving the problem at hand, and not the problem you solved in practice \$ Can you restate the problem? The GMAT question writer may have chosen a particular phraseology, but that won’t necessarily be the best phraseology for you. Frankly, she may have chosen the particular words specifically to obfuscate either the intent or the substance of the question (she might, for example, use the word obfuscate in order to confuse you). In the question about the barrels of oil, you might want to say to yourself: “What is the difference in volume between one cylinder with a capacity of 100 gallons and another cylinder that is twice as tall and twice as wide as the first cylinder?” \$ Can you solve a part of the problem? If you can solve part of the problem, then you can narrow the range of possibilities for a correct answer, and thereby maybe cross off some of the answer choices. In the oil barrel question, for example, if you can’t exactly determine the difference in volume between the two barrels, but you can determine that the second barrel is at least twice as big as the first barrel, then you can eliminate answer A and probably answer B. Making a guess with a 33% chance of being correct is much better than guessing with a 20% chance. Finally, you’ll want to sketch out your plan in a few high-level steps. For the oil barrel question, these would be: 1. Determine the volume of the second barrel in relation to the first. 2. Subtract the volume of the first barrel from the volume of the second.

Carrying Out the Plan
At this point, you can put that solution plan into action. \$ As you proceed, check each step. Do this quickly, but make sure that you check your work as you go. Take a page from manufacturing management: it’s easier to build the quality into the process from the start than to inspect it in later. Keeping your calculations on track is a matter of arithmetic and algebraic practice, so if your day job doesn’t involve math, you’ll want to spend some time getting familiar with this sort of thing again. Work as quickly as you can, but not so quickly that your error rate increases. You should try to gauge your maximum effective rate through repetitive work with practice tests and problem sets. \$ Can you see clearly that the step is correct? If not, you may have a problem. Many GMAT questions—for that matter, many standardized test questions in general—feature incorrect answer choices built around classic process errors. Move a decimal point when you shouldn’t? That answer will show up. Assume that the diagram is to scale when it isn’t? The result of that mistake will be in the list as well. \$ Can you prove that it is correct? Proof is sometimes difficult to come by on the GMAT. Proving that something is correct is both satisfying and relieving. As long as you haven’t committed some gross conceptual error, you will probably be able to move on to the next question

THE TECHNIQUES OF GMAT PROBLEM SOLVING

\$7

with some peace of mind. The problem is that you won’t always come away with this sense of finality. The “what is the next number in the sequence” problems are a good example of this. You may not be able to prove mathematically that the next number in the sequence is, say, answer choice B. With only two minutes in which to work, you won’t want to try. Then again, comfort with analytical ambiguity is an important attribute of management consultants and financial managers, so get used to some level of ambiguity. \$ Did you use all the data? Red herring is not just a name for an Internet business magazine; it’s also the name for a misleading bit of information that seems useful, but that has no real use in solving a problem. (The term red herring may have derived from the red ink in which the disclaimers on securities prospectuses used to be written—the implication of the term was that the prospectus was valuable mostly as a way to wrap fish.) Red herrings occasionally appear on Problem Solving questions, and they are the name of the game in Data Sufficiency. Since you’ll be looking at both types of questions mixed together, you’ll need to adjust your strategy as you go. In general, when working Problem Solving quantitative questions, you will need to use all of the pieces of information the question gives you. If you have not used all the data, check over your work again. You may very well have worked the problem correctly, but it’s worth another look.

Looking Back

8#

THE QUANTITATIVE SECTION

Those Barrels of Oil
So what was the answer to the question about the barrels of oil? A certain barrel, which is a right circular cylinder, is filled to capacity with 100 gallons of oil. The first barrel is poured into a second barrel, also a right circular cylinder, which is empty. The second barrel is twice as tall as the first barrel and has twice the diameter of the first barrel. If all of the oil in the first barrel is poured into the second barrel, how much empty capacity, in gallons, is left in the second barrel? A. There is no empty capacity B. 100 gallons C. 300 gallons D. 700 gallons E. 800 gallons The answer is D. We don’t know what the actual dimensions of the first barrel are, but we know that the volume of a cylinder = πr2h (r = radius and h = height), and in the case of the first barrel, πr 2h = 100 gallons. We don’t know the exact dimensions of the second barrel either, but we know that its height is twice that of the first barrel, so 2h, and its diameter is twice that of the first barrel, and since the diameter of a circle is double the radius, it follows that the radius of the second barrel must be twice that of the first barrel as well, so 2r. The volume of the second barrel, therefore, is = π(2r)2(2h) = 8πr2h = 8 × (πr2h). Therefore, the second barrel has a volume eight times that of the first barrel, so 8 × 100 gallons = 800 gallons. If the 100 gallons in the first barrel are poured into the second barrel, then the remaining empty capacity of the second barrel is 800 gallons minus the 100 gallons, which equals 700 gallons.

THE TECHNIQUES OF GMAT PROBLEM SOLVING

\$9

There is one more situation in which the answers can be your friends, sort of. Sometimes you just can’t work out the problem in a straightforward way. You’ve read the question three times, and you just can’t figure out how to set up the equation. In this case, and particularly if there is algebra involved, you can plug in the answers and see if one fits. For example, say that you see the following question: What number when multiplied by 4 yields 2 ? – – 3 9 A. 2 – 9 2 B. – 3 C. 3 – 2 9 D. – 4 E. 9 – 2 The direct way to solve this problem is with algebra: 4 × n = 2, and solve for n. But what if all of the – – 9 3 algebra you know, in the heat of the testing frenzy, immediately flies out of your brain? The GMAT has been known to do this to people. Should this happen to you, you have another option: simply multiply each of the answers by 4 until one of them yields 2. The answer, then, is simply a matter of reaching – – 9 3 4 × 3 = 12 = 2 . choice C and determining that – – –– – 9 2 18 3

10#

THE QUANTITATIVE SECTION

You can solve quite a few problems in this reverse way. If the straightforward approach isn’t working for you, take a few moments to see if you can work backward from the answers. We will explain several problems this way throughout the book, to help you learn and master the approach.

This isn’t really a theorem, in the formal sense. It is a technique for guessing if you can’t eliminate more than one or two answer choices. It doesn’t work all the time, but it works on Problem-Solving questions far more often than it probably should. Here’s what you do: if you don’t know which answer to choose, pick the one with the most elements in common with the other answer choices. What does this mean? Consider the following answer choices: A. B. C. 2x + 3y 7 2x + 3y x+y 2x + 3y xy 2

THE TECHNIQUES OF GMAT PROBLEM SOLVING

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CHAPTER 2

Data Sufficiency

f

13

“yes” or “no” answer. If the information at hand can allow you to produce one and only one answer, or if it provides a definitive “yes” or “no” under all conditions, then it is sufficient. If the answer is “yes” under some conditions but “no” under others, then the information is insufficient.

14#

THE QUANTITATIVE SECTION

If statement (2) alone is enough to answer the question, then the answer cannot be C or E. Each of these answer choices is mutually exclusive. Once you get the hang of these answer choices, you can develop a rhythm for approaching Data Sufficiency questions and dispatching them quickly and accurately. Many test takers find it helpful to visualize the Data Sufficiency process as a decision tree:

The Data Sufficiency Decision Tree

Every Data Sufficiency question should be answered with the same technique: by asking yourself the two or three questions listed in the flowchart. After you’ve practiced this technique on a few dozen questions, it should become second nature. We stress the importance of practice for all types of GMAT questions, but practice is doubly important for data sufficiency. People who have not internalized the Data Sufficiency decision tree tend to flounder around when they see these questions, and burn up precious minutes trying to figure out the answer choices instead of figuring out the questions themselves.

THE INTENT BEHIND THE QUESTION TYPE
Many people find Data Sufficiency questions to be strange and somewhat annoying. In some ways, though, they are more similar than Problem Solving questions to the kinds of management problems people in business school and actual businesses face: 1. In school you will find yourself digging through vast piles of information. You may need, on any given night, to read several 16-page case studies, run a series of numbers several times,
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write up position papers, and (if you’re foolhardy enough to try a really serious finance program) then turn to several problem sets involving efficient frontiers and swap-pricing calculations. It can get insane at times. If, however, you have the ability to sort quickly through what is essential and what is not, you can manage the workload. That’s really what the Data Sufficiency questions are designed to uncover: whether you can manage workload time-efficiently without having to work through the details of every calculation. Some of the more challenging Data Sufficiency questions don’t involve calculation at all, but rather demand that you glance at a problem and evaluate a series of standard questions accurately. That skill can really help you survive a top-flight MBA program. 2. After school, even if your quantitative workload decreases, you’ll (hopefully) one day find yourself at the head of the mahogany conference table making the Big Decisions. Management jobs bring a wide breadth of responsibilities over areas where you’ll have to listen to the answers generated by other people. When some consultant or engineer is explaining why this or that will work or can’t happen, you probably will not have the time to run the numbers yourself, so you will have to have a sense of whether the numbers could or could not work out as described. A sense for the possibilities and constraints in numbers is an invaluable tool for any business executive.

WORKING DATA SUFFICIENCY PROBLEMS EFFICIENTLY

Trickery
The test writers get tricky sometimes—well, most of the time—in the construction of the sufficiency statements. They might, for example, provide a partial but insufficient solution in statement (1) and then
16# THE QUANTITATIVE SECTION

provide the missing pieces in statement (2), leading most test takers to pick C, “BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.” The tricky part is that the pieces provided in statement (2) may be sufficient on their own to solve the problem, so the answer is really B, but the test taker was primed from statement (1) to look for a specific piece of information in statement (2). Here is a simple example: If x and y are nonzero integers, is x an integer? – y (1) x = 5 (2) y = x A careless test taker might reason as follows: statement (1) alone is not sufficient because it says nothing about y, but it gives half of the puzzle. Statement (2) gives us the other half by allowing us to x – conclude that y = 5, and therefore y = 5 = 1, which is an integer. Therefore, the answer is C. – 5 The problem here is that the answer is actually B. Statement (2) alone is sufficient to answer the question, because a nonzero integer divided by itself will always equal 1, which is an integer. It doesn’t matter that statement (2) filled in the pieces for statement (1); what matters is that statement (2) alone is sufficient. This question is not mathematically difficult, but many test takers would incorrectly answer C, just as the test writers intended. The only way to guard against this sort of trickery is to evaluate each statement apart from the other before you ever consider how they might be combined.

Guessing
You should be able to avoid completely random guessing on Data Sufficiency questions. The decision tree is a formalized process of elimination that should substantially limit your choices if you can determine the sufficiency of just one statement. If you do need to guess blindly, try to resist your initial impulse to pick C or E. Most test takers, when baffled by Data Sufficiency questions, tend to pick C or E because they look more complicated. ACT knows this, and designs the difficult questions with this in mind. Remember, difficult questions are just as likely to have A, B, or D as an answer. C or E might very well be the correct answer for a really puzzling question, but keep in mind that ACT might have crafted the question to steer you that way. Look through the statements again, and try to determine the sufficiency of at least one of them before you make a guess.

When It’s Not AD vs. BCE
And speaking of guessing, what do you do if you can’t tell whether statement (1) is sufficient? Should you just give up and pick E ? Well, no . . . Now it’s time for some extra credit. It is possible to start the decision tree with either statement (1) or statement (2), depending on which one is easier for you to evaluate. If you start with statement (2) and it is sufficient, the only possible answers are B and D (rather than A and D). If statement (2) is not sufficient, the only possible answers are A, C, and E (rather than B, C, and E). If that sounds really confusing, just remember that if you ever have to start the decision tree with statement (2), just flip A and B.
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Application Problems
Lest we scare you off of C and E answers entirely, we have to state that they still each make up about 20% of the Data Sufficiency answers, the same as the other answer choices. To show that we have no hard feelings against these answer choices, here are two application problems that demonstrate how you might encounter an answer of C or E.
1. x + y = 8. Does x = 3?

(1) 2x + z = 8 (2) 3y − 4z = 7 A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. D. EACH statement ALONE is sufficient. E. Statements (1) and (2) TOGETHER are NOT sufficient.

does x = 3? Let’s examine statement (1): (1) 2x + z = 8 Is it sufficient? No, because it does not give us a unique value for x. The statement could be true if x = 1 and z = 6, or if x = 3 and z = 2; the answer to the question might be yes or no—at this point we cannot say. So cross A and D off your list; it now has to be either B, C, or E. Let’s move on to statement (2): (2) 3y − 4z = 7 Is it sufficient? No. If it gave us a unique value for y, that, in conjunction with the question stem, would be sufficient to answer the question yes or no, but statement (2) gives us no unique value for y. The state7 ment could be true if y = 5 and z = 2, or if y = 0 and z = − – (remember, the question stem never said that the 4

variables were integers, whole numbers, or positive numbers; you should consider all possibilities). Therefore, statement (2) alone is insufficient, so the answer must be C or E. The step now is to consider whether the statements in combination, together with the question stem, can provide a definitive yes or no. You now have three equations and three variables. Since none of the statements is a restatement of any of the others—which has to be true, since they all have different pairs of variables—you actually have enough information right now to solve for x. Since you know that you can solve for x, you know that you will be able to answer the question, so you could just stop here with the assurance that answer C is the correct answer. But since we haven’t covered algebra yet, let’s work it out here for fun. First, let’s get rid of the z, since it isn’t in the question stem. If you multiply 4 times both sides of the equation in statement (1), 2x + z = 8, you get the equation 8x + 4z = 32, and if you then add both sides of this equation to the two sides of the equation in statement (2), 3y − 4z = 7, you get the equation 8x + 3y = 39. (4) (2x+z) = (8)(4) → 8x + 0y + 4z = 32 +0x + 3y − 4z = 7 8x + 3y
18# THE QUANTITATIVE SECTION

= 39

Now, multiply −3 times both sides of the equation in the question stem to get −3x − 3y = −24, and add both sides to both sides of our last equation: (–3) (x+y) = (8)(–3) → 3x + −3y = −24 +8x + 3y = 39 5x = 15 The only solution to the equation 5x = 15 is x = 3. So, although we technically did not have to arrive at this specific result, or even to know specifically whether the answer was yes or no as long as we knew that we could find out, we now have a definitive, resounding yes to the question, and a definitive and resounding C.
2. Is city A closer to city B than it is to city C?

(1) City C is 197 miles from city A. (2) City C is 163 miles from city B. A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. D. EACH statement ALONE is sufficient. E. Statements (1) and (2) TOGETHER are NOT sufficient
Solution. The first step is, look at the question stem. You need to compare two distances, and

you’re looking for a definitive yes or no: Is city A closer to city B than it is to city C? Now move on to statement (1): (1) City C is 197 miles from city A. Is this statement sufficient to answer the question? No, because it gives us only one of the two distances we would need to answer the question. The other distance we need is the distance between city A and city B. Since statement (1) alone is insufficient, you can cross off answer choices A and D. Let’s move on to statement (2): (2) City C is 163 miles from city B. Is this statement sufficient? No, because it does not give us either of the two distances we would need to answer the question. So the answer cannot be B; the only options left now are C and E. What happens if we combine the statements? You could draw a diagram that looks like this:

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What do the laws of geometry tell us about this diagram? Without knowing any angles, they don’t tell us very much. We could infer that the maximum possible distance between A and B is 163 + 197 = 360 miles and that the minimum possible distance between A and B is 197 − 163 = 34 miles. Clearly, city A could be closer to either city B or city C; we just can’t tell with the information given. We have a name for the answer to questions like this. That name is E.

PRACTICE PROBLEMS
Now that you’ve gotten a little more confident, we’re going to give you the opportunity to practice “without the training wheels.” When you want to check your work, you can turn to the solutions at the end. If you aren’t familiar with some of the mathematical concepts, make a note to pay particular attention to that chapter in this book; this practice set covers a wide range of topics tested on the GMAT. On all data sufficiency problems, the answer choices are the same (as you’ve learned). We’ve put them here for your reference. A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. D. EACH statement ALONE is sufficient. E. Statements (1) and (2) TOGETHER are NOT sufficient.
1. Is x an integer?

1 (1) x is evenly divisible by –. 2 (2) x is evenly divisible by 2.
2. What is the ratio of 2a to b?

a (1) – = 2 b (2) a + b = 5
3. What is the average of a list of n consecutive integers?

(1) The smallest number in the list is 5. (2) n = 8
4. Is s = r?

(1) s2 = r2 (2) s is positive.
5. In triangle ABC, what is the length of AB?

(1) The length of BC is 5 and the length of AC is 12. (2) Angle C = 90°.

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THE QUANTITATIVE SECTION

6. If there are only red, blue, and green marbles in a jar, what is the ratio of red to blue marbles?

(1) The ratio of red to green marbles is 2:3. (2) The ratio of green to blue marbles is 6:5.
7. Over a holiday weekend, a certain car dealer sold off the cars on its lot. If the cars sold for an

average of \$6,000 each, how many cars were on the dealer’s lot at the beginning of the weekend? (1) The average value of the remaining cars on the lot is \$5,000. (2) The car dealer made \$48,000 in car sales over the weekend.
8. What is the value of — ?

1 (1) f = –h 2 (2) h = 5g

fg h

9. Was the price of a certain stereo in March greater than its price in May?

(1) The price of the stereo in March was 80 percent of its price in April. (2) The price of the stereo in April was 120 percent of its price in May.
10. If the square root of t is a real number, is the square root of t positive?

(1) t > 0 (2) t2 > 0
11. If the ratio of brown cars to blue cars in a certain parking lot is 2:3, how many brown cars are

in the lot? (1) There are 15 blue cars in the lot. (2) There are 25 cars total in the lot.
12. What is the value of f 2 – g 2?

(1) f = –g + 8 (2) f = g – 2
13. A shelf contains only books of poetry, short stories, and non-fiction. If Jana draws a book

randomly off the shelf, what is the probability that the book will be non-fiction? (1) There are 15 books on the shelf. (2) There are 4 books of poetry and 5 books of short stories on the shelf.
14. A job opening was posted in September and again in January. In September, the number of

applicants for the position was 60. What was the percent change in the number of applicants from September to January? (1) The number of applicants in January was one-third the number of applicants in September. (2) The number of applicants in January was 20.

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15. Is a3 > 20?

(1) a4 > 80 (2) a5 > 200
16. What is the length of a side of a certain cube?

(1) The volume of the cube is 27. (2) The surface area of the cube is 36.
17. How many prime factors of x are also prime factors of y?

(1) x = 30 (2) y is a multiple of x.
18. Is m > 0?

(1) | m | = 2 2 3 (2) m = 64
19. What is the value of — ?

v w

w (1) — = –1.5 v (2) v > 0
20. There are twenty students in a class, all of whom scored between 0 and 100 on their final exams.

If the class average was 85, how many people scored below the average score on the exam? (1) Twelve people in the class scored higher than an 85. (2) The lowest eight scores added up to 640.

Solutions
1. B.

A reminder: The question stem starts with is, so this is a yes or no problem. The first step is to

determine whether statement (1) is sufficient, which we can do by trying out some real numbers. 1 If x is 2, which is evenly divisible by –– , then the answer would be yes. But if x were 1.5, which is 2 1 also evenly divisible by –– , then the answer would be no. Since you can get either yes or no, state2 ment (1) is not sufficient and you should cross off A and D. Now let’s move on to statement (2). There are no non-integer numbers that are divisible by 2, so yes is the only possibility. Statement (2) is sufficient, so we can eliminate C and E, and the correct answer is B.
2. A.

a 2a a Statement (1) says that –– = 2. We are looking for the ratio —– . If you substitute 2 for –– in b b b that ratio, you get 2 times 2, which equals 4. Statement (1) is sufficient. Cross off B, C, and E. How about statement (2)? Remember, you have to forget about the information you got from statement (1). Since there are several values for a and b that would add up to 5, let’s try a couple

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THE QUANTITATIVE SECTION

of variations to see if we always get the same ratio. If a is 3 and b is 2, the ratio of 2a to b would be 6:2 or 3:1. But if we used a = 2 and b = 3 instead (and nothing tells us that we can’t), the answer to the question stem becomes 4:3. When we can get different answers, we can tell the statement is not sufficient, so we can eliminate D. A is the correct answer.
3. C.

Statement (1) tells us the smallest number, but not how many numbers are in the list. It is not

sufficient. Cross off A and D. Statement (2) tells us the value of n, so the question becomes: What is the average of a list of 8 consecutive integers? Since those integers can be large, small, or even negative, we have no way to tell what the average is. Statement (2) is not sufficient, so we can eliminate B. Now let’s put the two statements together. If we know that 5 is the smallest number in a list of 8 consecutive numbers, then we can easily reconstruct the list and find the average. So the statements are sufficient when put together, and the answer is C.
4. E.

Here’s another question that is looking for a yes or no answer. Statement (1) allows for both

positive and negative values of both s and r, so we cannot tell if s = r. Statement (1) is not sufficient; cross off A and D. Statement (2) just tells us that s is a positive number; we don’t know anything about r at all and cannot tell if they are equal; statement (2) alone is not sufficient. Let’s eliminate B. What if we combine the two? Statement (2) tells us that s is positive, but r could still be either positive or negative. We still cannot tell if they are equal, so the answer is E.
5. C.

Statement (1) alone is tempting if you are familiar with the right triangles that tend to be

tested over and over on the GMAT; however, we don’t know from statement (1) that ABC is a right triangle, so we should cross off A and D. With only statement (2), we certainly don’t have enough information to answer the question, so B can be eliminated. Together, though, we can complete the picture of a right triangle with two known sides, which means we can figure out the third side using Pythagorean Theorem, and our answer is C. (Since the squares of the two legs add up to 169, the hypotenuse is 13.)
6. C.

Statement (1) doesn’t give us any information about the number of blue marbles at all. It is not

sufficient and we can cross off A and D. Statement (2) doesn’t give us any information about the number of red marbles, so we can eliminate B. When we combine both statements, we have ratios that involve all three colors of marbles. Let’s see what happens when we use some real numbers. If there are 6 green marbles, then there are 4 red marbles and 5 blue marbles, making the ratio of red to blue marbles 4:5. If we used a different number for the green marbles—say, 12—we would end up with the same ratio of red to blue. This happens frequently with relative numbers such as ratios, proportions, averages, and probability; keep in mind that you don’t always have to know the actual numbers to know the ratios. Statements (1) and (2) together are sufficient, so the answer is C.
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7. B.

Given statement (1) alone, we only know average values of both the cars that were sold and

the cars that remained; the dealer could have sold 4 cars and had 1 left, or sold 8 cars and had 2 left, or an infinite number of other options. So we can eliminate A and D. With statement (2), we are able to find the number of cars sold by dividing the total sales by the 4 average price. 48,000/6,000 = 8, so the dealer sold 8 cars. Since that is –– of the cars on the lot, 5 the dealer started off with 10 cars. Statement (2) is sufficient, so the answer is B.
8. E.

Statement (1) doesn’t tell us about g at all, so it is insufficient, and we can cross off A and D.

Similarly, statement (2) doesn’t tell us about f, so we can eliminate B. If we put the statements together, we have only two equations for our three variables, so we still cannot solve. Since the statements together are not sufficient, the answer is E.
9. C.

Again, this problem is looking for a yes or no answer. Statement (1) doesn’t tell us anything

about the May price, so it is not sufficient. We can cross off A and D. Statement (2) doesn’t tell us anything about March, so it is not sufficient and we can cross off B. With both statements together, we know relative prices, and no matter what numbers we were to assume, the May price ends up slightly higher than the March price. So the answer is definitely no, meaning that both statements together are sufficient, and the answer is C.
10. E.

This question is looking for a definite yes or no answer. Statement (1) is not sufficient since

all it tells us is that t is a positive number. Unless the radical sign

( ) is used, a positive number

has two square roots, a positive root and a negative root. For example, if t is 4, then it has two square roots, 2 and –2. So we can eliminate A and D. With statement (2) alone, we don’t get much more information; all it really tells us is that t is a positive number (it cannot be negative, since the square root of a negative number is a complex number, not a real number). So again, t could be 4, and its root could be either positive or negative. So we can eliminate B. Putting them both together doesn’t tell us whether the square root of t is positive either, so our answer has to be E.
11. D.

When we evaluate statement (1), we can tell that there are 10 brown cars in the lot, because

that’s the only number that would give us a ratio of 2:3 if there are 15 blue cars. So we can eliminate B, C, and E. Taking statement (2) alone, we can tell that we have 15 blue and 10 brown cars in the lot, because those are the only numbers that would add up to 25 and give a ratio of 2:3. So either statement is sufficient on its own, which means D is the correct answer.
12. C.

When we see a quadratic formula like f 2 – g 2, we almost always want to simplify it to see its

parts better. This formula simplifies into (f + g)(f – g), so if we can get values for each of those parenthetical statements, we can calculate the value of the whole. Statement (1) gives the value of f + g when it is rearranged, but doesn’t give the value of f – g. We can cross off A and D. Statement (2) gives the opposite: the value of f – g only. So it is not sufficient on its own—we can cross off B—but the two statements are sufficient together, so C is the correct answer.
24# THE QUANTITATIVE SECTION

13. C.

Statement (1) doesn’t tell us anything about the breakdown of the different types of books,

so we don’t know how likely Jana is to draw a non-fiction book. Eliminate A and D. Statement (2) alone doesn’t tell us anything about the number of non-fiction books. So we can eliminate B. Putting the statements together, we can tell that there are 6 non-fiction books on the shelf by 6 2 subtracting 4 and 5 from 15. Therefore, Jana has a — or –– probability of drawing a non-fiction 15 5 book at random, and our answer is C.
14. D.

Statement (1) lets us find the number of January applicants (20) and then we can find that 2 the percent change in applicants was 66 –– %, so it is sufficient and we can eliminate B, C, and E. 3 Statement (2) tells us the same thing; it is also sufficient, so we can cross off A and we are left with D.

15. B.

Here’s another question that is looking for a yes or no answer. Statement (1) allows for both

positive and negative values of a, so it is not sufficient, and we can cross off A and D. Statement (2), on the other hand, tells us that a is positive and must be a value of at least 3. If a > 3, then the answer to the question stem must always be yes. Therefore, statement (2) is sufficient, and our answer is B.
16. D.

Statement (1) tells us that the length of a side of the cube is 3, since the volume is just the

length of one side cubed. So we can cross off B, C, and E. Statement (2) is a little trickier, since surface area is generally a less familiar concept. If the surface area of the whole cube is 54, then the area of each one of the 6 faces is 9. That means each side is 3, so statement (2) is also sufficient, and our answer is D.
17. C.

Statement (1) tells us nothing about the prime factors of y, so it is not sufficient on its own.

We can eliminate B, C, and E. We do know at this point, though, that the set of prime factors in question is {2, 3, 5}. Statement (2) on its own tells us nothing about the prime factors of x, so it is not sufficient on its own. We can eliminate B. Putting them together, we can see that all of the prime factors of x would also be prime factors of y, so they have those same three prime factors in common. Since the statements are sufficient together, then answer is C.
18. B.

Statement (1) is not sufficient because m could equal either 4 or –4, giving us either a yes or

a no. So we can eliminate A and D. Statement (2) tells us that m has to be positive 4, so it is sufficient, and our answer is B.
19. A.

v 3 Statement (1) tells us the value of the reciprocal of — ... −1.5 or − –– . That means w 2 v 2 — has to equal − –– , so statement (1) is sufficient and we can eliminate B, C, and E. w 3 Statement (2) alone tells us nothing about w and very little about v, so it is not sufficient. A is our answer.

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20. E.

Statement (1) is tricky because it implies that eight people scored lower than 85, but in fact,

it is possible according to the question for some people to have scored exactly an 85, so it is not sufficient and we can eliminate A and D. Statement (2) doesn’t really give us any information; it tells us that the lowest eight scores had an average of 80, but we don’t know how many of those scores were below 85. So we can eliminate B. Putting the statements together, we can tell that 12 people made above an 85 and the 8 others had an average of 80, but we can’t tell how many of the 8 were below an 85, so we have to eliminate C. E is our answer.

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THE QUANTITATIVE SECTION

CHAPTER 3

Basic Principles of Numbers

d

INTRODUCTION: REMEMBERING YOUR HIGH SCHOOL MATH
Almost all of the mathematical concepts tested on the GMAT were probably taught in your high school math classes. The good news about that is at one time you knew this stuff. The bad news is that, unless you’re an engineer or financial analyst in your day job, you’ve probably forgotten some if not most of it. Don’t worry, though. The GMAT tests a relatively small number of mathematical concepts, and does so in fairly predictable ways. With a modest amount of preparation, you can earn quite a good score, provided that your mathematics knowledge was sound in the first place. If your math background is weak, you should devote a substantial amount of time to preparation for the quantitative section. The GMAT tests some very basic concepts that even people who are very good at math tend to forget over time. So, without further ado, let’s move onto some basic concepts about numbers.

NUMBER SYSTEMS
We will start with some terms that do not occur in the everyday practice of four-function (addition, subtraction, multiplication, division) office math: \$ Integer Integers are the positive and negative numbers in the set { . . . −3, −2, −1, 0, 1, 2, 3, . . . }. If you put a decimal point after an integer, only zeros would follow: 2.000, 27.0000, and so on. Numbers that are not integers include 2.34, 0.5, 1/3, and so on. There are an infinite number of both positive and negative integers. Particularly when working Data Sufficiency questions, it’s important to remember that when a problem says “number,” it could be referring to either an integer or a non-integer. So be careful, and don’t assume “a number” means “an integer.” \$ Whole number \$ Rational number Whole numbers are all of the positive integers, plus zero: {0, 1, 2, 3, 4, . . . }. A rational number is any number that can be expressed as a ratio of two other numbers—that is, any integer or fraction. Rational numbers include 3, 45.375, and 35/41. \$ Irrational number An irrational number is a number that cannot be expressed as a fraction. The decimal approximations of these numbers extend

27

indefinitely without a repeating pattern. Examples include π (the ratio of the diameter of a circle to its circumference) and e (the base of the natural logarithm). For the purposes of the GMAT, you should know that π ≈ 3.14. You are not likely to be tested on the concept of rational or irrational numbers. \$ Real and imaginary Unless the test states otherwise, all of the numbers you see on the GMAT are real numbers. The real numbers include all rational and irrational numbers. Imaginary numbers involve such things as −1 . Since all of the numbers on the GMAT are real unless stated otherwise, if you find yourself having to take the square root of a negative number on a GMAT problem, then you have probably made an error in your calculations. The GMAT is not interested in your powers of imagination. \$ Prime number The GMAT is interested in prime numbers. A prime number is an integer that has exactly two factors, itself and the number 1. The set of prime numbers includes {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, . . . }. No negative numbers are prime. The number 2 is the lowest prime number and the only even prime number. The number 1 is not a prime number, since it has only one factor. It is worth memorizing the first ten or so prime numbers because they often show up on GMAT problems. \$ Absolute value A number’s absolute value is its distance from zero on the number line. For positive numbers, that’s the number itself, and for negative numbers, that’s its positive cousin; e.g., the absolute value of 3 is 3, and the absolute value of −3 is also 3. The absolute value of a number is expressed by that number surrounded by two vertical lines; e.g., the absolute value of x is expressed as | x | . Mathematically, a number’s absolute value is equivalent to the square root of its square: | x | = x 2 . Absolute values are always positive.

ALGEBRAIC NOTATION AND THE ORDER OF OPERATIONS
A mastery of algebra is one of the most useful skills you can bring to the GMAT, because algebra applies not only to those problems that explicitly mention variables, such as
2 If x ≠ 3 then x ( x − 3) − x + 3 = x−3

but also to word problems with unknown variables: If Jim’s donut shop sold 220 donuts this morning for \$121.00, how much, on average, did Jim charge for each donut? The following chapter will deal with solving algebraic problems in greater detail. For now, let’s examine the type of notation used in algebraic problem solving. At the heart of algebra lies the concept of the variable—an unknown quantity, represented by a Latin or Greek letter, whose value, if it exists, can be found by successive application of
28# THE QUANTITATIVE SECTION

mathematical rules. Any letter can be used to represent the variable, but the GMAT favorites are a, b, n, x, y, and z. Most GMAT math involves only the four basic operations of addition, subtraction, multiplication, and division. Addition is expressed with the + sign: x + y. Subtraction is expressed with the – sign: x − y. Multiplication is expressed in a few different ways. With constants, a question might use the × sign: 5 × 3 = 15. When dealing with variables, GMAT questions generally place the variables either immediately next to one another or with adjoining parentheses: x y = ( x )( y ) Division is usually expressed fractionally, rather than with the division sign, as in x÷y = x y Any collection of variables multiplied—but not added—together is called a term. Examples include x , xy , x , and 15 y The algebraic order of operations governs which operation is performed first in simplifying an expression. In algebraic order, exponents precede multiplication and division, which in turn precede addition and subtraction. Parentheses are used to change this order and to apply operations to groups of terms simultaneously. So, x ( y + z ) = xy + xz That is, the parentheses dictate that we must apply the function “multiply by x” to all the terms grouped within the parentheses. This is the distributive rule of multiplication, since the x is said to be distributed over the other terms. The distributive rule does not, however, apply to addition or subtraction: x + (y + z ) = x + y + z not

(x + y ) + (x + z )

Division is just the inverse form of multiplication, so the distributive rule applies to division as well: y +z y z = + x x x A collection of two terms, such as the preceding y + z, is called a binomial, since it is composed of two terms. Three such terms (e.g., x + y + z) make up a trinomial, and any general collection of terms is called a polynomial. Multiplying two polynomials together requires multiplying every term in one polynomial by every term in the other. With binomials, the FOIL (First, Outside, Inside, Last) rule is a handy mnemonic:

( x + y ) (w + z ) = xw + xz + yw + yz
BASIC PRINCIPLES OF NUMBERS \$29

More often on GMAT questions, the binomials in a problem contain the same variables. Three common binomial expressions are

( x + y ) ( x + y ) = ( x + y )2 = x 2 + 2xy + y 2 ( x − y ) ( x − y ) = ( x − y )2 = x 2 − 2xy + y 2 ( x + y )( x − y ) = x 2 − y 2
These binomial expressions are useful to know, as they have appeared on many GMAT problems in the past. Of these, the most useful is (x + y)(x − y) = x 2 − y 2, which is in general (x n + y n)(x n − y n) = x 2n − y 2n for any integer n, because it allows us to simplify complex expressions. For example: Which of the following is equivalent to ( x + y )( x 2 + y 2 )( x 4 + y 4 )( x − y ) ? A. x – y B. ( x 2 − y 2 ) C. ( x 4 − y 4 ) D. ( x 8 − y 8 ) E. x 8 − 4x 2 y 2 + y 8 You could multiply out a series of four polynomials like that, but it would take a long time. If you remember that (x + y)(x − y) = x 2 − y 2, you can combine the first and last binomials into the simpler expression of (x 2 − y 2). You can then combine this with the next term and get

( x 2 − y 2 )( x 2 + y 2 ) = ( x 4 − y 4 )
You can then combine this with the following and final term to get

( x 4 − y 4 )( x 4 + y 4 ) = ( x 8 − y 8 )
And so the answer is D, (x 8 − y 8). As this problem shows, a familiarity with common binomial expressions can simplify your life, or at least the part of it dealing with the GMAT. For those of you who followed that problem and said, “Wait, what exactly did you do with those exponents?” it’s time to get up to speed with the wonderful world of exponents.

EXPONENTS AND ROOTS
You will see many, many exponents on the GMAT quantitative section. An exponent signifies that a variable or constant is to be multiplied by itself a given number of times. Thus, x 2 = ( x )( x )
30# THE QUANTITATIVE SECTION

x 3 = ( x )( x )( x )

x 4 = ( x )( x )( x )( x )

and so on. .

When you multiply an expression raised to an exponent by the same expression raised to an exponent, you add the exponents. Thus, x 2x 5 = ⎡ ( x )( x ) ⎤ ⎡ ( x )( x )( x )( x )( x ) ⎤ = x 2 + 5 = x 7 ⎣ ⎦⎣ ⎦ 32 × 33 = 35

Likewise, if you divide an expression raised to an exponent by the same expression raised to an exponent, you subtract the exponent in the denominator (the bottom) from the exponent in the numerator (the top): x 5 = ( x )( x )( x )( x )( x ) = x 5− 2 = x 3 ( x )( x ) x2 3 3 = 33− 2 = 31 = 3 32 y3 = y 3− 5 = y −2 Note : the exponent in the numerator is less than the exponent y5 in the denominator; therefore, the exponent in the answer is negative. e

When you see a number raised to an exponent raised to another exponent, you multiply the exponents: ( x 5 )2 = x 5× 2 = x 10 since since

( 32 )3 = 32× 3 = 36

( )( x 5 ) = x 10 ( 32 )3 = ( 32 )( 32 )( 32 ) = ( 36 )
( x 5 )2 = x 5

Questions asking you to add, subtract, or multiply exponents are common on the GMAT. Less common, but certainly still possible, are questions that deal with exponents with negative values, fractional values, or a value of zero. However, you should know how to handle these cases. First of all, any real number raised to the zero power equals 1: x0 = 1 3550 = 1 −170 = 1 0.000010 = 1 Nice and consistent, right? An expression raised to a negative exponent means that you put the expression raised to the positive exponent in the denominator of a fraction (i.e., on the bottom): x −5 = 15 x −3 = 1 = 1 3 33 27 Any number greater than 1 raised to a negative exponent will result in a number that is greater than 0 but less than 1. Try out a few numbers to verify that. Now, a number raised to a fractional power
BASIC PRINCIPLES OF NUMBERS

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is a much more wily phenomenon. Fractional exponents represent square roots, cube roots, and the like: x 5 = 5x 27 3 = 3 27 = 3 What is a root? The square root of x is a number that when squared will equal x. The cube root of x is the number that when cubed will equal x. Thus, 4=2 9=3
3 4 1 1

64 = 4 x5 = x

625 = 5
5

Higher-level root problems are considered difficult, so you are not likely to see them unless you’re earning a high score. The calculations for higher-level exponents and roots can get complicated in a hurry, so in order to make these problems possible, the GMAT tends to use the same numbers over and over. You should familiarize yourself with the exponent values that have appeared frequently on GMATs in the past: 02 = 0, 03 = 0 (0 to any power other than 0 is 0; 00 =1)

12 = 1, 13 = 1 (1 to any power is 1) 22 = 4, 23 = 8, 24 = 16, 25 = 32, 26 = 64, 27 = 128, 28 = 256, 29 = 512, 210 = 1,024 32 = 9, 33 = 27, 34 = 81, 35 = 243 42 = 16, 43 = 64, 4 4 = 256 52 = 25, 53 = 125, 54 = 625 62 = 36, 63 = 216 72 = 49, 82 = 64, 92 = 81, 102 = 100, 112 = 121, 122 = 144, 132 = 169

It wouldn’t be bad practice to do the calculations on all of these equations yourself in order to get your arithmetic skills up to speed. All of these numbers have appeared on GMAT problems in the past, and they will appear on them again. Note that the inverse of these equations provides you with square root values: 121 = 11, 5 32 = 2, and so on.

FACTORING NUMBERS
The factors of a number are those numbers that can be multiplied together to produce the number in question. Thus, the factors of 12 are 1, 2, 3, 4, 6, and 12, because you can produce 12 in all of the following ways: 1 × 12 = 12 2 × 6 = 12 3 × 4 = 12

32#

THE QUANTITATIVE SECTION

Thus if you saw the following question: Which of the following is a factor of 16? A. 5 B. 6 C. 7 D. 8 E. 9 you would think through all of the ways you can produce the number 16—1 × 16, 2 × 8, 4 × 4—and you would determine that the answer has to be 8, D, since that is the only factor of 16 among the answer choices. Most factoring questions on the GMAT are pretty simple, although some Data Sufficiency questions using factoring can get tricky. If a question does ask about factors of numbers, there’s a good chance that the question will involve one of the following numbers: 36, 48, 96 (= 48 × 2), 72 (= 36 × 2), or 144 (= 48 × 3 = 72 × 2). Why these numbers? Because they have many factors that you can easily calculate:

1 × 48 = 48 2 × 24 = 48 3 × 16 = 48 4 × 12 = 48 6 × 8 = 48

1 × 72 =72 2 × 36 = 72 3 × 24 = 72 4 × 18 = 72 6 × 12 = 72 8 × 9 = 72

It would be good practice for you to calculate all the factors of 96 and 144. A familiarity with these commonly appearing numbers can help you solve quantitative problems more quickly and with greater accuracy. A key fact to remember about factors is that 1 is a factor of all real numbers.

WORKING WITH NONINTEGERS
Integers are, generally speaking, easier to work with than nonintegers because the calculations necessary for manipulating them are shorter. But in the business world you have to deal with fractional numbers all the time. The price of a washer and dryer might be \$899.99 with a 5% rebate. Interest rates on mortgages move up and down an eighth of a percentage point at a time, e.g., from 5.625% to 5.750%. Questions involving percentages, decimals, and fractions appear on the GMAT all the time. To ace this test, you need to be equally comfortable on both sides of the decimal point.

Percentages
Per cent is Latin for “by hundred,” so percentages express numbers in hundredths. Thus, 45% = 45/100 = 0.45

BASIC PRINCIPLES OF NUMBERS

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This can get confusing when we speak of decimal percentages: 0.45% = 0.45/100 = 45/10, 000 = 0.0045 There is a reasonable chance that a GMAT question will attempt to confuse you by putting a decimal within a percentage, so remember to watch for this. Coincidentally, decimal percentages are commonly used in finance, where hundredths of a percentage point are called basis points. Thus, to a banker, 0.45% = 45 basis points Be very careful with questions asking about percentage increases. There is a difference between questions asking for the “percent increase” and the “percent of.” When a number is doubled, it is increased by 100%, not 200%, but the resulting number is 200% of the original number (and the original number is 50% of the resulting number). For example, if the price of an air conditioner increases from \$300 to \$600 over 10 years, the percent increase is 100% because the amount increased by \$300. It is also true, however, when you are not talking about percent increase but are just discussing what percent \$600 is of \$300, \$600 is 200% of \$300 (and \$300 is 50% of \$600). When a number is tripled, it is increased by 200%, and the resulting number is 300% of the original number. We can almost guarantee that one of the incorrect answer choices in a question involving percentage increases will feature a figure 100% greater than the correct choice.

Fractions
Fractions are usually—though not always—best reduced as far as possible before they are multiplied by anything in GMAT questions. You could burn up a lot of time trying to work with a fraction like 210 2772 So the first step when you see a mean looking fraction is to figure out ways to simplify it. There are four rules that you can follow, generally in order: 1. Try to divide both the top and bottom by 2. This is called reducing the fraction by 2. Two is the first prime number, so it is always where you should start. If the number is even, then it’s divisible by 2. Do this as many times as possible. In this case, that yields 210 ÷ 2 = 105 2772 ÷ 2 1386 2. Then try to divide both the top and the bottom by 3 (especially if reducing by 2 didn’t work). A number will be divisible by 3 if the sum of its digits is a multiple of 3. In this case, 105: 1 + 0 + 5 = 6 and 6 is a multiple of 3, since 6 ÷ 3 = 2 1386: 1 + 3 + 8 + 6 = 18 and 18 is a multiple of 3, since 18 ÷ 3 = 6

34#

THE QUANTITATIVE SECTION

So we know that 3 is a factor of both the numerator and the denominator; therefore, reducing by 3 yields 105 ÷ 3 = 35 1386 ÷ 3 462 3. Next, try to divide both the top and the bottom by 5. If a number ends in 5 or 0, it’s divisible by 5. Here, we could take it out of the numerator: 35 ÷ 5 but 462 is not divisible by 5 462 ÷ 5 4. Finally try to divide both the top and the bottom by 7: 35 ÷ 7 = 5 462 ÷ 7 66 And now we have a fraction that isn’t so hard to work with. If these four steps haven’t reduced the number to a workable level, you could consider whether it is divisible by other primes, such as 11 or 13. If the number is that complicated, though, check over the answer choices to see whether you really need to reduce the fraction any further; if the answer choices themselves contain unwieldy fractions, then maybe further reduction is unnecessary. If the number is really messy, you also may consider whether there might be an easier way to solve the problem.

Decimals
There is a time to work with decimals, and a time to work with fractions. For example, if a question asks you: If 37.5% of the 880 students at a certain college are enrolled in biology classes, how many students at the college are NOT enrolled in a biology class? A. 110 B. 330 C. 550 D. 430 E. 880 You could multiply 0.375 × 880, but you could probably work the problem faster if you realize that 0.375 = 3 8 then you could multiply 3 × 880 = 3 × 880 = 3 × 880 = 3 × 110 = 330 8 8 8

BASIC PRINCIPLES OF NUMBERS

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Remember that the question asked how many students are NOT enrolled in a biology class, so don’t forget to subtract: 880 − 330 = 550 which is answer choice C. Either method, multiplying by a decimal or by a fraction, works; the key is that if the quicker method can save you a few seconds here, those seconds might be the difference between a right answer and a wrong answer on a harder question near the end of the test. The rule of thumb is that if the answer choices are in decimals, you should probably work the problem with decimals, and if the answer choices contain fractions, then you should stick with fractions. If the answer choices do not steer you in either direction, go with the one that appears simpler and faster. There are some equivalences between fractions and decimals that can save you time if you remember them for the test: 1/8 1/4 3/8 1/2 5/8 3/4 7/8 = = = = = = = 0.125 0.25 0.375 0.5 0.625 0.75 0.875 1/100 = 0.01 1/50 = 0.02 1/25 = 0.04 1/20 = 0.05 1/10 = 0.1 1/3 = 0.3333… 2/3 = 0.6666…

Rounding
Occasionally a problem will involve a long string of digits to the right of a decimal point that are not particularly useful. Sometimes, rounding the number to a rough estimate will do the trick just as well. For example, a problem like the following has appeared on the GMAT: Which of the following is closest to 4.0456 × 9.99853 ? 201.73 A. 4 B. 20 C. 40 D. 200 E. 2,000 You don’t need to make the full calculation here, because the question asks you which number is “closest,” and the answer choices don’t have all of the decimal points that a really accurate answer would have. It is simpler to view the number as 4 × 103 = 4, 000 = 20 200 200 Rounding can sometimes help you find answers much faster, or at least determine quickly which answer choices cannot be correct.
36# THE QUANTITATIVE SECTION

KEY CONCEPTS TO REMEMBER
\$ Three binomial relationships:

( x + y ) ( x + y ) = ( x + y )2 = x 2 + 2xy + y 2 ( x − y ) ( x − y ) = ( x − y )2 = x 2 – 2xy + y 2 ( x + y )( x − y ) = x 2 − y 2
\$ Six rules about exponents and roots: x a x b = x a +b

( x a )b = x ab x1 = x x0 = 1 x −a = 1 xa 1/a = a x x

PRACTICE PROBLEMS
1. The sum of the non-prime numbers between 40 and 50, non-inclusive, is

A. 131 B. 176 C. 274 D. 405 E. 495
2. If x = –2, what is the value of 4x3?

A. –32 B. –24 C. –8 D. 8 E. 32
3.

3 + 7 1 1 = 7 3 A. 21 58

B. 58 21 C. 21 D. 42 E. 58

BASIC PRINCIPLES OF NUMBERS

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4. What is the decimal equivalent of ⎛ 1 ⎞ ?

2

⎝ 4⎠

A. 0.0016 B. 0.0625 C. 0.16 D. 0.25 E. 0.5
5. What is the smallest integer k for which 64k > 414?

A. 4 B. 5 C. 6 D. 7 E. 8
6. If x = –3, then

x2 + x = −2 x

A. –2 B. –1

1 2 D. 1 E. 2
C.
7. If (x – 1)2 = 144, which of the following could be the value of 2x?

A. –26 B. –22 C. –11 D. 12 E. 13
8. How many different positive integers are factors of 342?

A. 9 B. 11 C. 12 D. 20 E. 22
9. If 27p × 32 = 34 × 98 , what is the value of p?

A. 3 B. 6 C. 8 D. 15 E. 16

38#

THE QUANTITATIVE SECTION

10. 200 is what percent of 40?

A. 0.2% B. 2% C. 5% D. 20% E. 500%
11. If f and g are distinct prime numbers less than 10, which of the following cannot be the product

of f and g? A. 6 B. 9 C. 10 D. 14 E. 15
12. What percent of 180 is 45?

A. 0.25% B. 4% C. 25% D. 40% E. 250%
13.

(0.5)6 (0.5)3 A. 0.125 B. 0.25 C. 0.625 D. 12.5 E. 25

14. How many positive factors do 180 and 96 have in common?

A. 6 B. 12 C. 16 D. 18 E. 24
15. Which of the following is the closest approximation of 30.1 × 1.98 ?

1 A. – 6 1 B. – 4 1 C. – 2 D. 1 E. 5

120.9

BASIC PRINCIPLES OF NUMBERS

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16. Which of the following is equal to the cube of a non-integer?

A. –64 B. –1 C. 8 D. 9 E. 27 The following data sufficiency problems consist of a question and two statements, labeled (1) and (2), in which certain data are given.You have to decide whether the data given in the statements are sufficient for answering the question. Using the data given in the statements plus your knowledge of mathematics and everyday facts (such as the number of days in July or the meaning of counterclockwise), you must indicate whether A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. D. EACH statement ALONE is sufficient. E. Statements (1) and (2) TOGETHER are NOT sufficient.
17. If s r = t , what is the value of r?

(1) r 2 = 625 t (2) – = 5 s
18. Is ab > 2?

(1) a = 2 a (2) 0 < – < 1 b
19. Is f < g?

(1) f < g + 1 (2) f g 414, which is the same as finding the smallest integer k for which 3k > 14. The best answer is 5, or B.
6. D.

Be sure to follow the order of operations and plug in −3 for x. The equation becomes 6 which becomes – , or 1. 6

( −3)2 − 3 , −2( −3)

7. B.

Since there are only two possible values of 2x, it’s easiest to start with them and find one that

is also in the answer choices. Since (x − 1)2 could equal either 12 or −12, x could equal 13 or −11, which means that 2x could equal either 26 or −22. Of the answers, only B will work.
8. C.

From the answers we can see that the list of factors will be relatively small, so it’s easiest just

to list them out. The pairs of factors are 1 and 342, 2 and 171, 3 and 114, 6 and 57, 9 and 38, and 18 and 19. That makes 12 factors.
9. B.

Once we simplify 27p × 32 = 34 × 98, we get (33)p × 32 = 34 × (32)8, or 33p × 32 = 34 × 316. That is the

same as 3p + 2 = 4 + 16, so p must equal 6.
10. E.

x We can take this question directly into an equation, which would look like 200 = —– × 40. 100 When we solve, we get 500, choice E. The prime factors less than 10 are 2, 3, 5, and 7, so the product of any two of those cannot be

11. B.

correct. That eliminates choice A (the product of 2 and 3), C (the product of 2 and 5), D (the product of 2 and 7), and E (the product of 3 and 5). Since 9 is the product of 3 and 3, which are not distinct (or 1 and 9, which are not prime), B is the correct answer.
12. C.

x This question can also be put directly into equation form: —– × 180 = 45. When we solve, we 100 get 0.25, choice C. Simplifying gives us (0.5)3, which is 0.125. The positive factor pairs for 180 are: 1 and 180, 2 and 90, 3 and 60, 4 and 45, 5 and 36, 6 and

13. A. 14. A.

30, 9 and 20, 10 and 18, and 12 and 15. The positive factor pairs for 96 are: 1 and 96, 2 and 48, 3 and 32, 4 and 24, 6 and 16, and 8 and 12. They have 1, 2, 3, 4, 6, and 12 in common for a total of 6 factors.
15. C.

Approximating the equation gives us

30 × 2 1 , which simplifies to –. 120 2

BASIC PRINCIPLES OF NUMBERS

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16. D.

Of the answer choices, only 9 is not a “perfect” cube, which means that its cube root is a non-

integer.
17. D.

Statement (1) tells us that r = 25 or −25, but when you look at the question stem, the radical sign for r is present, which only allows for a positive root. So r = 5. Therefore statement (1) is

sufficient and we can eliminate B, C, and E. Statement (2) also gives us enough information to solve for r. If we rearrange the equation in the t t t question stem, we can get – on one side, giving us r = – . Since – = 5, r = 5. So statement (2) s s s is also sufficient, and our answer is D.
18. C.

Statement (1) does not give us a definite yes or no answer, because b could be a lot of different

numbers. So we can eliminate A and D. Statement (2) is also not sufficient, as a and b could equal 1 and 2, or 0.5 and 2, or 2 and 4, or an infinite number of other variations in which a is smaller than b. So B is not correct. Putting them together, we know that a = 2, and b must be larger than a to satisfy Statement (2). ab then must be larger than 2 and the answer to the question is definitely yes. C is the correct answer.
19. E.

Statement (1) is not sufficient because f could be less than g or it could just be g + 0.5. We can

cross off A and D. Statement (2) is not sufficient because while the absolute value of f must be less than the absolute value of g, the actual value of g could still be negative while f could be positive. The statement doesn’t give us enough information, so we can eliminate B. Putting the statements together doesn’t really give us any more information, so the correct answer is E.
20. C.

Because statement (1) just tells us that p could be any negative number, it is not sufficient to

answer the question. A and D can be eliminated. Statement (2) alone tells us that p could be either 3 or −3, which would give different values for 12 , so it is also not sufficient and we can eliminate B. 5p The statements together tell us that p must be −3, so we can solve for answer. 12 and C is the correct 5p

42#

THE QUANTITATIVE SECTION

CHAPTER 4

Algebraic Equations and Analytical Geometry

f

THE IMPORTANCE OF ALGEBRA
Understanding algebra is essential in analyzing almost any significant quantitative business problem; therefore it is one of the central mathematical skills tested on the GMAT. Indeed, several university studies of the GMAT scores of MBA students have indicated that a low quantitative score is an excellent predictor of which students will struggle in their first-year classes. High GMAT scores do not guarantee success, but low quantitative GMAT scores make admissions directors nervous. Thus, admissions committees are generally more interested in an applicant’s quantitative score than in his or her verbal score. If you attend one of the more quantitatively rigorous programs, you will probably need to understand calculus as well. For now, at least, you will not need that for the GMAT, but you will need algebra. Consider the following problem.
Application: The Breakeven Point.

Hector runs a one-product widget shop. Each month, his fixed costs, whether he produces anything or not, amount to x dollars. The marginal cost of producing and selling one widget is a constant y dollars, regardless of the number he produces. He generally can sell widgets for z dollars each. What is the minimum number of widgets he must produce, assuming he sells every widget he produces, to break even (neither make a profit nor incur a loss) in a given month? A. x (y − z )

x B. (z − y ) C. x x D. – z x E. – y In its general form, the breakeven point is an important question for any business, and so it appears in a number of different forms on the GMAT. The essence of dealing with a question like this is to take the facts and conditions given in the question and turn them into a mathematical equation that can give you the information you need. Algebra—the manipulation of variables in equations and inequalities—is the tool that will enable you to do this.

43

Forming the Equation
You are going to see a lot of word problems on the GMAT, and you will need to take the information in the question and turn it into a form you can work with. In the preceding question, you are going to need to form an equation before you can use any of your algebraic tools. Your first step is to consider the different items that need to have a place in your equation. The problem gives you the following: Fixed costs: Marginal cost: Revenue: x y per widget z per widget

You also need to consider the value that you’re solving for. Since you’re looking for the number of widgets, add that to your list: Number of widgets: n The problem asks for the point at which the total cost equals the revenue, so you need to set up an equation that puts all the costs on one side of the equal sign and all the revenues on the other. Your equation might look like this: x + ny = nz This equation adds the fixed costs to the total marginal costs (number of widgets times the marginal cost per widget), and sets that equal to the total revenue (number of widgets times the selling price per widget). Now, since the problem asks you for n, the number of widgets Hector sells, you need to solve for n.

Solving Algebraic Equations
Solving simple algebraic equations is a straightforward and easily repeated process.
Method: Solving an Algebraic Equation. The basic approach to solving an algebraic equation

in one variable is to isolate that variable. You do this by rearranging terms until all the variable terms are on one side of the equation, and all the constants are on the other side. Then, combine the variable terms together and the constants together until there is only one variable and one constant left. In the equation we just formed, we need to isolate n, which is the number we’re looking for: To get the n on one side of the equation, subtract ny from both sides. x + ny – ny = nz – ny

x = nz – ny Now it’s time to get n alone. To simplify matters, factor out the n on the right side. x = n(z – y) Now to get n alone, all you have to do is divide by (z – y).
44# THE QUANTITATIVE SECTION

n( z − y ) x = (z − y ) (z − y )

When you cancel out, you’re left with x answer choices is (z − y ) , or B.

x = n. So the solution for n that you’re looking for in the (z − y )

Solving equations involving just one variable is really quite simple: put your variable on one side and do the arithmetic. The trick, of course, is setting up the equation properly in the first place; the best way to practice this is to scan through the word problems in the practice test and then put their facts and conditions into algebraic form by writing an equation for each one. Another single-variable problem that is similar to the breakeven problem is that old classic, the time and distance problem. This sort of problem could look like this: Greg can bike from his home to Monkey Hill in 4 hours if he rides at a speed of 30 miles an hour. How much time in hours will it take him to return home if he bikes back on the same route at a pace of 20 miles per hour? What are your constants and variables? Distance between home and Monkey Hill: let’s call this D Pace on ride to Monkey Hill: 30 miles per hour Time of ride to Monkey Hill: 4 hours Pace of return trip: 20 miles per hour Time of return trip: the unknown The essence of any time and distance problem is the formula distance = rate × time. This formula has three equivalent forms. It is important to be familiar with all three forms so that you can use the one that is most efficient for what you need to find. D = R ×T D ÷R =T D ÷T = R To solve this problem, you actually need to set up two single-variable equations. First, you need to determine the distance from home to Monkey Hill: D=R×T D = (30 miles/hour) × (4 hours) D = 120 miles Then, you set up an equation for the return trip, but this time solving for time: D =T R 120 = 6 hours 20 Therefore, it will take Greg 6 hours to bike back home.
ALGEBRAIC EQUATIONS AND ANALYTICAL GEOMETRY

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Other similar problem types include: Fuel efficiency: distance = quantity of fuel × distance per unit of fuel Production of multiple units: number of total products = (production rate of unit A × time) + (production rate of unit B × time) The units here could be printers, lawnmowers, pretzel makers, or anything else. All of these word problems can be solved by following the same simple steps: 1. Understand what is being asked. 2. Identify the constants and variables. 3. State them as an equation. 4. Isolate the desired variable and solve the equation.

LINEAR EQUATIONS
The GMAT does not write out the algebra of word problems for you—that’s what makes them word problems. The simplest and probably most common type of algebraic equation that you are going to see printed in GMAT questions is the linear equation. Linear equations take the form y = mx + b Each of the constants and variables in a linear equation has a specific name and function: x is the independent variable, y is the dependent variable, and m and b are constants. The variables x and y are termed independent and dependent, respectively, because the value of y is said to depend on that of x, whereas the value of x is taken to be generally independent of that of any other variable. Equations of this form are called linear because they graph as straight lines. More specifically, following this form, m is the slope of the line, and b is the y-intercept, the point where the line meets the y axis. Graphically, the slope is the rate by which the y value (the dependent one) increases as the x value (the independent one) increases. Accordingly, it is the steepness with which the line moves up or down (in the positive y direction or in the negative y direction) as it moves to the right (in the positive x direction). It can also be calculated as the rise over the run—that is, the number of units that the line rises divided by the number of units that it runs, going from any one point on the line to another point on the line. For example, if you wanted to graph the equation y = 2x + 6, it would look like the following:

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THE QUANTITATIVE SECTION

Graphing a linear equation, or using one to solve a GMAT problem, is largely a matter of plugging in values for x and then determining the resulting value of y, or vice versa. For example, suppose you were to see a question along the lines of For the line described by the equation y = 5x − 3, what is the value of x when y = −8? To solve this problem you would just plug in the given variable y = −8 and solve: − 8 = 5x − 3 − 5 = 5x x = −1 A single linear equation is easy to work with. The situation gets more complicated, though, when the test makers throw another equation or two into the mix.

Systems of Linear Equations
A system of linear equations is two or more equations sharing one or more variables. A relatively simple system could take the form ⎧ y = ax + b where a, b, c, and d are real numbers ⎨ ⎩ y = cx + d Systems could be much larger than this; really complicated ones could involve dozens of equations and variables. On the GMAT, though, most of the linear equations you will see will involve only two equations with two variables, although you will occasionally see systems with three equations and three variables. Regardless of size, systems of linear equations can be solved if four conditions are met: 1. There is but one dependent variable (which is often y, but does not have to be). 2. The number of equations equals the number of independent variables. 3. None of the equations essentially restate another equation. 4. No pair of equations represents parallel lines. Let’s look at how these rules can be applied on the GMAT. Consider the following Data Sufficiency question: If 3y = 2x + 6, what is the value of x ? (1) 6y = 4x + 12 (2) 2y = 3x − 3 As with any Data Sufficiency problem, you want to approach this one systematically. First, what are you looking for? You are looking for a specific value of x along the line described by 3y = 2x + 6. If you like to picture equations graphically, you are looking for an equation describing

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a line that intersects the line in the question stem, because the x value at the point of intersection will be the only possible value for x that satisfies both equations. Let’s consider statement (1): (1) 6y = 4x + 12 Is this equation sufficient, when combined with the equation in the question stem, to answer the question? Let’s consider the four conditions for whether or not a system of linear equations is solvable: it meets conditions 1 and 2, but it fails condition 3, because statement (1) is merely a restatement of the equation in the question stem with both sides of the equation doubled. What this means is that it describes exactly the same line as the one described in the question stem, so it really gives us no new information. Since statement (1) is insufficient, you can cross choices A and D off your list and move on to statement (2): (2) 2y = 3x − 3 Does this system meet the 4 conditions stated above? Yes: it meets conditions 1 and 2, it is not a restatement of the equation in the question stem, and if you were to graph the line in (2), you could tell that it is not parallel to the previous equation. You actually have enough information right now to answer the question as B, statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. Let’s go ahead and solve the system anyway. 3y = 2x + 6 2y = 3x − 3 can be restated as can be restated as 6y = 4x + 12 −6y = −9x + 9 0 = −5x + 21 ⇒ 5x = 21 ⇒ x = 21/5 We now have a single value for x, which confirms that the system of equations was solvable with the equation in statement (2). If we wanted to solve for y now, we would only have to plug our value for x into either of the equations and we would have the corresponding value for y. The method we used to solve this system, which could be called the subtraction method, will work on all solvable systems of linear equations. The steps are as follows:
Method 1: Solving a System of Linear Equations through Subtraction

1. Arrange your equations so that the independent variables are on one side and the dependent variables are on the other, e.g., 3y = 2x + 6 2y = 3x − 3 2. Multiply both sides of both equations by the factors required for the independent variables to be preceded by the same number (remember, you can do anything you want to one side of an equation if you do the same thing to the other side): 2(3y) = 2(2x + 6) ⇒ 6y = 4x + 12 3(2y) = 3(3x − 3) ⇒ 6y = 9x − 9 3. Multiply the second equation by −1 and add the two equations together: 6y = 4x + 12 − 6y = −9x + 9 0 = −5x + 21

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THE QUANTITATIVE SECTION

4. Solve the resulting equation (from which y has been eliminated) for x, and substitute that value of x into one of the original equations to find y. 5x = 21 ⇒ x = 21 5 For simplicity, we can multiply 3y = 2x + 6 by 5 and restate it as 15y = 10x + 30; now we plug in our value for x: 15y = 42 +30 = 72; y = 72 = 24 15 5 Most linear equations you encounter on the GMAT will have integer solutions, but not all of them will. You should be prepared for fractional solutions, as in this example. There is another common way to solve linear equations. You can substitute the value of either x or y from either equation into that place in the other equation. Again, after you have finished finding x (or y), you will need to substitute that value into one of the original equations in order to find the other.
Method 2: Solving a System of Linear Equations through Substitution

There are four steps: 1. Simplify one equation so that it states y cleanly in terms of x. 2. Substitute that into the y place in the other equation. 3. Solve the equation for x. 4. Substitute that value into one of the original equations to find the value of y.

Example

Solve for x and y : 3 y = 2x + 6 2 y = 3x − 3
Solution

Divide both sides of the first equation by 3 in order to find y in terms of x : y = 2x + 2 3 Then, substitute the right-hand side of this equation into the place in which y appears in the second equation: 2 ⎛ 2 x + 2 ⎞ = 3x − 3 ⎜ ⎟ ⎝3 ⎠ Simplify the new left-hand side of the equation: 4 x + 4 = 3x − 3 3

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Then move all the x terms to the left, move all the constants to the right, and solve: 4 – x − 3x = −3 −4 3 4 9 – x − – x = −7 3 3 5 − – x = −7 3 − 5 x = − 21 21 x=— 5 As before, we can substitute this into one of the original equations to find the value of y : 3y = 2 ⎛ 21 ⎞ + 6 ⎝ 5⎠ 3y = 42 + 6 5 3y = 42 + 30 5 5 3y = 72 5 y = 72 ÷ 3 5 y = 72 × 1 5 3 y = 72 15 y = 24 5 Which of these two methods you use to solve a system is up to you. Glance over the equations and try to get a sense of which one might wind up with easier calculations. There is a third method for solving systems of linear equations that is specific to the GMAT and related multiple-choice tests. That method is to look at the answer choices, and if they offer choices for the value of either x or y (or whatever the variables are in the question), plug those values into the equations in the question until one value works for both equations. This method can often be faster than actually solving the equations algebraically.

Another type of algebraic equation that you will encounter on the GMAT is the quadratic. Quadratic equations are a type of what we call second-order equations—those in which at least one of the terms features the square of a variable or two different variables multiplied together, and no terms are raised to a power higher than 2. Quadratics feature one term with a squared independent variable, possibly another with a linear independent variable, and possibly a constant term as well. They take the general form

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y = ax 2 + bx + c where a, b, and c are constants, x is the independent variable, and y is the dependent variable. However, y = ax 2 + bx is also a quadratic equation, in which it could be said that c = 0, as is y = ax 2 + c where b = 0. The simplest quadratic is y = x2 where a = 1 and b = c = 0. Note that a step is to put them into the form 0 = ax 2 + bx + c This is generally not difficult. If you are faced with an equation that resembles x 2 + 2x − 16 = 8 simply subtract the constant on the right from both sides of the equation to yield x 2 + 2x − 24 = 0 At that point, you have two options for solving the equation: factoring it or using the quadratic formula. 0 if the equation is a quadratic.

Quadratic equations are a little more difficult to solve than the standard linear equation. The first

The most popular way to solve a quadratic equation is to factor the three terms into two binomial factors. In general, we would find two binomials (x − m) and (x − n) such that 0 = ax 2 + bx + c = ( x − m ) ( x − n ) This looks rather complicated, but remember that the numbers in GMAT math tend to work out smoothly. In plain English, factoring a quadratic means looking for two numbers that when multiplied together equal the last constant, and when added together equal the middle constant. In terms of what we have written above, this means two factors m and n such that m + n = b and mn = c for the polynomial x 2 + bx + c .

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In finding those two numbers, the multiplied term is generally the best place to start: list all the possible factors of the last constant in the equation, and then determine which of them will add to form the middle constant. Let’s consider an example equation: Which of the following is a solution to the equation 0 = x2 + 2x − 24? A. − 6 B. − 4 C. − 2 D. 2 E. 6
Solution: −24 can be factored eight ways, and each of these ways provides two constants with a

corresponding sum: 1 and − 24 − 1 and 24 2 and − 12 − 2 and 12 3 and − 8 − 3 and − 4 and 8 6 4 and − 6 − 23 + 23 − 10 + 10 −5 +5 −2 +2

Only in the last case do the two constants add to + 2. So, the constants in the factors are − 4 and 6, so the two factors of the equation are 0 = x2 + 2x − 24 = (x + 6)(x − 4) , and thus the solution is x = − 6 or 4 (remember, one of the factors must equal 0). − 6 is among the answer choices, but 4 is not, so the answer to the question must be A, − 6.
Caveat: Factoring a Quadratic Equation. Take care to flip the signs when converting from the

factors to the solutions. This is a common mistake on the GMAT. If the factors are x + 6 and x − 4, then the solutions are x = − 6 and + 4 (not x = + 6 and − 4). You may have observed a pattern concerning the signs of the possible factors of 24. The pairing of the signs of the constants b and c determines the pairing of the signs for the constants m and n. Here is the rule: Rule for Determining the Signs of the Factors of a Quadratic b + + − − c + − + − m&n both + one +, one −, and the one larger in magnitude will be + both − one +, one −, and the one larger in magnitude will be −

If the last term, the one that is the product of the two binomial constants, is positive, then the two constants n and m must be either both positive or both negative. But if the last term is negative and the middle term is positive, this means that m + n > 0, so the larger of the two in magnitude will

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be positive. Or if the last term is negative and, alternatively, the middle term is negative, this will mean that m + n < 0, so the larger of the two in magnitude will be negative. So using the previous example, x2 + 2x − 24 = 0, the last term is negative and the middle term is positive, so we are looking for two numbers, one positive and one negative, with the positive one having a greater magnitude than the negative.

Virtually every quadratic equation you will encounter on the GMAT is factorable with whole-number solutions: the people who compose test questions formulate them for relative ease of factoring so that test takers can concentrate on the problem, not on complicated factoring issues. Still, you may encounter quadratics that are somewhat more difficult to factor, or you may just find that it is simpler to use the quadratic formula than to factor. Should that happen, don’t allow yourself to spend three or four minutes that you don’t have searching for a pair of factors that will solve the equation. Instead, use the quadratic formula, which is the general solution to any quadratic equation. What is the quadratic formula? Well, in any given problem 0 = ax 2 + bx + c the solutions are given by THE QUADRATIC FORMULA
2 4 x = −b ± b − ac 2a

You may remember this formula from your high school or college algebra class. If not, you should memorize this formula before taking the test, as it may save your score on one or more problems. Let’s look at the same problem, using the quadratic formula instead of factoring.

Which of the following is a solution to the equation 0 = x2 + 2x − 24? A. − 6 B. − 4 C. − 2 D. 2 E. 6
Solution. Substitute 1 for a, 2 for b, and − 24 for c in the quadratic formula, and simplify:

− 2 ± 22 − 4 × 1 × ( − 24 ) − 2 ± 4 + 96 2 x = −b ± b − 4ac = = = 2a 2×1 2 − 2 ± 100 − 2 ± 10 = = −1 ± 5 2 2 Thus, x = − 1 + 5 or − 1 − 5, x = 4 or − 6.

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You may wonder about the ± sign in the numerator. Since the square root of b 2 − 4ac can be either added to or subtracted from the – b term, x can, as noted earlier, take on two different values. That is, a quadratic equation can have as many as two solutions. For Problem Solving questions, generally only one of these solutions will be among your answer choices. For Data Sufficiency questions, it’s important to remember that a quadratic equation might have two different solutions (but it could also have only one).

HYPERBOLIC EQUATIONS
A third type of equation you might see on the GMAT is the hyperbolic equation. Hyperbolic equations are of the form: xy = c which can also be written as y = c x The dependent variable y does not vary directly or linearly with the independent variable x. Rather, it has an inverse relationship with x: as x increases, y decreases, and as x decreases, y increases. These equations are called hyperbolic because graphically they are represented as hyperbolas. Hyperbolic equations occasionally appear in GMAT questions paired with a linear equation in a system of equations. The addition of the hyperbolic equation means that the system will not be a system of linear equations, but it may still be solvable. If it is, you will generally need to solve a quadratic equation after substituting the linear equation into the hyperbolic equation. This will yield two, one, or zero solutions to the system. The method for solving a system of equations that has a linear equation and a hyperbolic equation is as follows:
Method: Solving a System of a Linear Equation and a Hyperbolic Equation

1. Solve for y in the linear equation and then substitute the x side of it into the y place of the hyperbolic equation. 2. Rearrange the terms in order to simplify this equation into a quadratic equation. 3. Solve the quadratic equation for x, either by factoring or with the Quadratic Formula. 4. Substitute this value into one of the original equations to find the value of y. 5. Check whether the problem is asking for two solutions or just for the positive solution. (Keep in mind that there may only be one solution.)
Example

1 If y = x + 2 and xy = 6 , what are the possible values of x and y ? 2
Solution. Since y is already isolated in the linear equation, substitute the right-hand side of the first

equation into the y place of the second equation and simplify: xy = 6 → x ⎛ 1 x + 2 ⎞ = 6 → 1 x 2 + 2x = 6 ⎜ ⎟ ⎝2 ⎠ 2
54# THE QUANTITATIVE SECTION

Then, rearrange the terms to find the resulting quadratic equation: 1 x 2 + 2x − 6 = 0 2 Multiply both sides of the equation by 2. This will facilitate factoring the equation (remember, GMAT quadratics are generally factorable). x 2 + 4x − 12 = 0 Factor the quadratic:

( x + 6 )( x − 2 ) = 0 which yields the solutions x = − 6 or 2. Substitute these values one at a time into the second equation to find two values of y : xy = 6 → −6 y = 6 → y = −1 xy = 6 → 2y = 6 → y = 3 So, the solutions to the system are (− 6, − 1) and (2, 3).

APPLICATION PROBLEM: DEPRECIATION
At this point, you should try to apply these principles to another practical problem. The following problem is of a type sometimes encountered on the GMAT; it tests your ability to identify variables, construct systems of linear equations, and solve those equations with basic algebraic techniques. It is challenging by the standards of the test, but it is definitely representative of typical problems that you will encounter in an MBA program, particularly in an introductory course on financial accounting. Ace Transport has acquired two trucks to carry different types of cargo. One costs \$70,000; the other costs \$52,000. The company expects that the first will last 165,000 miles, after which it can be sold for salvage for about \$4,000. The other will fetch the same salvage price, but will last 200,000 miles. The two trucks convoy together, so they always show the same mileage readings. If the value of each truck declines at different constant rates for every mile driven, at what mileage reading will the residual values of the two trucks be equal? A. 87,500 miles B. 100,000 miles C. 107,750 miles D. 112,500 miles E. The residual values will never be equal.
Solution. We can take the value of the truck to depend on the reading on the odometer, which makes

the mileage the independent variable and the value of the truck the dependent variable. The clue that the values of the trucks decline by an equal amount every mile indicates that this is what accountants
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call a straight-line depreciation problem. That is, the rate of decrease is constant, so the slope is constant. We can determine rather quickly the respective rates of decrease, or depreciation, using the equation r = vi − v m

where v is the current value of the truck; “v-sub-i” is the initial value, or price, and m is the reading on the odometer. At the final point of usage, this is r = vi −v f mf

where “v-sub-f ” is the final, or salvage, value, which in both cases is \$4,000; and “m-sub-f ” is the final reading on the odometer. For trucks 1 and 2, these work out to be r1 = \$70, 000 − \$4, 000 = \$0.40/mile 165, 000 miles n and r2 = \$52, 000 − \$4, 000 = \$0.24/mile 200, 000 miles

and since these are rates of depreciation, they are both negative. Thus, r1 = − \$0.40/mile and r2 = − 0.24/mile. Note: These equations are just using the formula for slope, y2 − y1/x2 − x1, where for the first truck, (x1,y1) = (0, 70,000) and (x2,y2) = (165,000, 4,000) (since at 0 miles the truck’s value is \$70,000, and at 165,000 miles the truck’s value is \$4,000). Therefore, r1 = 70, 000 − 4, 000 66, 000 4 = = − 0.4 dollar per mile − 165, 000 0 − 165, 000

For the second truck, (x1,y1) = (0, 52,000) and (x2,y2) = (200,000, 4,000) (since at 0 miles the truck’s value is \$52,000 and at 200,000 miles the truck’s value is \$4000). Therefore, r1 = 52, 000 − 4, 000 48, 000 2 = = − 0.24 dollar per mile − 200, 000 0 − 200, 000

Next, we can graph these declines, remembering that depreciations are negative effects on value, so the slopes will be − 0.40 and − 0.24 dollar/mile. (This is shown in the figure that follows.) From the graph, we can tell that the answer lies somewhere around 100,000 miles. While we’re not sure exactly where, we can at least rule out answer choice E. However, we can determine this exactly by equating the values. To do that, we need to set up the equations with the current value terms exposed: r = vi − v → rm = vi − v → v = −rm + vi m

Now we have a general linear equation with a slope (the depreciation rate) and a y intercept (the price paid). (Note also that our slope is −r, not m; we have been using m as the variable for slope, but really any letter will do. In this problem, we chose to use m as the number of miles.) We can establish a system of two equations by plugging in the values from the original question: v = − ( 0.40 ) m + 70, 000

v = − ( 0.24 ) m + 52, 000
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Note that since we are looking for the point at which the values and the mileage readings are equal, we can use but one v and one m. Since in both equations v is isolated, we can set the right sides of the equations equal to each other and solve for m. Equating the two values, we find − ( 0.40 ) m + 70, 000 = − ( 0.24 ) m + 52, 000 Subtracting 52,000 from both sides and adding 0.40m to both sides yields 18, 000 = 0.16m → m = 18, 000 0.16

If you are wondering about how to tackle this without a calculator, factor 18,000 and 0.16 and simplify: m= 18, 000 18, 000 18, 000 × 100 18 = = = × 100, 000 = 9 × 100, 000 0.16 16 8 16 16 100

This is not as complicated as it looks. Remember that nine-eighths is also one and one-eighth, and from the list of memorable fractions in the preceding chapter, one-eighth is 0.125. So, m = 1.125 × 100, 000 = 112, 500 or answer choice D. If you are very diligent, you can check your math at this point by substituting 112,500 into both equations for current value. Both give the same result: \$70, 000 − ( 0.40 \$/mile )(112, 500 miles ) = 25, 000 miles

\$52, 000 − ( 0.24 \$/mile )(112, 500 miles ) = 25, 000 miles which both confirms our work and yields the interesting result that the common current value of the trucks, when those values are equal, is \$25,000. The following chart represents graphically the point where the depreciation equations for the two trucks meet. You won’t have time on the GMAT to make a precise graph for any problem like this, but a quick sketch can give you visual confirmation that your answer is in the right ballpark.

Finally, before proceeding, work the following sample problems. Brief solutions are provided after the problems.
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PRACTICE PROBLEMS
1. Which of the following equations has a solution in common with x 2 − 2x − 15 = 0 ?

A. x 2 − 6x + 9 = 0 B. x 2 + 2x − 15 = 0 C. 2x 2 + 9x + 9 = 0 D. 2x 2 + x − 3 = 0 E. none of the above
2. If

5+x = x , then which of the following is a possible value of x? x−3

A. − 2 B. 5 C. 7 D. −3 E. 1
3. In three years, Janice will be three times as old as her daughter. Six years ago, her age was her

daughter’s age squared. How old is Janice? A. 18 B. 36 C. 40 D. 42 E. 45
4. If apples cost x dollars per m dozen, how many dollars will it cost to buy n apples?

xn A. —— 12m xn B. —– m m C. —– xn 12m D. —— xn 12mn E. ——— – x
5. Which of the following is a solution to the equation x2 – 4x – 32 = 0?

A. – 12 B. – 8 C. – 4 D. 4 E. 12

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6. Abby, Brandon, Cedric, and Deirdre are planning to attend a concert. If their friend Kim also

goes with them, they will get a group discount on their tickets. If the total price of the tickets with the group discount is the same as the total price of the tickets without the group discount, how much is the discount? A. 5% B. 10% C. 20% D. 25% E. 33%
7. Two boards are being cut for a construction project. If the total length of the boards is 100 inches

and the shorter board is 5 inches less than half the length of the longer board, what is the length of the shorter board? A. 25 inches B. 30 inches C. 35 inches D. 65 inches E. 70 inches
8. If the average (arithmetic mean) of a list of s integers is 18, what is the sum of the integers?

A. 9s 18 B. — s C. 18s 9 D. — s E. 18 + s
9. What are the roots of the equation x2 – 12x = –27?

A. (18, 9) B. (18, – 9) C. (– 3, – 9) D. (– 3, 9) E. (3, 9)

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10. A group of hikers is planning a trip that will take them up a mountain using one route and back

down using another route. They plan to travel down the mountain at a rate of one and a half times the rate they will use on the way up, but the time each route will take is the same. If they will go up the mountain at a rate of 4 miles per day and it will take them two days, how many miles long is the route down the mountain? A. 4 B. 6 C. 8 D. 12 E. 16

Solutions
1. C.

The equation in the question factors out to (x − 5)(x + 3) = 0; x = 5 or −3. The equations in the

answer choices factor out to A. x 2 − 6x + 9 = 0 = (x − 3)(x − 3); the solution is x = 3 B. x 2 + 2x − 15 = 0 = (x + 5)(x − 3); the solution is x = 3, −5 C. 2x 2 + 9x + 9 = 0 = (2x + 3)(x + 3); the solution is x = −3, −3/2 D. 2x 2 + x − 3 = 0= (2x + 3)(x − 1); the solution is x = −3/2, 1 Of these choices, only C shares a solution, −3, with the equation in the question.
2. B.

You could either solve this problem algebraically or just plug in the values for the answer

choices until one works. To solve algebraically, you restate the equation as 5 + x = x2 − 3x; 0 = x2 − 4x − 5 = (x − 5)(x + 1); the solutions to the equation are x = 5 or −1; of these choices, 5 is the only available answer choice.
3. D.

For this problem you need to set up two equations representing the statements in the question;

then you can either solve algebraically or plug in the answer choices and find the one that works. The equations we need, if J = Janice’s current age and D = daughter’s current age, are J + 3 = 3(D + 3) which can be restated as J + 3 = 3D + 9 and J − 6 = D2 − 12D + 36 Note that when talking about times in the past or future, we need to make the same adjustments to both Janice’s and her daughter’s age. If we use the subtraction method, we can subtract the first equation from the second to remove the J variable: J − 6 = D2 − 12D + 36 −J − 3 =
2

and

J − 6 = (D − 6)2

− 3D − 9

−9 = D − 15D + 27 which we can restate as 0 = D2 − 15D + 36 = (D − 12)(D − 3)

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So the daughter’s age must be either 12 or 3. The age 3 makes no sense given the condition in the statement referring to 6 years ago, so the daughter’s age must be 12. We can then plug this into one of the original equations to get Janice’s age: J + 3 = 3(12 + 3) → J + 3 = 45 → J = 45 − 3 = 42
4. A.

If we set up this problem as a proportion with dollars on top and apples on bottom, you get x = y (let’s call the amount of money we’re trying to solve for y). Cross-multiplying gives us 12m n 12my = xn, and to get y alone, we would just divide by 12m on both sides, giving us xn . 12m The equation x2 – 4x – 32 = 0 expands out into (x – 8)(x + 4) = 0, so the solutions are 8 and – 4.

5. C.

Watch out for trap answers such as – 8 and 4.
6. C.

This is a great problem to use the answer choices instead of writing a lot of complex equa-

tions. Let’s say the price of a ticket without the discount is x. If the discount is 5%, then 4x = (5x) – 0.5(5x). We can simplify that and instead of finding the discount and subtracting it, we’ll just take the percentage we would pay with the discount included. So, our new equation is 4x = 0.95(5x). That doesn’t work out mathematically, and in fact, it’s way off. So A is incorrect, and B is close to A, so let’s skip B and try C. A 20% discount means that each person will pay 80% of the individual price, so the equation is 4x = 0.8(5x). That works out perfectly, so C is our answer!
7. B.

Again, this is a great problem to just try the answer choices. If the shorter board is “5 inches

less than half” the longer board, we could just use the answer choices as the length of the shorter board, add five, and multiply by two. A doesn’t work—if the shorter board is 25, the longer board would be 60, and those don’t add up to 100. B works—a shorter board of 30 gives us a longer board of 70 (remember, add 5 then multiply by 2), and those add up to 100.
8. C.

To find a mean, you add up a list of numbers and then divide by the number of numbers. So

if you have the average already (18), you just need to multiply by the number of numbers (s) to get your answer: 18s.
9. E.

First we have to manipulate the equation to get it into a standard form. By adding 27 to both

sides, we get x2 – 12x + 27 = 0 ... something we’re a little more used to seeing. Factoring this quadratic gives us (x – 3)(x – 9) = 0, so our roots are 3 and 9.
10. D.

The rate formula is a great help on problems like these, so remember r = d . For the trip – t down the mountain, the rate is 1.5 times the “up” rate of 4 miles per day, so the rate is 6 miles per day. The time is 2 days because it is equal to amount of time it takes to go up the mountain. Substituting those numbers in the formula allows you to solve for the distance, which is 12 miles.

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CHAPTER 5

Probability and Statistics

d

INTRODUCTION: WHAT DO NUMBERS MEAN?
Probability and statistics are some of the most relevant quantitative skills tested on the GMAT. The essence of probability and statistics is looking at a set of numbers and figuring out what they mean. Does this product have a chance on the market? Is this sales office performing up to standard? Business schools spend a great deal of time instructing students on the quantitative tools necessary for deriving meaningful inferences from sets of numbers. Those of you who are not currently financial analysts can be glad that the more complex concepts addressed in B-school—t-tests, Poisson distributions, heteroskedacticity, and so on—are not tested on the GMAT. In most cases, the probability and statistics questions on the GMAT can be addressed with only high school or even middle school math. Statistics questions on the GMAT involve a limited set of concepts, most of which are mentioned in the following question: If the set S is composed of the following numbers {99, 100, 100, 105, 106, 116, 123}, which of the following is largest? A. The average (arithmetic mean) of set S B. The median of set S C. The mode of set S D. The range of set S E. The standard deviation of set S If you are familiar with the basic concepts of statistics, you should be able to discard three of these answers in approximately the first 10 seconds after reading the question, and then decide between the remaining two choices in another 20 seconds. If you are not familiar with these concepts, read on.

THE MEAN
The mean is simply the average value of a set of numbers. On the GMAT this concept is usually written as “the average (arithmetic mean),” as in the preceding problem. To find the

63

mean, sum the values of all the elements, and divide by the number of elements. So, for example, the mean of the set {99, 100, 100, 105, 106, 116, 123} is 99 + 100 + 100 + 105 + 106 + 116 + 123 = 749 = 107 7 7 When dealing with this sort of calculation, there are two strategies: 1. Just do it. If the list is short and the numbers are relatively uncomplicated, then you shouldn’t be averse to whipping out the pencil for a little addition and long division. 2. Get clever. The other approach is to look for a pattern, either among the numbers in the set or in the answer choices. The GMAT often makes this possible. Consider this example: What is the average (arithmetic mean) of the set {105, 106, 107, 108, 109, 110, 111, 112, 113}? A. 108.5 B. 109 C. 110 D. 968 E. 981 You could do this the long way—add up the numbers, determine that the sum is 981, divide by 9, and pick answer B. Or, you could look over the numbers, recognize that these are 9 consecutive numbers, and conclude that the mean has to be the fifth (the middle) number, 109, because there is exactly one number that is 1 greater than 109 and exactly one number that is 1 less than 109, exactly one number that is 2 greater than 109 and exactly one number that is 2 less than 109, and so on. Tricks like this can save you a minute or more on a question, and savings like that will pay off on the more difficult questions later in the test. If you get a question asking for a mean, be alert to patterns such as consecutive numbers or consecutive even or odd numbers (e.g., 102, 104, 106, 108, and so on). When the numbers in a set are consecutive integers, consecutive even numbers, or consecutive odd numbers, the mean is equal to the median (discussed next) of the set. GMAT questions are often solvable by tricks like this because the GMAT actually wants to know whether you can spot these sorts of shortcuts. Knowing how to navigate through large data sets and complicated series of numbers quickly can make a big difference in, say, a complicated marketing case, so this sort of ability will be very important in your first year of MBA studies.

THE MEDIAN
The median is just the middle value in a set. By the middle value, we mean the value that has just as many elements in the set that are less than it as it has elements in the set that are greater than it. Returning to our set in the last example, {105, 106, 107, 108, 109, 110, 111, 112, 113} 3 the median is 109, as 109 is the middle value, i.e., it is the fifth value in a set of nine. If we rearrange the order of the values to {113, 107, 111, 109, 108, 110, 106, 105, 112} 2
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the median is still 109, since four elements in the set are still less than 109 and four elements in the set are still greater than 109. Therefore, the order of values in a set does not affect the median. In this set the median coincides with the mean, but it does not have to. Consider the following set: {99, 100, 100, 105, 106, 116, 123} The median is 105, because it is the fourth highest number in a set of seven. When a set has an odd number of elements, the median is simply the number in the middle: the second out of three, the sixth out of eleven, and so on. However, if there are an even number of elements in the set, then the median is the number halfway between the two middle numbers. For example, in the set {105, 108, 110, 112, 114, 115} the median value is 111, since this is halfway between the two middle values. If there are eight elements in a set, then the median is the average of elements four and five. If there are ten elements in a set, then the median is the average of elements five and six. Remember that a set can have only one median.

THE MODE
The mode is just the most common element in a set. In the set {99, 100, 100, 105, 106, 116, 123} the mode is 100, because this number appears twice, while all other elements appear only once. Note that a set can have more than one mode. In the set {2, 2, 3, 3, 4, 5, 6, 7, 7, 8, 9} there are three modes: 2, 3, and 7. Each value appears twice. The mode is not a difficult thing to calculate. If you encounter this sort of question, inspect the set, watch for tricks (like values out of order), pick the appropriate answer choice, and move on. If you are having trouble figuring out the mode, rewrite the elements in increasing order and the mode (or modes) will become apparent.

THE RANGE
The range of a set is just the difference between the largest and smallest elements. If that seems simple, it is. For example, the range of the set {105, 106, 107, 108, 109, 110, 111, 112, 113} 3 is 8, since 113 – 105 = 8. Similarly, the range of the set {99, 100, 100, 105, 106, 116, 123}

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is 24, since 123 – 99 = 24. The number of times that the smallest and largest elements appear is not relevant; what matters is that they are the smallest and largest elements.

CALCULATING THE STANDARD DEVIATION
Quickly, the standard deviation is the square root of the quotient of the summation of the differences of the individual values of the set and the mean, divided by the number of items in the set. Does that sound like something you could do in two minutes? No? Well, don’t worry, because the GMAT won’t ask you to. In plain English, the standard deviation tells us how spread out the values are in a set. A set with values that are tightly clustered together, such as {105, 106, 107, 108, 109, 110, 111, 112, 113} 3 will have a small standard deviation, while a set with widely separated numbers, such as {2, 43, 187, 500, 1024} will have a large standard deviation, because the numbers deviate more from the standard. This means that you can get a sense of the standard deviation just by inspecting the elements in the set. There are really only two ways that the GMAT tends to test this concept. Try this example, which resembles some of the standard deviation questions that have appeared on past GMATs: Which of the following sets has the largest standard deviation? A. {107, 107, 108, 108, 109, 110, 110, 111, 111} B. {105, 106, 107, 108, 109, 110, 111, 112, 113} C. {101, 103, 105, 107, 109, 111, 113, 115, 117} D. {106, 106, 107, 107, 108, 108, 109, 109, 1111} E. {0, 106, 107, 108, 109, 110, 111, 112, 113} The answer is D. Since standard deviation is a measure of the average deviation from the mean, clearly answer choices A, B, and C, which all have numbers clustered very closely together, will have small standard deviations. D and E both have “outlying” numbers that are farther away from the cluster of similar numbers (and therefore farther away from the mean). The 0 in answer choice E is about 100 away from the mean, but the 1111 in D is about 900 away, meaning the standard deviation of D will be much larger. It is doubtful that you will ever have a problem on the GMAT that requires you to actually calculate the standard deviation instead of estimating, as we just did. If you want to be superprepared, though, here is how to do it: Mathematically, the standard deviation is

σ =

i =1

∑ ( x – xi ) n n

2

where x is the mean, and n is the number of elements.

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To calculate this by hand, 1. Calculate the mean: ( x ) 2. Subtract each value in the set from the mean (thus creating another set): ( x − x i ). 3. Square each of the values: ( x − x i )2 n 4. Add together all the values in this set (that is, sum the squares): ∑i =1( x − x i )2 n 5. Divide the sum by the number of values in the set: ∑i =1 ( x − x i )2 /n n ( x − x )2/ n 6. Take the square root of this value: ∑i =1 i

The other type of standard deviation question you might encounter on the GMAT provides you with the standard deviation for a set and tests whether you know what that means. A question could appear like the following: A set has an average (arithmetic mean) of 42 and a standard deviation of 1.8. Which of the following values is two standard deviations away from the mean? A. 36 B. 38.4 C. 40.2 D. 43.8 E. 75.6 To find the numbers that are one standard deviation away from the mean, you add the standard deviation to, and subtract it from, the mean. To find the numbers that are two standard deviations from the mean, you add the standard deviation to the mean twice or subtract it twice from the mean. In this question, this means 42 + (1.8) + (1.8) = 45.6 or 42 – (1.8) – (1.8) = 38.4. Thus, answer B is the correct answer. If you wanted a number that was three standard deviations from the mean, you would add the standard deviations to the mean three times or subtract it three times from the mean, and so on. You should have enough information now to answer the question posed at the beginning of the chapter: If the set S is composed of the following numbers {99, 100, 100, 105, 106, 116, 123}, which of the following is largest? A. The average (arithmetic mean) of set S B. The median of set S C. The mode of set S D. The range of set S E. The standard deviation of set S Let’s start with choice A. We’ve calculated the mean, and we know that it is 107. This is larger than the median, which is 105; even if we had not calculated the mean exactly, we could estimate that the mean is greater than the median because the three numbers greater than the median are relatively farther away from 105 than the three numbers less than the median. We know that the mode is 100, which is less than 107. We know that the range is 123 – 99 = 24, which is less than 107. And while we don’t want to waste time calculating the standard deviation of this set, we can see that the numbers

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aren’t too far apart, so we can assume that the standard deviation is a relatively small number (it’s actually around 9). Therefore, the answer has to be A, the average of set S.

WHAT YOU NEED TO REMEMBER
The mean The median is the average of a set, or the sum of its values divided by the number of elements. is the middle value of a set. Note that if there is an odd number of elements in the set, the median will be in the set, but if there is an even number of elements, the median will be the value halfway between the two middle-most elements. The mode The range The standard deviation is the most common element in the set. Note that there may be more than one mode. is the span of the set. It is the smallest value subtracted from the largest. is a measure of the degree to which the values in a set are spread out.

APPLICATION PROBLEMS—STATISTICS
The GMAT sometimes tests statistical concepts visually. The next several problems involve the data set at the right and the graph below. Each of the points at the right is plotted on the graph as an X-Y pair (the Xs run horizontally, and the Ys vertically). Since these are drill questions, they will differ a bit from those on the GMAT. While you can calculate the values by hand, you shouldn’t need to do so, and you probably wouldn’t be able to do so in the two minutes or so that you’ll have for each question. X 22.3428 7.6654 8.5955 14.3589 17.6411 6.4042 21.6396 19.4805 12.9962 10.5549 18.3253 19.0539 6.7122 11.9699 7.9197 9.7871 11.0604 4.3302 5.6040 8.5695 2.5882 1.0875 3.1519 0.7774 0.9194 0.0596 0.8907 2.8510 1.9444 0.5687 Y 0.2141 11.1677 0.8881 0.5454 1.7067 13.4480 0.3005 6.6545 7.2681 10.5108 3.8199 24.7435 8.4796 2.8641 3.2149 3.0499 1.4132 0.8355 1.7807 3.0499 1.7312 0.1513 0.4525 1.3067 0.2024 0.0367 0.1811 0.3191 0.9149 0.3620

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1. Which is greater, the mean of the Xs or the mean of the Ys? 2. Which is greater, the median of the Xs or the median of the Ys? 3. Which is greater, the range of the Xs or the range of the Ys? 4. Which is greater, the mode of the Xs or the mode of the Ys?

Solutions
1. X.

The mean of the Xs is approximately 8.5, and the mean of the Ys is around 3.5. You could

add up the sums by hand and then divide by 30 to get an exact figure, but if the GMAT gives you a distribution like this, you would be better off saving your time by estimating it visually. Six of the X values are over 15, while only one Y value is over 15, which is a pretty strong indicator that the Xs have a higher mean.
2. X.

The median X is 7.7925, but the median Y is only 1.5600. You could line the numbers

up from least to greatest, and then pull out the middle values, but that would take time. The quicker approach is to see where the weight lies along each dimension. The Xs appear to be reasonably evenly distributed along their axis, but the Ys clearly cluster toward the bottom. You might note that there are times when the mean of one set will be larger, but the median of the other will be the greater. That would be a fine observation; it’s just not the case here.
3. Y.

The range of the Xs is 22.2832, and the range of the Ys is 24.7068. Range is an easy value to

calculate; you just need to identify the outliers for both X and Y and see which ones have the bigger range. You could also do this visually; there are both X and Y values very close to 0, but there is a Y value, 24.7435, that is clearly larger than the largest X value, 22.3428. Even without calculating an exact range, you could estimate that the range of the Ys would be about 2.5 larger than the range for the Xs.
4. Y.

The Ys have two points with values of 3.0499, while the Xs have no repeat value. Since the

Ys have a mode and the Xs do not, the Ys have the higher mode.

PROBABILITY
The GMAT tests your knowledge of probability in a number of different ways, but all of the questions boil down to the same concept. The probability that an event X will occur = The number of possible outcomes in which X occurs The total number of possible outcomes e This probability can have a maximum value of 1 or 100 percent if every possible outcome results in X, and a minimum value of 0 or 0 percent if none of the possible outcomes result in X. For example, if you reach into a bag filled with nothing but green jellybeans and pull out a jellybean, the probability that that jellybean will be green is 100 percent. If you reach into the same bag and pull out another jellybean, the probability that that jellybean will be purple is 0 percent, because there are no possible outcomes in which a purple jellybean can be removed from a bag filled only with green jellybeans.
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Of course, if we dealt only with certainties, it wouldn’t be called “probability,” so the test makers generally ask probability questions in which the probability of an event is somewhere between 0 and 1. A simple probability question might ask: A bag contains 26 purple jellybeans, 15 green jellybeans, and 9 yellow jellybeans; these jellybeans are the only items in the bag. If a person picks a jellybean at random out of the bag, what is the probability that the jellybean will be green? A. 15% B. 20% C. 25% D. 30% E. 35% To get the answer, we divide the number of outcomes in which the desired event occurs by the total possible number of outcomes. If there are 15 green jellybeans out of a total of 26 + 15 + 9 = 50 jellybeans, then the probability that one picked at random will be green is 15/50 = 0.3 = 30%, answer D. The test makers make these problems more complicated by changing the number of items in the middle of the question and by asking the question from a different angle from what you may be expecting. A more difficult probability question might look like this: A bag contains 26 purple jellybeans, 15 green jellybeans, and 9 yellow jellybeans; these jellybeans are the only items in the bag. If a person reaches into the bag and picks out only purple jellybeans, how many jellybeans would the person have to pick out in order to double the probability that a jellybean picked out of the bag at random would be a green jellybean? A. 5 B. 15 C. 19 D. 24 E. 25 To solve this problem, you would first need to figure out what it means to double the probability of picking a green jellybean at random. Your first step would be to determine the initial odds of picking a green jellybean; we know from the last question that those odds are 15/50 = 0.3 = 30%. Doubled odds, therefore, are 60%, or 0.6. Since the person picking out the jellybeans in this question is picking only purple jellybeans, we know that the number of green jellybeans remains the same, 15. If x is the new total of jellybeans after the person picks out the purples, we can set up the equation: 0.6 = 15 ⇒ 0.6x = 15 ⇒ x = 15 = 25 x 0.6 So the new total of jellybeans must be 25. If the original total was 50, a person would have to pick out 50 – 25 = 25 purple jellybeans in order to double the probability of picking a green jellybean at random.

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Conditional Probabilities
Things get a little more complicated when you need to model events that depend on whether other events have occurred or not. We’ll use an example from real life in which otherwise ordinary people become consumed with the minutiae of conditional probability: the last two rounds of a hypothetical ACC basketball tournament. Duke is about to play North Carolina in the first game of the next-to-last round. After that, regardless of what happens in that game, Maryland (fear that turtle) will play Virginia. We’ll assume that this year North Carolina has the strongest team, but that anything can happen when two teams meet on the court. Well, not quite: we’ll include some probabilities in our model so that we can estimate, ex ante, what might happen. We’ll use the table shown here as our compilation of those probabilities.

Example: ACC Tournament Matchups—Probability that the Team at Left will Win Duke UNC UVa Maryland Duke UNC 0.65 UVa 0.45 0.50 Maryland 0.30 0.35 0.45

What is the probability, from the vantage point of the opening buzzer of the Duke–UNC game, that any of these teams will win the tournament? To determine that, the first thing to do is to lay out a probability tree. The tree has three stages: 1. The Duke–UNC game, with two possible outcomes. Duke has a 35 percent chance of winning, and (since the totals sum to one) UNC has a 65 percent chance of winning. 2. The Maryland–Virginia game, with (again) two possible outcomes. This part of the tree is replicated for each possible outcome of the Duke–UNC game. That’s because there are four ways that this could play out: a. Duke could beat UNC, and Maryland could beat UVa. b. Duke could beat UNC, and UVa could beat Maryland. c. UNC could beat Duke, and Maryland could beat UVa. d. UNC could beat Duke, and UVa could beat Maryland. In this case, the probabilities do not affect one another—that is, the Duke–UNC game and the UVa–Maryland game are said to be independent events. 3. Lastly, the winners of the two games will meet in the final. As with our four possible two-game outcomes, we’ll have four corresponding possibilities for a final round: a. Duke plays Maryland b. Duke plays UVa c. UNC plays Maryland d. UNC plays UVa

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Example: ACC Tournament—Probability Tree

But how do we calculate the probability that those underdog Terrapins (i.e., Maryland) will win the tournament? By multiplying the probabilities. In general, if there is a probability X that Event 1 will happen, and a probability Y that Event 2 will happen, then the probability that both will happen is XY. Thus, the probability that Duke will beat UNC in the first game of the next to last round, that Maryland will beat Virginia in the second game, and that Maryland will then beat Duke in the finals is 0.35 • 0.045 • 0.30 = 0.0473 or 4.73% That doesn’t look so good, but there are other possibilities. As the following spreadsheet shows, we can multiply all of these triplets through to find the probability for any one specific outcome.
Example: ACC Basketball Tournament—Outcomes Winner Duke Duke Duke Duke UNC UNC UNC UNC Probability 0.35 0.35 0.35 0.35 0.65 0.65 0.65 0.65 Winner Maryland Maryland UVa UVa Maryland Maryland UVa UVa Probability 0.45 0.45 0.55 0.55 0.45 0.45 0.55 0.55 Winner Duke Maryland Duke UVa UNC Maryland UNC UVa Probability 0.70 0.30 0.55 0.45 0.65 0.35 0.50 0.50 Total Overall Probability 0.1102 0.0473 0.1059 0.0866 0.1901 0.1024 0.1788 0.1788 1.000

If you add the numbers in the rightmost column, you’ll note that they actually add to 1.0001. That’s rounding error—the point is that the probabilities actually sum to 1, or 100 percent, which is

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what we need to see. At this point, to find the probability that the Terrapins will go all the way, we add the probabilities of the two ways in which it could happen: \$ Duke beats UNC, Maryland beats Virginia, Maryland beats Duke (4.73%). \$ UNC beats Duke, Maryland beats Virginia, Maryland beats UNC (10.24%). Thus there are two possible ways, with a combined probability of 14.97 percent, for Maryland to win the whole thing. Please note that on the actual GMAT, you are very unlikely to see any questions dealing with actual sports teams, on the grounds that such questions would give an unfair advantage to those test takers who are well versed in the sport in question. So no, your time spent watching ESPN does not count as preparation for the GMAT.

PRACTICE PROBLEMS
1. Lottery balls numbered consecutively from one through one hundred are placed in a spinner.

If one ball is drawn at random, what is the probability that it will have the number 1 on it exactly once? 9 A. —– 100 1 B. — 10 11 C. —– 100 19 D. —– 100 1 E. – 5 Month 1 2 3 4 5 Noah’s Landing 3 2 0 2 1 Bellaville 2 0 4 x 1

2. Monthly rainfall was recorded for two towns over a five-month period using the chart above. If

the median rainfall in Noah’s Landing was equal to the average (arithmetic mean) rainfall in Bellaville, what is the value of x? A. 1 8 B. – 5 C. 2 D. 3 E. 10
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3. If x is a positive, single-digit integer such that – x, 2x, x, and x + 2, and 3x – 2 form a non-ordered

4 3 list of consecutive integers, which of the following could be the median of that list? A. 3 B. 4 C. 5 D. 6 E. 8

4. If the sum of a list of consecutive odd integers is 5, which of the following could be true?

I. The average (arithmetic mean) of the list is equal to 5. II. The median of the list is equal to 5. III. The range of the list is equal to 5. A. None B. I only C. II only D. I and II E. I and III
5. A jar contains only red, yellow, and orange marbles. If there are 3 red, 5 yellow, and 4 orange

marbles, and 3 marbles are chosen from the jar at random without replacing any of them, what is the probability that 2 yellow, 1 red, and no orange marbles will be chosen? 1 A. — 60 1 B. — 45 2 C. — 45 3 D. — 22 5 E. — 22

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Day Monday Tuesday Wednesday Thursday Friday

Price 17.94 18.19 18.06 17.54 17.38

6. Closing prices for a certain stock were recorded each day for a week in the table above. If the

monthly average (arithmetic mean) was 18.43 and the standard deviation was 0.27, how many days during this week did the closing price fall within two standard deviations from the average? A. 1 B. 2 C. 3 D. 4 E. 5
7. A freight elevator can carry a maximum load of 1200 pounds. Sean, who weighs 200 pounds, is

in the elevator with two packages weighing 150 pounds and 280 pounds. If he needs to fit three more packages in the elevator that weigh as much as possible without exceeding the elevator limit, what is the difference between their average and the average of the two packages already in the elevator? A. 25 B. 85 C. 190 D. 215 E. 210
8. WINK, Inc. follows a certain procedure that requires two tasks to be finished independently in

7 order for a job to be done. On any given day, there is a – probability that task 1 will be 8 3 completed on time, and a – probability that task 2 will be completed on time. On a certain day, 5 what is the probability that task 1 will be completed on time, but task 2 will not? 1 A. — 20 3 B. — 40 13 C. — 40 7 D. — 20 13 E. — 40
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The following data sufficiency problems consist of a question and two statements, labeled (1) and (2), in which certain data are given.You have to decide whether the data given in the statements are sufficient for answering the question. Using the data given in the statements plus your knowledge of mathematics and everyday facts (such as the number of days in July or the meaning of counterclockwise), you must indicate whether A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. D. EACH statement ALONE is sufficient. E. Statements (1) and (2) TOGETHER are NOT sufficient.
9. Kara attends a university where students study for an average (arithmetic mean) of 13.4 hours

per week. How many hours per week does Kara study? (1) The standard deviation of study time at Kara’s school is 2.8. (2) Kara’s study time is one standard deviation away from the mean.
10. The cards in a deck are numbered consecutively from 1 to 20. If some cards are red and some

cards are black, what is the probability of drawing a red card? (1) The odd-numbered cards are all red. (2) The even-numbered cards are all black.

Solutions
1. D.

The balls with the number 1 on them exactly once are 1, 10, 12, 13, 14, 15, 16, 17, 18, 19, 21, 31,

41, 51, 61, 71, 81, 91, and 100. Count them up and we get 19 balls out of 100.
2. D.

Noah’s Landing had a median rainfall of 2 inches, because if we put the numbers in an

ordered list (0, 1, 2, 2, 3), the middle number is 2. That means Bellaville had a mean of 2 inches. Since the mean is just the total of the numbers divided by the number of numbers, and there are five numbers in the list, the total of that list must be 10. When we subtract the existing values from 10, we get 10 – 2 – 0 – 4 – 1 = 3.
3. C.

Since there are only nine single-digit, positive integers, and not all of them will yield integers

when we use them in these algebraic expressions, let’s start with trying to find a value for x that 4 will give us a list of consecutive integers. 1 won’t work, since – × 1 is not an integer. Same with 2. 3 4 When we use 3, though, we get – × 3 = 4; that’s an integer. The other expressions give us 3 2 × 3 = 6, 3, 3 + 2 = 5, and 3 × 3 − 2 = 7. So our group includes 4, 6, 3, 5, and 7. They aren’t in order, but they don’t have to be according to the problem, and they are consecutive. But be careful! The problem asks for the median of the list, not the value of x. The median of the list 3, 4, 5, 6, 7 is 5.

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4. A.

Let’s start by finding a list of consecutive odd integers that add up to 5. –3, –1, 1, 3, and 5 is one

such list. In fact, can you think of another? There isn’t one, so now we just have to see which of the Roman numerals is true in this case. I isn’t true—the mean is 1. II is also untrue—the median is also 1. And the range is 8, so none of the Roman numerals are possible, and A is our answer.
5. D.

It doesn’t really matter in which order we draw the marbles since they’re really all drawn at

once, but from a mathematical standpoint, it’s much easier to take these probabilities one at a time. Let’s first take the probability of drawing a yellow marble from the jar. Since there are 5 5 yellow marbles out of 12 marbles total, the probability of drawing a yellow marble is — . 12 4 The probability of drawing a yellow marble after that is — , since one yellow marble is missing and 11 3 one marble is missing from the total. Finally, the probability of drawing a red marble is — . So the 10 5 4 3 60 probability of drawing the specified combination of marbles is — × — × — = —— . Once we 12 11 10 1320 1 reduce, we get — . But since the order we draw in does not matter, we need to multiply this by the 22 number of ways to arrange the three drawn marbles. It could be YYR, RYY, or YRY, for a total of 1 3 3 possible arrangements. So our total probability is — × 3, or — . 22 22
6. C.

Since two standard deviations away from the mean works out to 18.3 − 2.7 × 2 = 17.89, there

are 3 days during which the stock prices fell between 17.89 and 18.3: Monday, Tuesday, and Wednesday. We really don’t have to worry about prices above the mean, because there were none of them during this time frame.
7. A.

Sean and the two packages in the elevator weigh 630 pounds together, so the three packages

Sean wants to put into the elevator must weigh a maximum of 1200−630, or 570. If we divide that by 3, we get the average weight of each package, 190. The two packages already in the elevator weigh a total of 430 together, so their average weight is 215. Subtract 190 from 215 and we get the difference in the averages, or 25.
8. D.

7 3 Task 1 has a – probability of being completed on time, and task 2 has a – probability of being 8 5 2 completed on time, which can also be expressed as a – probability of not being completed on time, 5 7 2 14 which is what the problem asked for. Multiply the probabilities and we get – × – , or — , which 8 5 40 7 reduces to — . 20 Statement (1) alone tells us more about the student population, but nothing in particular

9. E.

about Kara, so it is not sufficient and we can cross off A and D.
Statement (2) alone tells us nothing because we don’t know what the standard deviation is, so we can eliminate B. Together, the statements tell us that Kara studies for either 16.2 hours or 10.6 hours, but because we don’t know whether she studies more or less than the mean, the statements are not sufficient together and our answer is E.

PROBABILITY AND STATISTICS

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10. C.

This is a very deceptive problem. Statement (1) tells us that 10 of the 20 cards are red, but it

doesn’t say that those are the only red cards in the deck, so it’s not sufficient on its own and we can eliminate A and D. The same thing applies to statement (2); it doesn’t say that those are the only black cards in the deck. When we put the statements together, on the other hand, we see the whole picture and know that exactly 10 of the 20 cards are red. So our answer is C.

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THE QUANTITATIVE SECTION

CHAPTER 6

GMAT Geometry

f

INTRODUCTION
Geometry problems are one of the more puzzling inclusions on the list of skills tested by the GMAT. It’s an unusual day when a business analyst needs to measure an angle or calculate an area. No doubt there are exceptions, as we will cover in the applications section. But generally, geometry is a topic that most people learn in high school and then largely forget. This lack of business relevance may be part of what makes it particularly useful in the GMAT. As an aptitude test, and pointedly not an achievement test, the GMAT asks nothing about the appropriateness of accounting reserves or the correct discount rate to use in financial models. If it did, undergraduate business and economics majors would have a distinct advantage. Asking questions about geometry levels the playing field. Perhaps the best news in this regard is that the handful of geometry questions you will encounter on the GMAT can generally be solved using only a small set of geometric principles. These involve parallel lines, triangles, quadrilaterals, circles, and a few regular cylinders.

PARALLEL AND INTERSECTING LINES
Parallel lines are lines in the same plane that, if extended to infinity, would never intersect:

Most problems involving parallel lines will include either a geometric shape with parallel lines, such as a rectangle or parallelogram, or two parallel lines that are intersected by another line. The angles formed by the intersection of a line with two parallel lines have some interesting properties.

79

When lines intersect, the measures of the angles on opposite sides of the intersection are equal; these angles are called vertical angles. In the diagram, all of the angles labeled x have equal measures, and all of the angles labeled y have equal measures. The measures of the angles on the same side of a line, here represented as x and y, must add up to 180°; these are called supplementary angles. A line that intersects two parallel lines will produce angles of equal measure with both of the parallel lines, as shown by the x and y angles in the preceding diagram. The GMAT tests this concept in a number of ways. Consider the following Data Sufficiency question:

In the diagram above, if lines L1 and L2 are parallel, what is the value of x? (1) y = 70° (2) x > 90° A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. D. EACH statement ALONE is sufficient. E. Statements (1) and (2) TOGETHER are NOT sufficient. To answer this question, you need to recognize that if L1 and L2 are parallel, then all of the acute angles in this diagram are going to have a measure of y ° and all of the obtuse angles are going to equal x°, and that x and y are supplementary angles. Now consider statement (1): (1) y = 70° If x and y are supplementary, then x ° + y ° = 180° → x ° = 180° − y ° = 180° − 70° = 110°. Thus, you can answer the question with statement (1) alone, so the answer to this question must be either A or D. Now consider statement (2): (2) x > 90° What does this tell you? Just that x is an obtuse angle. It could have a value anywhere between 90° and 180°. Therefore, statement (2) alone is not sufficient, so the answer must be A. Parallel lines questions don’t get much more difficult than this. Remember, when you have a line intersecting two parallel lines, and you know the measure of one of the angles, then you can determine the measures of all the other angles.
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TYPES OF TRIANGLES AND THEIR ATTRIBUTES
Triangles figure very heavily in the GMAT because they are the simplest type of polygon (a polygon is a multisided figure). They are thus at once easy to understand, but also rich in mathematical detail.

Angles, Sides, and Area
Every triangle has three sides, here denoted as A, B, and C, and three angles, here denoted as δ, ε, and φ (these names are arbitrary; the GMAT will identify sides and angles in a variety of ways). The sum of the lengths of the sides equals the perimeter, and the sum of the measures of the angles of any triangle is 180°: A + B + C = P (perimeter) δ + ε + φ = 180° Of the interior angles of a triangle or any polygon, an angle with a measure of less than 90° is called an acute angle, an angle with a measure of exactly 90° is called a right angle, and an angle with a measure of greater than 90° but less than 180° is called an obtuse angle. Since the angles of a triangle must add up to exactly 180°, in any triangle with a right or obtuse angle, the other two angles must be acute angles. Another attribute of triangles is that no one side can be greater in length than the sum of the lengths of the other two sides. Likewise, no side length of a triangle can be less than the difference of the remaining two side lengths. In the triangle in our example, A cannot be larger than B + C, and B cannot be smaller than A – C, i.e. A < B + C and B > A – C. Many of the triangle questions on the GMAT deal with the area of triangles. The most direct way to find the area of a triangle is to determine the height of the triangle and plug it into the following formula: A = 1 bh 2

Here, b is the base, h is the height, and A is the area. We all remember from high school or earlier the “one-half the base times the height” mantra, but as shown here, it’s not always obvious what the base should be. Base can be a misleading term, as it doesn’t need to be on the bottom of the figure. The GMAT often will not include the height, also called the altitude, on the diagrams it provides, but usually you will have sufficient information to draw it in on your own diagram.
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There is one more way to find the area of a triangle, though it isn’t much used. Heron’s Formula is handy when you know nothing more than the measures of the three sides. In this formula, the lengths of the sides are represented as a, b, and c, and s represents the semiperimeter, which is just half the perimeter. Heron’s Formula is as follows: A = s (s − a )(s − b )(s − c ) where s = 1 ( a + b + c ) 2

It’s not easy to remember, but it can be useful if finding that third side of a triangle is quicker for you than finding an altitude.

Isosceles Triangles
Triangles with two sides of equal length are called isosceles triangles. No, they aren’t named after some Dead Greek Guy named Isosceles (yes, we’ve gotten this question before). Isoskelos is just Greek for “equal legs.” There are two key things you need to remember about isosceles triangles:

\$ Two of the sides are of equal length. \$ The two angles opposite the sides of equal length are also of equal degree measure (e.g., in the diagram φ = φ).

Equilateral Triangles
Equilateral triangles are a special case of isosceles triangles in which all the sides are of equal length. From this it follows that all the angles are of equal measure as well, and each of these angles measures 60∞. Identifying a triangle as equilateral on the GMAT can be very useful because you can then determine that any side can be immediately related to any other side, as can any angle to any other angle. There’s also a special formula for the area of an equilateral triangle:

A = 3 s2 4

where s is the length ofany given side d

As an exercise, you can try to derive this using Heron’s Formula.
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Right Triangles
Right triangles are triangles in which one of the angles has a measure equal to 90°. The beauty of a right triangle is that the lengths of its sides relate to one another according to the Pythagorean Theorem. The Pythagorean Theorem has been invoked over and over by GMAT problems in the past. We’re not sure who decided that mastering the Pythagorean Theorem was an important hurdle to clear for admission to an MBA program, but there it is. The good news is that you almost certainly knew it once, and if you don’t remember it, it’s easy to memorize again. The theorem states that, where A and B are the lengths of the legs of a right triangle and C is the length of the hypotenuse:

A2 + B2 = C 2 Pythagoras is a Dead Greek Guy, and his original proof is a beautiful thing to behold. Fortunately, you will never in your life be asked to reproduce it. As we noted earlier, however, you do need to be very careful in identifying just which are the sides, and what is the hypotenuse. There are a few problems from past GMATs in which those things have not been obvious. You also need to be careful when applying the Pythagorean Theorem that you use the order of operations correctly. Remember to square A and square B separately and then add the results together. This is especially important to remember when you are solving for the length of the hypotenuse. A very common mistake made when using the Pythagorean Theorem is to “distribute” the square root over the A 2 + B 2: A2 + B2 ≠ A + B Note that the little square at the vertex of sides A and B is meant to denote that the angle is a right angle (90°). That will be important on the GMAT, since the current test-writing regime uses the same notation. Note also that there are right triangles that are also isosceles triangles (as in the figure here), but that there are no right equilateral triangles. In the latter case, that’s because we cannot (at least not in Euclidean space) have a triangle with three angles each of 90°. That would violate the rule that the measures of the three angles of a triangle must add up to 180°.

A special case of triangle that shows up frequently on GMAT questions is the right isosceles triangle. The three angles within right isosceles triangles have measures of 45°–45°–90°. For right isosceles triangles, the Pythagorean Theorem reduces to C 2 = A 2 + A 2 → C 2 = 2A 2
GMAT GEOMETRY \$83

If you take the square root of this formula, you can determine the ratio of the length of the hypotenuse to the length of the sides in a right isosceles triangle: C2 =

( 2A 2 ) → C =

2A

Thus, if one of the legs of a right isosceles triangle has a length of 5, then you know that the other leg also has a length of 5 and the hypotenuse has a length of 5 2 .

Some Special Triangles
In addition to the right isosceles triangle, there are a few other special-case right triangles that appear frequently on GMAT questions.
The 3–4–5. The 3–4–5 triangle is a right triangle with side lengths in the ratio of 3 to 4 to 5.

The lengths could be 3–4–5, or they could be 6–8–10, 9–12–15, and so on. The sides of the basic 3–4–5 triangle square through the Pythagorean Theorem as 9 + 16 = 25, and the other triangles with this ratio square through as well (e.g., 36 + 64 = 100, 81 + 144 = 225, and so on). The GMAT frequently uses these ratios so that you can work through the calculations more quickly; if you know to expect them, you can work through them still more quickly.
The 5–12–13. The 5–12–13 triangle is a right triangle with side lengths in the ratio of 5 to 12 to 13. The

sides square in the Pythagorean Theorem as 25 + 144 = 169. This one appears in questions somewhat less frequently than the 3–4–5. Note that you could see a 10–24–26 triangle as well.
The 30°–60°–90°, a.k.a. the 1 – 3 – 2 . If you see that a triangle has legs of 1 and 3 , you can

calculate that 12 +

( 3)

2

= 1 + 3 = 4 = 22

The 30° −60° −90°, or 1− 3 − 2 triangle

And therefore the hypotenuse has a measure of 2. Triangles with lengths of this ratio always have angles with the measures of 30°, 60°, and 90°, and triangles with angles of those measures always have sides with lengths in the ratio of 1 to 3 to 2 (i.e., they could be 5, 5 3 , and 10, or 8, 8 3 , and 16,
84# THE QUANTITATIVE SECTION

and so on.). This kind of triangle appears in all sorts of GMAT problems involving geometry. For reference, 3 is approximately equal to 1.7, so it is greater than 1 but less than 2. It is important with these triangles to remember which angle corresponds with which side: the 30° angle is opposite the side with length 1, the 60° angle is opposite from the side with length 3 , and the 90° is across from the side with length 2. If you’re having trouble remembering this, here’s a good rule of thumb: the largest angle is always directly opposite the largest side, the smallest angle is always directly opposite the smallest side, and so on.

After triangles, the next most common polygon on the GMAT is the quadrilateral. A quadrilateral is a polygon with four sides. Occasionally you’ll run into pentagons, hexagons, and octagons on the test, but these are rare.

Squares and Rectangles
Squares and rectangles are by far the most common quadrilaterals encountered on the GMAT. Both squares and rectangles have four right angles and two sets of parallel sides. All four sides of a square are of equal length, while a rectangle can have pairs of sides of different lengths:

The area of a square, of course, is just the square of one of its sides (s 2), and the perimeter of a square is 4 times any side (4s). For a rectangle, things are only slightly more complicated: P = 2a + 2b ; A = ab (rectangle) A square is a special case of a rectangle. Note that a square divided along a diagonal makes two isosceles right triangles. Since the diagonal of the square is the hypotenuse of the isosceles right triangle, the diagonal of the square has a length of 2s . A rectangle divided along a diagonal makes two right triangles as well, and you can determine the length of a diagonal of a rectangle by means of the Pythagorean Theorem.

Rhombi and Parallelograms
A rhombus is a quadrilateral with sides of equal length and two sets of opposite angles with equal measures, but the measures of all four angles are not necessarily equal. If the measures of all four angles were equal, then you would have a square. A square is a special case of the rhombus in which all four angles are equal. A parallelogram is a quadrilateral with two pairs of parallel sides; the sides in each parallel pair are of equal length, but not necessarily the same length as the other pair of sides.
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A rectangle is a special case of a parallelogram in which the measures of all of the angles are equal, a rhombus is a special case of a parallelogram in which all sides are of equal length, and a square is a special case of a parallelogram in which all sides are of equal length and all angles are of equal measure. In both rhombi and parallelograms, the angles on opposite sides of the figure have equal measures (i.e., the two acute angles have equal measures, and the two obtuse angles have equal measures). The diagram here shows not just the shapes, but also the beginning of an approach to calculate their areas:

The area of a parallelogram is easy to deduce, if you just remember that it’s basically composed of a rectangle and a pair of triangles. The area, then, is just A = ( b – x ) h + 2 ⎛ 1 xh ⎞ = bh – xh + xh = bh ⎜ ⎝2 ⎟ ⎠ That is, it’s no different from the area of the analogous rectangle, but if you forget that, you can get it back quickly with a little geometric reasoning. You can work out the same relationship for the rhombus. Once again, remember that the opposite sides in rhombi and parallelograms are parallel to each other. That is, after all, the meaning of “parallelogram.”

Trapezoids
The last quadrilateral of note is the trapezoid, which has just one pair of parallel sides. In isosceles trapezoids, the other two sides have matching lengths—kind of like isosceles triangles do. The diagram here shows how to calculate its area. Divide the figure into a rectangle and two triangles, much as you would for a parallelogram. Then, add the areas of those components:

A = ah + 2 ⎛ 1 xh ⎞ = ah + xh = h ( a + x ) ⎜ ⎝2 ⎟ ⎠

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This means that the area of a trapezoid is the height times the average of the lengths of the two parallel sides.

CIRCLES
There is a small set of things to remember about circles for the GMAT. First, some notation:

\$ The radius is generally, but not always, denoted with an r, and it is half the length of the diameter, which is generally (but again, not always) denoted with a d. \$ The center is frequently labeled with a C. \$ Unlike diameters and radii, not every line segment inscribed in a circle is anchored in the center. Those line segments that have their endpoints on the circle are called chords. (A diameter is a special case of a chord that crosses the center.) Now, on to the few formulae to remember: \$ The circumference is the distance around the circle (or what’s called the perimeter in a polygon). It’s also often denoted with a c, which can be confusing. You’ll find it with the formula c = πd = 2πr Whether you use the diameter or the radius is just a matter of personal preference, or of which is more clearly provided in the question. As for π (otherwise known as “pi”), it is reasonably approximated by 3.14, though in many problems it will appear as itself in the answer choices. If it does, don’t convert it to 3.14 in your calculations or you will waste a great deal of time. When dealing with circles, always check the answer choices first to determine whether you need π in your answer. \$ The area of a circle is also found with π: A = πr 2 It’s generally not convenient to try to substitute the diameter into this formula. You’re probably better off dividing it in half to find the radius, then plugging that number in. Most of the time, this is the more profitable route in GMAT geometry.

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\$ Finally, there is one formula involving chords that you may need to know, since questions involving it have appeared a few times in the past. In the diagram shown here, the dotted line is a diameter, the solid line is a radius, and the dashed line is a chord. When the angle between a chord and a diameter is subtended by an angle between a radius and the same diameter, the measure of the second angle is twice that of the first. If that’s a mouthful, just study the diagram. If you see that, remember that the inside angle is twice the outside angle. If you can’t remember which is supposed to be larger, then just look to see which appears larger. This is probably the one place where the diagram will always be more or less drawn to scale.

VOLUME OF BOXES AND RIGHT CIRCULAR CYLINDERS
Geometry questions can sometimes become more difficult conceptually when they extend into a third dimension. When the GMAT does ask about the volumes of solid figures, it tends to ask about either boxes—the three-dimensional forms of squares or rectangles—or right circular cylinders, as depicted in the figure. Calculating volumes is actually pretty easy: just find the area of the base and multiply that by the figure’s height. The volume of a cube is the cube of a side, s3. The formula for the volume of a box with a rectangular base is Volume = length × width × height

The volume of a right circular cylinder is likewise the area of the base times the height: V = Abh = πr 2h since the base of a right circular cylinder is a circle and the area of a circle is πr 2 .
88# THE QUANTITATIVE SECTION

WHAT YOU NEED TO REMEMBER
The area of a triangle: A ∆ =
1 2

bh

Heron’s Formula for the area of a triangle: A = s(s − a )(s − b )(s − c ), s = 1/2(a + b + c ) 3 s2 The area of an equilateral triangle: A = 4 The Pythagorean Theorem: A 2 + B 2 = C 2 The 3–4–5 triangle: 32 + 4 2 = 52 The 5–12–13 triangle: 52 + 122 = 132 The 30°–60°–90° triangle: 12 + ( 3 )2 = 22 The area of a parallelogram: Ap = bh The area of an isosceles trapezoid: AT = h(a + x ) or = 1 h(a + b ) 2 The circumference of a circle: c = 2πr The area of a circle: Ao = πr 2 The volume of a right circular cylinder: V = πr 2h

PRACTICE PROBLEMS
1. In a right isosceles triangle, the lengths of the two nonhypotenuse sides are designated a. What

is the area of the triangle in terms of a? A. 1 a 2 3 B. 2 a 2 3 C. 1 a 2 2 D. 3 a 2 2 E. 2a 2
2. The U.S. Defense Department has decided that the Pentagon is an obsolete building and that

it must be replaced with an upgraded version: the Hexagon. The Secretary of Defense wants a building that is exactly 70 feet high and 200 feet on a side, and that has a hexagonal bulls-eye cutout in the center (somewhat like the current one) that is 50 feet on a side. What will be the volume of the new building in cubic feet? A. 3,937,500 cubic feet B. 15,750 cubic feet C. 11,550 3 cubic feet D. 15,750 3 cubic feet E. 3, 937, 500 3 cubic feet

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3. What is the area of the shaded figure?

A. (9 + 3 ) 8 (5 + 3 2 ) B. 3 C. 9 2 D. 3 + 3 2 (9 + 3 ) E. 2

4. In the figure above, x = 2. What is the area of circle O ?

A.

2π B. 2π C. 2 2π D. 4π E. 4 2π

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THE QUANTITATIVE SECTION

5. Which of the following could be the equation of line l in the figure above?

A. 2x = 3y – 2 B. 2x = 3y – 6 C. 3x = 2y – 6 D. 2 x = 2y –2 3 E. 2 2x = 3y – 6 3

6. In the rectangular figure above, the area of the shaded region is equal to the area of the non-

shaded rectangle. If AB = 6, BC = 4, and the longer side of the non-shaded rectangle is an integer, what is one possible measurement for the shorter side of the non-shaded rectangle? A. 3 4 3 2

B. 1 C.

D. 12 5 E. 16 3

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7. In the figure above, what is the value of 2s – r?

A. 60 B. 70 C. 100 D. 140 E. 220

The following data sufficiency problems consist of a question and two statements, labeled (1) and (2), in which certain data are given. You have to decide whether the data given in the statements are sufficient for answering the question. Using the data given in the statements plus your knowledge of mathematics and everyday facts (such as the number of days in July or the meaning of counterclockwise), you must indicate whether A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. D. EACH statement ALONE is sufficient. E. Statements (1) and (2) TOGETHER are NOT sufficient.

8. In the figure above, what is the area of the shaded region?

(1) AB = 8 (2) Angle AOR = 45°.

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THE QUANTITATIVE SECTION

9. In the figure above, what is the value of x?

(1) 2y = 100. (2) ABCD is a parallelogram.

10. In the figure above, what is the length of RT?

(1) RU = 5 (2) RS = 12

Solutions
1. C.

The formula for the area of a triangle is 1/2 bh . You can orient an isosceles

right triangle so that the two equal sides form both the base and the height. If these sides are of length a, then plugging these values into the area formula gives us the result 1/2 a 2 , which is answer C. The diagram shows how the equal sides form both the base and the height:

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2. E.

This is very definitely a multi-step problem. First, you need to recognize that we’re dealing

with nothing more than an oddly-shaped cylinder: the base is a regular polygon, so by dividing it into a number of manageable pieces, we can calculate its area. However, before we do that, we’ll need to figure out how to treat that hole in the middle of the six-sided doughnut. The easiest thing to do is to think about it as “negative area”—to calculate its area, and then subtract that area from the area of the larger, filled-in shape to find the area of the region around it. The following diagram below shows the three steps:
Step 1 Draw the Hexagon, including bull’s-eye Step 2 Divide it into a solid part and a hole Step 3 Cut each of the resulting pieces into six smaller ones

Next, we’ll need to calculate the areas of those two different triangles. If you happen to remember the formula for the area of an equilateral triangle, great; skip to that step. If not, you’ll need to derive it. That’s not that hard: using the diagram that follows, you can divide the equilateral triangle into two right triangles, each with height h, hypotenuse a (there go those shifting variable names again), and base a/2. Since we don’t know what h is, it would be nice to state that in terms of a as well. We’ll do that first, by relying on the Pythagorean Theorem: ⎛ a ⎞ + h2 = a2 → 1 a2 + h2 = a2 → h2 = 3 a2 → h = 3 a ⎜ ⎟ ⎝ 2⎠ 4 4 2 Step 4: Calculate the area of the triangle The area of the entire equilateral triangle is just twice the area of the right “half triangle” on either side:
2

⎞ ⎛ A = 2 ⎛ 1 bh ⎞ = 2 ⎜ 1 a 3 a ⎟ = 3 a 2 ⎜ ⎝2 ⎟ ⎠ ⎝22 2 ⎠ 4

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THE QUANTITATIVE SECTION

Six of these form the whole of the large (outer) hexagon, so that area is a hex = 6 × 3 a 2 = 3 3 a 2 4 2 Six of the smaller triangles form the whole of the hole in the middle. We’ll need a different variable for these, since we’re talking about a different a at this point. We can define these as the outer ao and inner ai sides: The area of the Hexagon (minus the bull’s eye) =
2 Aouter − Ainner = 3 3 ao − 3 3 ai2 2 2

Then, the height is a uniform 70 feet all around, so finding the volume is just a matter of multiplying through by that height: ⎞ 2 ⎞ ⎛ ⎛ 2 V = h ⎜ 3 3 Ao − 3 3 Ai2 ⎟ = h ⎜ 3 3 ⎟ Ao − Ai2 ⎠ ⎝ 2 ⎠ ⎝ 2 2

(

)

Of course, that doesn’t look much like the answer choices, so we’ll need to substitute the values for the variables: ⎞ ⎛ V = 70 ⎜ 3 3 ⎟ 2002 − 502 = 35 × 3 3 × ( 40, 000 − 2, 500 ) = 105 3 × 37, 500 = 3, 937, 500 3 ⎝ 2 ⎠

(

)

If you looked over the answer choices, you will know that 3 is an acceptable component of your answer; the thrust of this question is geometry, so the GMAT would not make you calculate a square root as part of the problem. The volume corresponds with answer choice E.
3. A.

This figure may look intimidating, but it’s actually quite harmless. To tackle it, you must first

recognize that it can be split into two smaller triangles, as shown in the diagram. Once you’ve separated the triangles, you can start labeling the lengths. The lower triangle has two 45° angles, so it is clearly a right isosceles triangle. That means that we should be able to find the area quickly. An intermediate step will be calculating the lengths of the (equal) sides, which we’ll designate as x. That will also have a follow-on purpose. We’ll be able to use the length x with the full length of the left side of the figure to calculate the length of the rising side of the smaller triangle. First, though, we’ll get back to the lower triangle and the Pythagorean Theorem:

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⎞⎛ ⎞ ⎛ ⎞ ⎛ x 2 + x 2 = ⎜ 2 + 2 ⎟ → 2x 2 = ⎜ 2 + 2 ⎟ ⎜ 2 + 2 ⎟ ⎝ ⎝ 2 ⎠ 2 ⎠⎝ 2 ⎠ 2x 2 = 2 + 2 2 + 2 2 + 2 2 9 → x2 = 9 → x = 2x 2 = 2 4 2 2 = 2 +1+1+ 1 4 2 3 2

2

Now we can use the result for x to find that smaller length: 3+ 3 −x = 3+ 3 − 3 = 3 2 2 2 2 The triangle may not look familiar yet, but the angle at the right is a give-away. Since it’s a 120° angle, the supplementary angle θ must be 60°. This is because interior and exterior angles along the same line segment must always sum to 180°. Since another angle in the triangle is right (90°), we now can assert that angle σ measures 30°, since all the angles inside a triangle must sum to 180° as well. This means that we have a 30°–60°–90° triangle. One needs to be careful at this point, as it is easy to misidentify the lengths in one of these. Remember, it is not that the lengths are always 1, 3 , and 2; but that they are always in the ratio of 1: 3 :2. If the long nonhypotenuse side has a length of one-half of 3 , then the other sides should be halved as well. The short side will have length 1/2, and the hypotenuse will have length 1.

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THE QUANTITATIVE SECTION

At this point, as shown in the last diagram, we can ignore all our calculations but those for a few lengths. The area of the original figure is found with just the four numbers in black:

A = A ∆up + A ∆down = ⎛ 1 b∆uph∆up ⎞ + ⎛ 1 b∆downh∆down ⎞ ⎟ ⎜ ⎟ ⎜ ⎠ ⎝2 ⎠ ⎝2 ⎞ ⎛ = ⎜ 1 × 1 × 3 ⎟ + ⎛ 1 × 3 × 3⎞ = 3 + 9 = 9 + 3 ⎜ ⎟ ⎝ 2 2 2 ⎠ ⎝ 2 2 2⎠ 8 8 8

or answer choice A. That’s about it. There are other ways of finding the area, but if you can handle the steps here, you should have little trouble with GMAT geometry.
4. B.

Since we are looking for the area of the circle, we really need to find the radius. The line

segment from the center of the circle to the vertex of the square is 2, so we can use that to find the radius. If you extend line x to the opposite vertex of the square, you have drawn a diagonal of that square, which is also the hypotenuse of a 45°–45°–90° triangle. The diagonal measures 4. You normally multiply a leg of a 45°–45°–90° triangle by 2 to get the hypotenuse, so we have to divide the hypotenuse by 2 to get the leg (which is also the side of the square and the diameter of the circle). Therefore, the diameter is equal to 4 and the radius is equal to 2 . 2 2 But we’re not done; we still have to find the area. The formula for area of a circle is A = πr2, so 4 we have to substitute 2 in for r. Squaring both the top and bottom of the fraction, we get 2 , 2 or 2. So the area of the circle is 2π.
5. B.

Since none of the answer choices are actually in the recognized form for an equation of a line,

the best thing in this case is to figure out what the equation of the original line is in y = mx + b form, and then figure out which of the answer choices can be manipulated to form that same equation. This line crosses the y axis at 2, so the y-intercept is 2 and our equation becomes y = mx + 2. Now we need to figure out the slope. Since the point goes through (0, 2) and (3, 4), the slope is 2 2 . The equation we’re looking for is now y = x + 2. If we manipulate the equa3 3

tions in the answer choices so that the y always has a coefficient of 1 and everything is on the correct side of the equal sign, B is the only correct answer.
6. D.

The larger rectangle has an area of 24, so the non-shaded rectangle must have an area of

12. Starting with the answer choices for the length of the shorter side, we can divide them into 12 until we find a valid length for the longer side. A would give us 16 for the longer side, which wouldn’t work because that wouldn’t fit inside another rectangle with 6 as the longest side. B would give us 12 for the longer side, which is still too big. C gives us 8, which is also too big. D gives us 5, which is possible and therefore is the correct answer.
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7. E.

Since 4r and 5r form a straight line, which is 180 degrees, 4r + 5r = 180. When we simplify that

to 9r = 180, we can solve to get r = 20. Therefore 5r = 100, and s – 20 = 100. So we can tell that s = 120. Using those numbers, the equation 2s – r becomes 2(120) – 20, which equals 220.
8. C.

Statement (1) alone lets us find the radius, which can tell us the area of the whole circle, but

we still don’t know what portion of the circle is made up by the shaded region, so we have to eliminate A and D. Statement (2) alone tells us what proportion of the circle is encompassed by the shaded region, but doesn’t tell us the area of the whole circle, so we can eliminate B. Putting the statements together, we have both pieces of information, which we can use to find the area of the shaded region, so statements (1) and (2) are sufficient together, and our answer is C.
9. C.

Statement (1) is tempting, because the figure appears to be a parallelogram, but we don’t

really know that it is without some indication that there are two sets of parallel lines. So statement (1) is actually not sufficient, and we can eliminate A and D. Remembering that we have to take statement (2) alone, it is not sufficient by itself to solve for the value of x, so we eliminate B. Putting both statements together, we have the information we need: If the figure is a parallelogram, then the angles add to 360. If 2y = 100, then 2x = 260 and x = 130. So our answer is C.
10. E.

Statement (1) is not sufficient on its own, since you can never solve for one side of a triangle

given only one other side. Let’s eliminate A and D. Statement (2) is not sufficient for the same reason, so we can eliminate B. Putting the statements together, it appears that we have enough information to solve for the diagonal of the rectangle (also known as hypotenuse of a right triangle) . . . except that we don’t have any indication that the figure is actually a rectangle. So the statements are still not sufficient and the answer is E.

98#

THE QUANTITATIVE SECTION

CHAPTER 7

Boolean Problems and Combinatorics

d

INTRODUCTION
The GMAT contains a variety of logic problems designed to test your ability to think clearly and quickly about classes of objects and the relationships between them. This ability is very valuable for any business analyst, as it is important to generating defensible answers about complex business questions. It is particularly useful in the design of complicated spreadsheets, which are an important tool for financial and operations analysis. However, since the authors of the GMAT have been instructed not to favor those with business analysis experience too greatly, they rely on a number of other types of problems for testing this aptitude. These include basic logic problems in set theory, number theory, the binary mathematics of Boolean algebra, and combinatorics.

BOOLEAN PROBLEMS ON THE GMAT
Boolean problems are those in which you are asked to determine whether a mathematical expression corresponds to one of two states. These questions could ask whether an expression is \$ True or false \$ Even or odd \$ Positive or negative \$ Integer or noninteger These either/or groupings are called binary categories, in which an expression must fit in one category or the other, but not both simultaneously. For example, an expression can be positive for certain values of x and negative for other values, but it cannot be both positive and negative at the same time. Boolean tools, such as truth tables, can allow you to answer this type of question quickly and accurately. Let’s consider some examples.

Odd/Even Problems
Before sitting for the GMAT, you should absolutely know the following rules about even and odd numbers: \$ An even number multiplied by an even number yields an even number. \$ An even number multiplied by an odd number yields an even number. \$ An odd number multiplied by an odd number yields an odd number.

99

With these rules in mind, consider the following problem: If x and y are positive integers and y ≠ 1, then xy(y −1) is A. Always even B. Always odd C. Odd only when x is odd D. Even only when y is even E. Odd only when xy is odd Solving this problem is most reliably accomplished with a truth table and a little recollection of number theory. Note that an odd number results only when both factors are odd. This relationship can be converted into a sort of truth table: x Even Even Odd Odd y Even Odd Even Odd xy Even Even Even Odd

The even/odd combination for integers is thus equivalent to the logical operator OR. We can solve the problem by extending the table by two more columns and including all of the mathematical expressions in the problem. Note that if y is even, y − 1 must be odd, and if y is odd, y −1 must be even. x Even Even Odd Odd y Even Odd Even Odd xy Even Even Even Odd y −1 Odd Even Odd Even xy(y −1) Even Even Even Even

To fill out the table, it may help to plug actual even and odd numbers into the expressions: if x = 2 and y = 3, then xy = 6, which is even, and y −1 = 2, which is also even. If the values of x and y are reversed, then xy still equals 6, but y −1 = 1, which is odd. Plugging in simple numbers like this will allow you to determine quickly whether the more complicated expressions are even or odd. Reading over the table, we can determine that xy(y −1) is always even, regardless of whether x or y is even. Therefore, the answer to this question is A. It may not always be worthwhile to write out a whole truth table. If you can keep the x’s and y’s straight in your head, it might be more useful for you to write down a table for only a few of the expressions, such as y −1 and xy(y −1). The truth table is a powerful tool for organizing your knowledge about the mathematical expressions at hand, but you need to make it work best for you. The best way to do this is to practice through many problems and see how much of the table you need to write down to keep your evens and odds or positives and negatives straight. Speaking of practice: If x and y are positive integers, then xy + x is A. Always even B. Always odd
100# THE QUANTITATIVE SECTION

C. Even whenever x is even D. Even whenever x + y is odd E. It cannot be determined from the information given This problem raises a second set of even/odd rules to memorize: \$ An even number added to an even number yields an even number. \$ An even number added to an odd number yields an odd number. \$ An odd number added to an odd number yields an even number. For additional practice, one can demonstrate that addition in even-odd problems is equivalent to the XOR logical operator. For this problem, though, we can just construct a truth table, and let fly with the entries: x Even Even Odd Odd y Even Odd Even Odd xy Even Even Even Odd x+y Even Odd Odd Even xy + x Even Even Odd Even

From inspection, it is clear that the answer is C, xy + x is even whenever x is even.

Positive/Negative Problems
The GMAT also can feature similar questions in which the odd/even question is turned into a positive/ negative one, as in the following example: If x, y, and z are integers, then x 2y 2z will be negative whenever A. x is negative B. y is positive C. z is negative D. xy is negative E. It cannot be determined from the information given To answer questions like this, it is extremely helpful to know the following rules about positive and negative numbers: \$ A positive number multiplied by a positive number yields a positive number. \$ A positive number multiplied by a negative number yields a negative number. \$ A negative number multiplied by a negative number yields a positive number. You should also know the following corollaries, which follow logically from the previous statements: \$ Any number raised to an even exponent will be positive. \$ A negative number raised to an odd exponent will be negative.
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Solving the preceding example could be accomplished with the construction of a very large truth table. Note the alternation of the x, y, and z values needed to cover all eight possibilities:

x + + + + − − −

y + + − − + + − −

− − − −
+ + +

z +

x2 + + + + + + + +

y2 + + + + + + + +

x2y2 + + + + + + + +

x2y2z +

− − − −

+ + +

Enough looking about the table will tell you that x 2y 2z < 0 if and only if z < 0. (If and only if, or IFF; this by the way, is yet another logical operator, to which we will return a bit later.) But why go to that much trouble? You should instead just recognize that the square of any number is always positive––this is why we cannot find real square roots of negative numbers. Thus, x 2 > 0 and y 2 > 0, so x 2y 2 > 0. This makes for a much simpler table (if one is even necessary at this point): z + x 2y 2 + + x 2y 2z +

We really are not concerned about the values of x and y, since only a negative z will make the entire expression negative. So, the answer to this question is C. This is not to say that the truth tables will always work out this cleanly, whether the values are true/false, even/odd, or positive/negative. Consider this example: If x and y are integers, then xy(x + y) is A. Always positive B. Always negative C. Positive when x is positive D. Negative when x is negative E. It cannot be determined by the information given We can construct a truth table as before, but the results are a bit different: x + + y + + xy + + x+y + ? ? xy(x + y) + ? ? -

Adding two positive numbers together clearly yields a positive number. Adding two negative numbers together clearly yields a negative number. So, one might be tempted to select answer choice
102# THE QUANTITATIVE SECTION

C or D: xy(x + y) is known to be positive in the table in the first row in which x is positive. That is, we know that xy(x + y) is positive where x and y are both positive. We also know that xy(x + y) is negative where x and y are both negative. The problem is that we cannot say much about it otherwise. Adding a positive number to a negative number could yield either a positive or a negative number—it simply depends on what numbers we select. Since we are unable to comment on x + y, we can further say little about xy(x + y). So, the best answer choice we have is E.

Constructing Truth Tables Efficiently
Sometimes a little logical reasoning and algebraic manipulation before you construct the truth table can simplify your task. Consider this example: x and y are positive integers. If xy + x is odd, then which of the following must be even? A. x B. y C. x + y D. xy − x E. x2 − y Before you do anything else, you could factor the x out of xy + x: xy + x = x(y + 1) We know that the only way you can get an odd number through multiplication is by multiplying two odd numbers together. Therefore, x and (y + 1) must both represent odd numbers. If (y + 1) is an odd number, then y itself must be an even number. This is another property of odd and even numbers that you would do well to keep in mind for the test: \$ Any even number plus or minus 1 equals an odd number. \$ Any odd number plus or minus 1 equals an even number. Since y has to be even in order for the statement in the question to be true, the answer to this question must be B. In this case, there is hardly any reason to write out a truth table, because you know that any value of y for which xy + x is odd must be an even number.

What You Need to Remember
To tackle these types of problems quickly, it is best to remember the following aforementioned rules:
Even-Odd Multiplication Even × Even r Even Even × Odd r Even Odd × Odd r Odd Even-Odd Addition Even + Even r Even Even + Odd r Odd Odd + Odd r Even

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Positive-Negative Multiplication Positive × Positive r Positive Positive × Negative r Negative Negative × Negative r Positive

Positive-Negative Addition Positive + Positive r Positive Positive + Negative r ??? Negative + Negative r Negative

Note in particular that little can be said about the sum of a positive number and a negative number unless we know the actual numbers in question. Also, remember that subtraction is just the inverse of addition, so do not be concerned by the appearance of a subtraction sign in a problem of this type.

COMBINATORICS PROBLEMS: TWO APPROACHES
Combinatorics is the body of math that deals with combinations and permutations. Questions of this type are relatively rare on the GMAT, but you may see one, and if you are shooting for a high score, you will want to answer it correctly. Combinatorics problems tend to be conceptually difficult and timeconsuming, so you need to approach them with a strategy if you don’t want them to eat up all of your time. There are two approaches you can take to a combinatorics problem. The first could be called “reasoned brute force”: understand what is being asked, reason through the problem, and then write down every combination or permutation asked for. On the GMAT these questions tend to involve fewer than 30 or so permutations, so it may be possible for you work out a problem like this in little more than 2 minutes if you dive right in. The second approach is to solve the problems using combinatorics formulas. These formulas can be mathematically difficult and hard to apply, but they can give you the answer to a particularly difficult question far faster than brute force. We’ll discuss the brute force method first. Let’s consider a question: In a family with 3 children, the parents have agreed to bring the children to the pet store and allow each child to choose a pet. This pet store sells only dogs, cats, and monkeys. If each child chooses exactly one animal, and if more than one child can choose the same kind of animal, how many different arrangements of animals could the family leave with? A. 6 B. 8 C. 9 D. 10 E. 12 The first step with a problem like this is to figure out what you’re looking for. You’re looking for combinations of three variables—let’s call them D, C, and M—in groupings of three, in which a variable can be repeated more than once and in which order does not matter (i.e., DDC is the same as DCD). Let’s look at all the combinations the children could choose involving dogs: DDD DDC DDM DCC DMM DCM
104# THE QUANTITATIVE SECTION

So there is 1 possibility involving 3 dogs, 2 possibilities involving 2 dogs, and 3 possibilities involving 1 dog. Since all possibilities involving dogs are exhausted, it should be easier to pick out all the remaining combinations involving the remaining two variables: CCC CCM CMM MMM Can you think of any other possibilities? Let’s hope not, because there are no others. The answer is 10, which is choice D. Note that this system would have worked just as well if you’d started with monkeys or cats. The trick is to start on a system that will inevitably exhaust all possibilities. Brute force has its limitations, though. Say you encounter the following question: A sock drawer contains seven socks, each one a different solid color. The colors of the socks are red, orange, yellow, green, blue, indigo, and violet. If the socks are laid next to each other, how many different arrangements of socks could be made? A. 24 B. 240 C. 1,024 D. 2,520 E. 5,040 First, understand what is being asked. You’re looking for permutations of seven variables—let’s call them R, O, Y, G, B, I, and V—in groupings of seven, with no repeat variables in each grouping, and order in this case does matter (i.e., ROYGBIV is not the same as ROYGBVI). You could write out every possible permutation, starting like this: ROYGBIV ROYGBVI ROYGVIB ROYGVBI ROYGIVB ROYGIBV ROYBGIV ROYBGVI ROYBVIG ROYBVGI ROYBIVG ROYBIGV ROYVBIG … and so on
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As you can see, with some problems, the brute force method could take a very long time. On this particular problem, it might take you the whole test, as you might be able to guess by looking at the scope of the available answers. It is in problems like this one that combinatorics formulas come in handy.

Factorials
The key concept in combinatoric math is the factorial. The factorial of an integer n is the successive product of n times all the positive integers smaller than n, right down to 1. In practice, that means that n! = n × (n − 1) × (n − 2) × (n − 3) × . . . 1

Actually, the 1 is wholly unnecessary, but you get the point. The factorial function blows up rather quickly, so you’ll not be asked to calculate a factorial much larger than these: 0! = 1 (it is simply defined that way) 1! = 1 2! = 2 × 1 = 2 3! = 3 × 2 × 1 = 6 4! = 4 × 3 × 2 × 1 = 24 5! = 5 × 4 × 3 × 2 × 1 = 120 6! = 6 × 5 × 4 × 3 × 2 × 1 = 720 7! = 7 × 6 × 5 × 4 × 3 × 2 × 1 = 5,040 Before we move on to the formulas, let’s consider how the concept of factorials alone could be used to solve the sock problem above. Suppose the question asked: In how many different ways could you arrange a single red sock in a sock drawer if there are exactly 7 spaces for socks? The answer, clearly, is 7. Now, what if the question asked: In how many different ways could you arrange a single red sock and a single orange sock in a sock drawer if there are exactly 7 spaces for socks? The answer is slightly more complicated this time. There are 7 ways you could arrange the red sock. Once the red sock is put in the drawer, there are now only 6 remaining spots in which to put the orange sock, so the total possible number of arrangements is 7 × 6 = 42. Now what if the question asked: In how many different ways could you arrange a single red sock, a single orange sock, and a single yellow sock in a sock drawer if there are exactly 7 spaces for socks? This time, we have 7 ways to put in the red sock, 6 places left to put in the orange sock, and then 5 remaining places left to put in the yellow sock. So the total number of possible arrangements is 7 × 6 × 5 = 210 possible arrangements of these 3 socks in 7 spaces.
106# THE QUANTITATIVE SECTION

Hopefully you see where this is going. To find seven unique spaces for seven unique spots in which the order matters, we will have: 7 × 6 × 5 × 4 × 3 × 2 × 1 = 5,040 possible arrangements The answer to the question, therefore, is E. The factorial argument we just walked through is essentially a longhand version of the formulas we are about to discuss. The point of this explanation is that, even if you don’t remember the specific formulas to use, you can combine the concept of the factorial with your own mathematic reasoning to work through most combination and permutation problems.

Combinations
When we refer to combinations instead of permutations, we are talking about groupings in which order does not matter, e.g., a red sock and a green sock instead of a red sock and then a green sock. In the following formula, C stands for the total number of possible combinations, n stands for the total number of elements involved (e.g., 7 socks), and k is the subset of unordered elements taken from n (e.g., 3 socks out of the 7): Ck = n! k !(n − k )!

n

This formula may look imposing, so let’s apply it to a problem: A sock drawer contains seven socks, each one a different solid color. The colors of the socks are red, orange, yellow, green, blue, indigo, and violet. If a person reaches into the drawer and pulls out two socks, how many different color combinations are possible in the selected pair of socks? A. 12 B. 15 C. 21 D. 36 E. 42 You could write out every possibility and solve this problem that way, but it is almost certainly faster to use the formula. In this case, n = 7 and k = 2: Ck = n! 7! = = 7 ! = 7 × 6 × 5 × 4 × 3 × 2 = 7 × 6 = 42 = 21 k !(n − k )! 2 !(7 − 2)! 2 !(5)! 2×5×4×3×2 2 2

n

Note that it was not necessary to calculate 7! out to 5,040. By canceling out common elements in the numerator and denominator, we were able to produce an equation that was quite simple to calculate. Most combination problems you see on the GMAT will work out smoothly like this; the test writers figure that if you can use this formula correctly, they don’t need to test your multiplication skills.

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Just for a visual verification, let’s consider how we would have worked this problem by brute force: RO RY RG RB RI RV OY OG OB OI OV YG YB YI YV GB GI GV BI BV IV

Add up the combinations: 6 + 5 + 4 + 3 + 2 + 1 = 21. Clearly, either method works for a problem of this scope. One interesting thing to note with combinations is that picking 2 and leaving 5 behind is mathematically the same thing as picking 5 and leaving 2 behind. The formula for the latter situation would look like: n Ck =

n! 7! = = 7 ! = 7 × 6 × 5 × 4 × 3 × 2 = 7 × 6 = 42 = 21 k !(n − k )! 5 !(7 − 2)! 5 !( 2)! 5×4×3×2×2 2 2

Now let’s move on to a slightly more complicated situation, in which the order of the elements matters.

Permutations
When order matters, the number of permutations is almost always larger than the equivalent number of unordered combinations. The formula for permutations, using the same variables of n for the total number of elements involved and k as the ordered subset of n, is as follows: n k

P =

n! (n − k )!

This is described as “n pick k,” and it is always a larger number than “n choose k.” Note that, as opposed to the combinations formula, there is no k! on its own in the denominator. Let’s apply the formula to an ordered variant of our previous example problem: A sock drawer contains seven socks, each one a different solid color. The colors of the socks are red, orange, yellow, green, blue, indigo, and violet. A person reaches into the drawer, pulls out two socks, and puts a single sock on each foot. If each sock can fit either the left or the right foot, and if it matters whether a particular sock is on the left or the right foot, how many different sock fashion combinations could the person make from the seven socks? A. 12 B. 15 C. 21 D. 36 E. 42 Applying the formula, with n = 7 and k = 2, yields the following:
7 2

P =

7 ! = 7 ! = 7 × 6 × 5 × 4 × 3 × 2 = 7 × 6 = 42 (7 − 2)! (5)! 5×4×3×2

108#

THE QUANTITATIVE SECTION

Working this problem by brute force would require writing down twice as many permutations as in the previous example if you wrote down every permutation, but you wouldn’t necessarily need to. You could recognize that for each of the 21 combinations possible for pairing RO, RY, and so on, there is the mirror image form if the person switches the socks from right to left. In other words, for every RO there is an OR, for every RY there is a YR, and so on. Therefore, there must be exactly twice as many permutations as there are combinations, so 21 × 2 = 42. Finally, let’s consider how we would apply the permutation formula to a previous question: A sock drawer contains seven socks, each one a different solid color. The colors of the socks are red, orange, yellow, green, blue, indigo, and violet. If the socks are laid next to each other, how many different arrangements of socks could be made? A. 24 B. 240 C. 1,024 D. 2,520 E. 5,040 Applying the permutation formula, with n = 7 and k = 7 (since there is no subset), we get the following:
7 7

P =

7 ! = 7 ! = 7 × 6 × 5 × 4 × 3 × 2 × 1 = 5, 040 (7 − 7)! 0 ! 1

Clearly, knowing the formula allows you to sidestep the ugly process of writing out over 5,000 different permutations. If you don’t feel that you can memorize the formulas, don’t worry. As we stated earlier, combinatorics problems are rare on the GMAT.

PRACTICE PROBLEMS
1. An art gallery owner is hanging paintings for a new show. Of the six paintings she has to choose

from, she can only hang three on the main wall of the gallery. Assuming that she hangs as many as possible on that wall, in how many ways can she arrange the paintings? A. 18 B. 30 C. 64 D. 120 E. 216
2. A composer’s guild is planning its spring concert, and ten pieces have been submitted

for consideration. The director of the guild knows that they will only have time to present four of them. If the pieces can be played in any order, how many combinations of pieces are possible? A. 40 B. 210
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C. 1090 D. 5040 E. 10000
3. If x and y are odd integers, which of the following must always be a non-integer?

A. xy B. x y y C. x D. xy 2

E. –xy
4. Dan has a membership at a local gym that also gives classes three nights a week. On any given

class night, Dan has the option of taking yoga, weight training, or kickboxing classes. If Dan decides to go to either one or two classes per week, how many different combinations of classes are available? A. 3 B. 6 C. 7 D. 9 E. 12
5. Terry is having lunch at a salad bar. There are two types of lettuce to choose from, as well as

three types of tomatoes, and four types of olives. He must also choose whether or not to have one of the two types of soup on the side. If Terry has decided to have the salad and soup combo and he picks one type of lettuce, one type of tomato, and one type of olive for his salad, how many total options does he have for his lunch combo? A. 9 B. 11 C. 24 D. 48 E. 54
6. If r is negative and s is positive, which of the following cannot be negative?

A. B.

r s s r

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THE QUANTITATIVE SECTION

C. r2+s D. r2s2 E. −r s

Solutions
1. D.

This problem asks for us to arrange the paintings, so it is a permutation. Using the n! 6 × 5 × 4 × 3 × 2 ×1 (n − k )! formula and using 6 as our n and 3 as our k, we get the following: 3 × 2 ×1

P = n k

When we cancel out, we get 6 × 5 × 4, which is 120.
2. B.

This problem is a combination, so we would use the formula

n

Ck =

n! k !(n − k )! . Since 10 is

our n and 4 is our k, the equation works out to multiplying gives us 210 combinations.
3. D.

10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 . Simplifying and 4 × 3 × 2 ×1× 6 × 5 × 4 × 3 × 2 ×1

xy Since we know that x and y are odd, xy ust always be odd. Therefore, 2 will always be a non-integer. None of the other answer choices has this relationship; in all of the other cases, it is possible to have values of x and y that would yield integer results.

4. D.

This problem is best done by brute force. First, we must establish that Dan has the option

of taking one or two classes per week. If he only takes one class, the three possibilities are Y, W, and K. If he takes two classes per week, the six possibilities are YY, KK, WW, YK, YW, and WK (because the problem is looking for combinations, not arrangements). So that adds up to nine possible combinations.
5. D.

This is a relatively simple problem if you know the process—and you read carefully. All you

have to do is multiply the number of options: 2 types of lettuce, 3 types of tomatoes, 4 types of olives, and 2 soup options. (You did remember the soup, didn’t you?) 2 × 3 × 4 × 2 = 48, so 48 is our answer.
6. B.

Based on the rules of positive and negative numbers, the only answer choice that must be

negative is B, since it takes a positive and divides it by a negative. All other manipulations end up positive.

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f
PART TWO

The Verbal and Writing Sections

CHAPTER 8

Critical Reasoning

d

INTRODUCTION

115

deceptive answers. To maximize your chances for getting the high score you want, you need to familiarize yourself with the basic structure and common patterns of Critical Reasoning questions, and you must approach the questions with an efficient and critical approach: 1. Read the question stem first, and determine what type of question you are facing. 2. Read the passage critically; analyze the basic components of the argument in light of the question. 3. Formulate a correct answer to the question in your head or on scratch paper. 4. Attack the answer choices until only one remains.

WHAT IS AN ARGUMENT?
Critical Reasoning passages are all arguments of one form or another. What argument means here is a statement in which a premise, or piece of information, is used to support a conclusion. Most questions of this type include a premise or series of premises followed by a conclusion, although it is also fairly common for the conclusion to lead off the passage. An argument does not rest only on its stated premises, however, but also on the unstated assumptions that help support the conclusion. These unstated assumptions are the subject matter of most Critical Reasoning questions. For example, an argument could look like the following: Earthquakes often destroy houses that are not built according to the building code. Dora’s house was built according to the building code, so it will survive the next earthquake.

116#

THE VERBAL AND WRITING SECTIONS

In this argument, there are two premises: Premise 1: Earthquakes often destroy houses that are not built according to the building code. Premise 2: Dora’s house was built according to the building code. And one conclusion: Therefore, Dora’s house will survive the next earthquake. The stated premises alone, however, are not sufficient to prove that the conclusion is correct. Stating that substandard houses are sometimes destroyed by earthquakes does not provide sufficient evidence to conclude that standard houses are never destroyed by earthquakes. In order for the argument to hold up, it must rely on one or more unstated assumptions. These assumptions could include the following: \$ Buildings that comply with the building code will survive any earthquake. \$ The next earthquake will not be so severe that it will destroy all buildings in the area. \$ The building code in question is relevant to whether or not a building will survive an earthquake (as opposed to dealing exclusively with fire safety, flood safety, and so on). This argument is somewhat simpler than that in most of the questions you will see on the GMAT, but its type of logic is representative. You could look at a Critical Reasoning argument as a kind of stool, with the conclusion as the seat held up by the legs of premises and assumptions. Most of these stools are slightly wobbly. GMAT questions may ask you to kick one of the legs (assumptions) out from under the stool to weaken the argument, or they may ask you to strengthen the stool by propping it up with another leg.

ASSUMPTION QUESTIONS
The most basic type of Critical Reasoning question asks you to identify an assumption of the argument. A question of this type might have the following wording: \$ Which of the following is an assumption that enables the conclusion above to be properly drawn? \$ Which of the following is an assumption made in drawing the conclusion above? \$ The conclusion of the argument above cannot be true unless which of the following is true? \$ Any of the following, if introduced into the argument above as an additional premise, makes the argument above logically correct EXCEPT Assumption questions ask you to examine the relationship between the premise and the conclusion in an argument, and to determine what other conditions are necessary in order for the argument to be valid. In the example given about Dora’s house surviving the earthquake, the correct answer will need to bridge the logical gap between the statement “Dora’s house meets the building code” and the conclusion “Dora’s house will survive the next earthquake.” The answer will be some variant on Houses that meet the building code will survive the next earthquake. Note that the specific wording of the question will determine the specific wording that is acceptable for the answer. For example, if the question asks, “Which of the following is an assumption made in
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drawing the conclusion above?” then a statement like “The building code contains provisions that help protect houses from earthquake damage” could be sufficient. However, if the question asks, “Which of the following is an assumption that enables the conclusion above to be properly drawn?” then this relatively noncommittal statement would be insufficient, because it alone is not sufficient to prove that Dora’s house necessarily will survive the earthquake. Critical Reasoning questions often hinge on the fine meaning of individual words, so always read the passages carefully, and read the question stems very carefully.

WEAKEN THE ARGUMENT
The most common type of Critical Reasoning question by far is the weaken-the-argument question. If the argument in the passage is a stool held up by assumptions, then this type of question asks you either to locate the spot where a leg is missing or to kick a leg out from under the stool. These questions could have the following wording: \$ Which of the following, if true, would most weaken the conclusion above? \$ Which of the following, if true, most severely undermines the argument presented above? \$ Which of the following, if true, most clearly points to a flaw in the manufacturer’s plan? The thinking required here is very similar to that required for an assumption question, but you have to take it a step further. With these questions, you determine what assumptions have to be true in order for the argument to be true, and then find the answer that challenges one of those assumptions. In the example of Dora’s house, a correct answer could look like one of these: \$ When the last major earthquake occurred in the area, many houses that met the building code were destroyed. \$ Geologists predict that the coming earthquake will be far more severe than any earthquake previously recorded in the area. \$ The building code in Dora’s area is designed exclusively to protect homes against flood and fire damage. Each of these answers kicks at the assumptions holding up the conclusion, thereby weakening the argument. The thinking here is similar to the kind of thinking you use every day when you evaluate arguments: you look for flaws in the argument, and you consider ways in which the plan might not work exactly as promised. When answering these questions, be careful not to pick an answer that actually strengthens the argument. These answers are tempting because they often deal with the same themes as answers that weaken the argument, but they use slightly different wording that produces the opposite effect. ACT usually puts at least one answer choice like this in every weaken-the-argument question.

STRENGTHEN THE ARGUMENT
Strengthen-the-argument questions use very similar thinking to weaken-the-argument questions, but instead of kicking the assumptions out from under the argument, you are asked to prop them up. This type of question comes up perhaps half as often as weaken-the-argument questions.

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Strengthen-the-argument questions could have the following wording: \$ Which of the following, if true, would most significantly strengthen the conclusion drawn in the passage? \$ Which of the following, if true, offers the strongest support for the manager’s conclusion that the locks were not at fault? \$ Which of the following, if true, provides the strongest evidence in favor of the professor’s hypothesis? In the case of Dora’s house and the earthquake, you must look for a statement that confirms one of the assumptions upon which the conclusion rests. Strengthening answers for that question might look like this: \$ In the last earthquake, no buildings that met the building code were severely damaged, although several substandard buildings collapsed. \$ Geologists predict that the next earthquake will be so minor that no damage is expected for any building in the area. \$ The local building code was designed by architects who used data from previous earthquakes in the area to determine the best ways to protect homes from earthquake damage. Each of these answers addresses potential flaws in the argument—the same flaws that a weakenthe-argument question would try to exploit. Remember, most of these arguments could go either way, and you need to be careful to make sure that the answer you choose points in the desired direction. As with weaken-the-argument questions, strengthen-the-argument questions almost always have at least one answer that deals with the correct subject matter, but in a way that is actually the opposite of what the question asks for. Don’t be fooled. Note that the correct answer to a strengthening question does not necessarily have to prove that the argument is correct. An answer that eliminates a single potential flaw in the argument could be the correct answer, as long as it is the best among the available answer choices.

INFERENCE QUESTIONS
Inference questions ask you to make a logical inference based on the information presented in the passage. The wording of these questions can vary widely, but the basic question behind them is the same: if the statements in the passage are true, what else has to be true? Assumption questions are actually a specific kind of inference question that asks: if the argument is valid, you can infer that which of the following assumptions must be true in order to logically connect the premise and the conclusion? The same type of critical thinking is used for both assumption and inference questions, but the nature of the inference is slightly different. The inferences discussed here are not necessarily vital components of the argument, but rather logical extensions from it; in the metaphor of the stool, if you kicked over one of these inferences, the stool would not necessarily topple over. Inference questions might relate to the assumptions of an argument, to its premise, to its conclusion, or to its application to a related situation. Questions of this type might look like this: \$ If the statements above are true, which of the following must be true? \$ The statements above, if true, best support which of the following assertions?
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LESS COMMON QUESTION TYPES
The previously discussed question types will make up the majority of the questions you see. If you master these question types, you can earn a good score on the Critical Reasoning section. If you want a great score, though, you should master the less common question types as well. There is a very good chance that at least a couple of the following question types will appear among the 12 or 50 Critical Reasoning questions you see on the GMAT.

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Explain/Resolve the Discrepancy

This variant on the explanation question asks you to take a step back and ask what else you would need to know in order to analyze or explain the situation. Questions of this sort could have the following wording: \$ Which of the following must be studied in order to evaluate the argument presented above? \$ Which of the following investigations is most likely to yield significant information that would help to evaluate the geologist’s hypothesis?
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\$ The answer to which of the following questions would be most useful in evaluating the significance of the experimental data described above? Although these questions look somewhat different from the strengthen/weaken-the-argument questions discussed previously, the reasoning involved is not so different. The question/investigation/ experiment in the correct answer should examine one of the premises or assumptions upon which the conclusion is based. You are not asked to strengthen or weaken the argument, but to provide a question for which the answer will strengthen or weaken the argument. Let’s consider an example: Many houses that do not meet the building code will collapse in the next earthquake. The foundation of Dora’s house contains structural stabilizers designed to withstand any earthquake of 6 or lesser magnitude on the Richter scale. Consequently, Dora’s house will survive the earthquake. The answer to which of the following questions would be most useful in evaluating the accuracy of the conclusion above? The answer you’re looking for should be something on the order of, “What will be the magnitude of the next earthquake?” The answer to this question will tell you whether or not the argument can logically proceed from the premise—“Dora’s house can withstand an earthquake of less than 6 magnitude”—to the conclusion—“Dora’s house will survive the earthquake.” The thinking is the same as that used when you look for the assumptions in an argument, only with this type of question, you need to take a step further back and ask the question that will validate or disprove a key assumption.

Parallel Reasoning
These questions ask you to analyze the logical structure of the passage, and then find the answer choice that displays the most similar reasoning. Questions of this type might look like one of the following: \$ Which of the following is most like the argument above in its logical structure? \$ Which of the following supports its conclusion in the same way as the argument above? \$ The logical flaw in the reasoning above is most similar to that in which of the following statements? What you need to do with these questions is break the argument down into its most basic parts. Critical Reasoning passages often contain convoluted wording and unnecessary details that obscure the main point of the passage. You need to look past these distractions and distill the basic argument. Consider the following question: Over the past year, Robert won several medals in running competitions, including races of 400 meters and 800 meters. He was recently involved in a minor automobile accident, however, and as a result of his injuries, he currently is required to wear a cast. Consequently, when he competes in the big race next month, he will be unlikely to win. Which of the following is most like the argument above in its logical structure? A. The best runners are unlikely to be the best swimmers. B. The student probably will not finish his paper on time because his computer is not working.
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Find the Conclusion
This question type is the counterpart to assumption questions. The passage will present you with a series of premises, and you will be asked to draw a logical conclusion from the information in the passage. Questions of this type could look like this: \$ Which of the following conclusions can properly be drawn from the information above? \$ The economist’s argument, as presented above, is structured to lead to what conclusion? The key to these questions is to choose the answer that has to be true if the premises in the passage are true. If you can think of a reasonable scenario in which an answer choice would not be true, then it is probably wrong. Keep your logic very tight here. The proper conclusion will require a logical hop, not a leap. It will most likely be consistent in content and tone with the premises in the passage.

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Fill In the Blank
This type of question presents you with most of an argument, but leaves a blank space at the end, which you are asked to fill in. The blank space will usually represent the conclusion of the argument, but it could also represent a key premise. The wording for these questions will always be some variant of \$ Which of the following best completes the passage below? These questions are really quite straightforward. Examine the argument in the passage. Determine whether it is the conclusion or a premise that is missing. Formulate the answer in your head, then look through the answers for the one that fits. For example, if you see a question that looks like Which of the following best completes the passage below? Over the past year, Robert was unbeaten in running competitions at the distances of 400 meters and 800 meters. He was recently involved in a minor automobile accident, however, and as a result of his injuries he is required to wear a cast that will significantly restrict his movement for the next six months. Consequently, when an important running competition of 400 meters is held next month, _______________________. The answer will be something on the order of “Robert will not be able to win the race” or, preferably, “Robert is unlikely to win the race”; the more moderate answer is usually the correct one. Look for the conclusion that the stated premises are directing you toward. In general, you should treat these questions the same as you would a find-the-conclusion question: keep your logic tight, and look for the answer that has to be true if the premises in the passage are true.

Boldface/Structure of the Argument
This is a relatively uncommon question type that has started to appear on the GMAT in recent years. It is somewhat different from all the question types described so far because it asks you to analyze the structure of an argument in addition to the argument’s validity. A boldface question may look something like the following: Many houses that do not meet the building code will collapse in the next earthquake. To meet the building code, houses must contain structural stabilizers sufficient to withstand an earthquake of 6 or lesser magnitude on the Richter scale. Dora’s house meets the building code, so Dora’s house will survive the next earthquake. In the argument above, the two portions in boldface play which of the following roles? A. The first portion is a conclusion that must be true based on the evidence; the second portion is a conclusion that is not necessarily true based on the evidence. B. The first portion is a conclusion that must be true based on the evidence; the second portion is evidence in support of that conclusion. C. The first portion is a conclusion that is not necessarily true based on the evidence; the second portion is evidence in support of that conclusion.

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D. The first portion is evidence that supports the argument; the second portion is a conclusion that is not necessarily true based on the evidence. E. The first portion is evidence that supports the argument; the second portion is a conclusion that must be true based on the evidence. These questions, although different in structure from most Critical Reasoning questions, are still largely concerned with your ability to understand and appraise an argument. In this case, you should be able to read the passage and determine that the first portion in boldface—Dora’s house meets the building code—is a premise, or “evidence that supports the argument,” while the second

portion—Dora’s house will survive the next earthquake—is the conclusion. By determining these facts, you can eliminate choices A, B, and C. The difference between D and E is whether or not the conclusion must be true based on the evidence. In this case, the conclusion does not have to be true, since the argument is lacking a key assumption regarding the magnitude of the next earthquake. Therefore, the conclusion is not necessarily true, and D is the correct answer. Remember, boldface questions, like all Critical Reasoning questions, test your ability to understand and evaluate arguments—and you understand and evaluate arguments every day of your life. This is just a different way of testing those skills. Read the passage slowly, determine which portion is the conclusion and which portions are premises, and evaluate the strength of the argument.

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PRACTICE ARGUMENTS
The best way to prepare for the Critical Reasoning questions on the GMAT is to work through lots of practice questions. Before you dive into the Practice Problems at the end of this chapter (or the Practice Tests at the end of this book), it will be useful to practice the basic skills that apply to every Critical Reasoning question: breaking the argument into its component parts and evaluating the logic of the argument. For each of the five following arguments, determine: 1. The premises 2. The conclusion 3. The assumptions 4. Two statements that weaken the argument 5. Two statements that strengthen the argument

The Arguments
1. The reticulated alligator is found in nature only in the coastal wetlands of North America. Unfortunately, because of urban expansion and industrial development, the coastal wetlands of North America are disappearing at a rate of 100,000 acres per year. With only two million acres of coastal wetlands left on the continent, it is inevitable that the reticulated alligator will become extinct within 20 years. Premises: ___________________________________________________________________________ ____________________________________________________________________________________ ____________________________________________________________________________________ Conclusion: _________________________________________________________________________ ____________________________________________________________________________________ ____________________________________________________________________________________

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Assumptions: _______________________________________________________________________ ____________________________________________________________________________________ ____________________________________________________________________________________ Weaken: ___________________________________________________________________________ ____________________________________________________________________________________ ____________________________________________________________________________________ Strengthen: _________________________________________________________________________ ____________________________________________________________________________________ ____________________________________________________________________________________ 2. A state government is facing a budgetary shortfall in which expected income meets only half the costs of the projected budget. The state legislature has called an emergency session to address the fiscal crisis. One legislator, after reviewing the situation, concluded that the only way for the state to resolve the 50 percent shortfall in the budget is to double the state’s personal income tax rate from 4 percent to 8 percent. Premises: ___________________________________________________________________________ ____________________________________________________________________________________ ____________________________________________________________________________________ Conclusion: _________________________________________________________________________ ____________________________________________________________________________________ ____________________________________________________________________________________ Assumptions: _______________________________________________________________________ ____________________________________________________________________________________ ____________________________________________________________________________________ Weaken: ____________________________________________________________________________ ____________________________________________________________________________________ ____________________________________________________________________________________ Strengthen: _________________________________________________________________________ ____________________________________________________________________________________ ____________________________________________________________________________________ 3. The MegaTek company has invested approximately \$10 million in microphotonics product development in each of the last five years. Last year MegaTek’s microphotonics products brought in revenues of \$8 million, which was higher than the company had earned from these products in any previous year. The CEO, observing that in five years the microphotonics line had failed to ever yield a profit, concluded that canceling the microphotonics product line would be the correct economic decision for his company. Premises: ___________________________________________________________________________ ____________________________________________________________________________________ ____________________________________________________________________________________ Conclusion: _________________________________________________________________________ ____________________________________________________________________________________ ____________________________________________________________________________________
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Assumptions: _______________________________________________________________________ ____________________________________________________________________________________ ____________________________________________________________________________________ Weaken: ____________________________________________________________________________ ____________________________________________________________________________________ ____________________________________________________________________________________ Strengthen: _________________________________________________________________________ ____________________________________________________________________________________ ____________________________________________________________________________________ 4. After experiencing disappointing sales results in the spring, a clothing company hired a consultant to analyze its sales data to determine how the company could boost its sales for the fall season. The consultant studied the sales data for the company’s retail outlets in April and May and observed that during this period, the company sold 50 percent more pink sweaters than sweaters of any other color. The consultant concluded that the company should develop a whole line of pink clothes for the fall season. Premises: ___________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ Conclusion: _________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ Assumptions: _______________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ Weaken: ____________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ Strengthen: _________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ 5. The National Academy of Health has released findings that people who weigh over 200 pounds have a higher incidence of heart disease than do people weighing less than 200 pounds. A pharmaceutical company has developed a new drug called HeartApart, which improves the quality of life for people with heart disease. A representative from the pharmaceutical company has suggested to physicians that they should recommend HeartApart to their patients who weigh over 200 pounds in order to improve these patients’ quality of life. Premises: ___________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________

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Conclusion: _________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ Assumptions: _______________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ Weaken: ____________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ Strengthen: _________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________

Solutions
Passage 1, the Reticulated Alligator

Premises: The reticulated alligator is found in nature only in the coastal wetlands of North America; coastal wetlands are disappearing at a rate of 100,000 acres per year; there are two million acres of coastal wetlands left in North America. Conclusion: The reticulated alligator will become extinct within 20 years. Assumptions: The reticulated alligator cannot survive anywhere other than the coastal wetlands of North America; the rate of disappearance of coastal wetlands will remain steady or increase until all the wetlands have disappeared. Weaken: Viable populations of reticulated alligators have been maintained in captivity for decades. Reticulated alligators introduced into wetlands in Africa have thrived. Over a million acres of coastal wetlands have been declared permanent national wildlife preserves, which prohibit any form of building or industrial activity in the preserve. Strengthen: The rate of destruction of coastal wetlands has increased in every decade of the twentieth century and has shown no signs of slowing down. Reticulated alligators kept in captivity have been found to be particularly vulnerable to diseases. The reticulated alligator population has already been diminished to the point that most biologists think the species will never recover.
Passage 2, State Budgetary Shortfall

Premise: A state government is facing a budgetary shortfall of 50 percent. Conclusion: The only solution is to double the state’s personal income tax rate. Assumptions: Doubling the personal income tax rate will provide sufficient revenue to meet the 50% budget shortfall; there is no other source of revenue that can help address the budget shortfall; the problem cannot be addressed through reduced spending; it will be possible to double the personal income tax rate; doubling the personal income tax rate will actually result in twice as much personal income tax revenue.

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Weaken: Personal income tax currently accounts for only one-third of the state’s income. The majority of the state’s income comes from excise taxes on natural resource production. The projected budget for this year is far higher than in previous years because it contains a provision to build a sports stadium to help lure a professional sports franchise to the state. Personal income tax rates in this state can be increased only through voter referendums, and the last three voter referendums to increase the personal income tax rate failed by large margins. Substantial increases in personal income tax rates often result in increased attempts by citizens to avoid paying taxes, up to and including the decision to leave the state. Strengthen: The personal income tax accounts for 100 percent of the state government’s income. Almost all of the state’s annual budget is dedicated to fixed expenditures that cannot reasonably or legally be reduced. The citizens of the state are, in general, extremely happy to live there and would be willing to pay higher taxes in order to maintain the state services they have come to expect.
Passage 3, Microphotonics Product Development

Premises: MegaTek has invested \$10 million in microphotonics in each of the last five years; last year microphotonics products brought in \$8 million, which was greater than in any previous year; microphotonics products have not yielded a profit in any year. Conclusion: Canceling the microphotonics product line is the correct economic decision. Assumptions: MegaTek’s microphotonics product line will not become sufficiently profitable in a sufficiently short span of time to justify further investment in the product line. Weaken: MegaTek sold \$1 million of microphotonics products two years ago, which was the first year in which MegaTek realized any sales from its microphotonics product line. (This answer suggests a rapid growth rate that could soon lead to profitability.) Industry experts consider MegaTek’s microphotonics products to be the best products in a market that is expected to grow to over \$5 billion per year within the next decade. Strengthen: Industry experts do not believe that the microphotonics market will ever exceed \$10 million. The introduction of nanophotonics technology last year made all microphotonics products obsolete. The \$8 million MegaTek earned from its microphotonics product line last year was only marginally higher than the sum it earned from these products five years ago.
Passage 4, Pink Clothing Line

Premises: Spring sales for a clothing company were disappointing; in April and May the company sold 50 percent more pink sweaters than sweaters of any other color. Conclusion: The company can increase sales by developing a whole line of pink clothes for the fall season. Assumptions: The primary reason that the pink sweaters sold better than sweaters in other colors was that customers liked the color pink, and not some other factor involving these sweaters; the sales edge that the pink sweaters enjoyed will also apply in another season and on other articles of clothing. Weaken: More than two-thirds of the sweaters offered in the spring at the company’s retail outlets were pink. Because of a minor error that affected production of all of the company’s
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pink sweaters in the spring but no other color of sweater, all pink sweaters were sold at a substantially lower price than sweaters of any other color. People tend to associate the color pink with springtime, but tend to favor earth tones in the fall. Strengthen: People who have purchased pink sweaters are likely to buy other articles of clothing in the same color to match. Although the company’s pink sweaters were priced slightly higher than the other colors of sweater sold in the spring, the company still sold out of pink sweaters by the end of May. The fashion trends that favored pink clothing in the spring continued to gather strength through the summer.
Passage 5, Heart Disease Drug

Premises: People who weigh over 200 pounds have a higher incidence of heart disease; HeartApart improves the quality of life for people with heart disease. Conclusion: Doctors should recommend HeartApart to their patients who weigh more than 200 pounds in order to improve these patients’ quality of life. Assumptions: A sufficient percentage of the people who weigh more than 200 pounds have heart disease, that recommending the drug to the group in general is sensible; weight is the best criterion on which to recommend use of this drug to a group of people; the side effects of this drug are not so onerous that they will harm the quality of life of this group of people more than the drug will improve the group’s quality of life. Weaken: While heart disease is more prevalent among people who weigh more than 200 pounds than it is among people who weigh less than 200 pounds, only 5 percent of people who weigh more than 200 pounds currently have heart disease. HeartApart has been shown to induce side effects such as headaches and nausea in a significant percentage of people who take the drug. Epidemiological studies have shown that high blood pressure, a biometric that is approximately as easy to obtain as a patient’s weight, is a far more reliable predictor of heart disease than weight alone. Strengthen: HeartApart has no known side effects. HeartApart has been shown to prevent or delay the incidence of heart disease in people who are at risk for the disease but have not yet developed it. HeartApart offers such substantial benefits to people with heart disease that it will improve the average quality of life for a group even if only a minority of the group has heart disease.

PRACTICE PROBLEMS
Questions 1–2 are based on the following: A community college is experiencing high turnover rates among its computer science faculty members. To rectify this problem, the computer science department head has proposed to the dean that beginning next year, starting salaries for computer science instructors be increased by ten percent to provide a more competitive pay package.
1. Which of the following indicates a flaw in the department head's plan?

A. Computer science faculty members generally indicate satisfaction with the number and type of classes they are given to teach.
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B. The community college is in a relatively safe area of town with affordable housing. C. Local technology companies provide good supplemental consulting work to many faculty members. D. Yearly pay increases for instructors in all departments are set at a level below the current inflation rate. E. There are several academic institutions nearby with similar pay structures to the department head's proposal.
2. Which of the following must be studied in order to evaluate the validity of the department

head's plan? A. What effects do changes in technology have upon the way classes are assigned? B. Is the majority of turnover in the computer science department initiated by the faculty or the administration? C. What factors are involved in recruiting the most talented computer science instructors? D. What are the technological benefits to having advanced computer science classes taught on campus? E. How would better turnover rates improve the quality of education offered by the community college? Questions 3–4 are based on the following: The Hanks Manufacturing Company has been receiving complaints about the quality of the products in the WWWidget product line. To eliminate these complaints, the operations director has decided to adopt a quality assurance program similar to that of WINK, Inc., which has a high customer satisfaction rate.
3. Which of the following may most reasonably be inferred from the statements above?

A. Products in the WWWidget line have been breaking shortly after being installed. B. The WWWidget line is a relatively new line of products for The Hanks Manufacturing Company. C. The operations director used to work for WINK, Inc. and is therefore familiar with the quality assurance program. D. The WWWidget line is in danger of costing The Hanks Manufacturing Company its profitability. E. The complaints about the WWWidget line indicate a customer satisfaction rate that is lower than that of the WINK, Inc.’s customer satisfaction rate.
4. Which of the following, if true, offers the strongest support for the operations director's plan?

A. The Hanks Manufacturing Company and WINK, Inc. both produce consumer-level Internet connectivity products and market them to similar target audiences. B. The quality assurance program that the operations director is recommending will decrease the margins of the WWWidget line by 10%.

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C. Despite the complaints about the WWWidget line, The Hanks Manufacturing Company still has a high customer satisfaction rate based on industry standards. D. WINK, Inc. provides its customers with personal, onsite training on the use of its products. E. The Hanks Manufacturing Company has been in business for over a decade longer than WINK, Inc. Questions 5–6 are based on the following: A survey was recently given to all high school students in a certain town to measure the effect of environmental factors on attitudes and behavior, and the results indicated that students who play a minimum of two hours per day of violent video games are more likely to engage in violent behavior in school and at home. Therefore, playing violent video games encourages violence among teens.
5. Which of the following is most like the argument above in its logical structure?

A. A developing country gained access to televisions on a widespread basis for the first time, and as a consequence, the population has become more entertainment-oriented. B. A census report shows that more highly educated people live in areas of heavy pollution than in other areas; therefore, educated people are more likely to pollute. C. A survey of homeowners indicated a strong preference for a reduction of property taxes; therefore, the upcoming proposal to reduce property taxes is likely to win. D. A driver's education uses a video simulator to teach driving skills to students; only after passing the simulation can one obtain a learner's permit to drive an actual car. E. A record company knows that most of its buyers are 18–25-year-old males; therefore, it markets its albums to stores where that target is most likely to shop.
6. Which of the following, if true, would most weaken the argument above?

A. The same survey was conducted in a neighboring town with similar results. B. Playing violent video games keeps violent teenagers at home and prevents them from engaging in publicly aggressive behavior. C. The survey used a standard question format that did not allow students to produce responses that could not be interpreted incorrectly. D. Students who play violent video games often have a history of behavioral issues leading back to early childhood. E. The survey was given over a period of days to ensure that all students attending the high school would participate. Questions 7–8 are based on the following: In the week before a local election, a news company polled registered voters in the area to ask them which candidate they planned to vote for. Voters from a representative sample of genders, ages, races, and political affiliations were polled, and 53% of them said they would vote for incumbent Jana Reyes for mayor over any other candidate. Based on the poll results, the news company concluded that Reyes would win the mayoral race.

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7. Each of the following, if true, could weaken the conclusion presented above except:

A. The news company conducted the poll by phone, mainly in the middle of the day over two weekdays. B. This race has been a particularly tumultuous one in which public opinion has often turned very quickly. C. In this town, any mayoral race in which the top candidate receives less than 55% of the vote will result in a runoff election. D. In the past, polls given by the news organization that showed more than a 5% lead by a particular candidate have predicted the outcome of the race with a high degree of accuracy. E. Due to an administrative error, Jana Reyes will be a write-in candidate on the ballot in the actual election.
8. In the argument above, the portion in boldface plays which of the following roles?

A. It is a conclusion that must be proven in order for the argument to be valid. B. It is an assumption that provides little support for the conclusion of the argument. C. It is a premise that has questionable validity in the context of the argument. D. It provides evidence to support another premise of the argument. E. It provides evidence to support the news company’s conclusion. Questions 9–10 are based on the following: Gary Johnson, a major star in track and field, advertises a certain brand of vitamin supplements for aspiring athletes. Alan runs cross country for his university and has decided to start a fitness regimen including the vitamins to improve his event rankings.
9. The statements above, if true, best support which of the following assertions?

(A) The vitamins have been shown to improve stamina in scientific studies. (B) Alan's regimen also includes changes in his workout and diet. (C) Alan is not satisfied with some aspects of his current athletic performance. (D) Gary Johnson used the vitamins to become a major track and field star. (E) Alan has fallen victim to the marketing strategies of the company that manufactures the vitamins.
10. Which of the following, if true, most clearly points to a flaw in Alan's reasoning?

(A) Gary Johnson runs the 400-meter dash, not cross country events. (B) The vitamins are designed to build muscles for shot put and discus throwers. (C) Alan's coach recommends a fitness program that includes vitamins and conditioning exercises. (D) While Alan’s performance has remained steady over the last year, his event rankings have dropped because of the improved performance of his competitors. (E) The efficacy of the vitamins has mainly been tested on college-aged athletes.

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Solutions
1. D.

The department head’s plan states that a more competitive pay package will solve the

turnover problem; therefore, the assumption is that the current pay package isn’t adequate to keep faculty members there. If D is true, the value of the pay package will decrease over time, making it unlikely that the turnover problem won’t return.
2. B.

The department head’s plan also assumes that the faculty members have at least some

choice in remaining at the school; otherwise, a competitive pay package wouldn’t matter. So B brings up an issue that must be considered in order for the validity of the plan to be evaluated. By the way, did you notice the answer choices dealing with computers and technology? While they may bring up some issues that are peripherally important to computer science instructors, they are mostly distraction and not core to evaluating the plan.
3. E.

Since the operations director is recommending the quality assurance program as a way to

eliminate the complaints, it is reasonable to infer that the company using that program has a higher rate of customer satisfaction than The Hanks Manufacturing Company. The other answer choices could very well be true and are, by and large, reasonable, but they can’t be inferred from the information in the passage.
4. A.

Since the argument hinges on whether the two things being compared (the two compa-

nies) are actually comparable, anything that draws a similarity between them supports the operations director’s proposal.
5. B.

The argument states that two phenomena are present; and assumes that one causes the

other. It ignores the possibility that a separate factor causes both of those phenomena, and it also ignores the possibility that the cause and effect is actually reversed. The reasoning in B is similar. Again, notice the answers dealing with videos and other types of entertainment? They’re just there to distract you from actually examining the structure of the argument.
6. D.

Again, the argument assumes that since two phenomena are there, one is actually the

cause of the other and there is no alternate cause. Answer choice D attacks that assumption, so it weakens the argument.
7. D.

This argument, like many arguments that rest upon a poll or survey, assumes that the

sample being polled is representative of the whole with respect to what is being asked about. The answers that weaken the argument either bring up ways in which the survey was not representative, or they introduce mitigating factors that would call the survey’s validity into question. Answer choice D supports the conclusion of the survey because if Jana Reyes received 53% of the surveyed votes (and, according to the language of the survey, only one candidate could be chosen), then the most her nearest competitor could have received is 47%. That’s a spread of more than 5%, so this survey falls into the category that the news organization typically predicts correctly.
8. E.

Since the statement in italic supports the survey results by saying the survey was representa-

tive with respect to some factors that may have influenced the results, it supports the conclusion. And since the statement was actually stated, it is a “premise” or “support,” not an assumption.
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9. C.

If Alan is trying to improve his event rankings, it can be assumed that he is not satisfied

with his current performance. Yes, this is a very wishy-washy statement, but remember, that means it is better supported by the argument than an extreme statement would be. And again, the rest of the answer choices may be reasonable, but they are not supported by the information in the argument.
10. B.

Alan’s plan assumes that the vitamins are appropriate for all track and field athletes,

when their needs may actually be very different. Something designed for a heavy lifter who wants to build muscles may be entirely counterproductive for a runner like Alan.

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CHAPTER 9

Sentence Correction

f

INTRODUCTION

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VERBS: WHERE THE ACTION IS
Verbs are the engines of English grammar, and as such they play an important role in differentiating between a good sentence and a bad one. Two of the major types of errors you will find in GMAT questions are subject–verb agreement and verb tense.

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Subject–Verb Agreement
For any verb in a sentence, it must be clear who is the subject of the verb, and the verb must agree in number with the subject. For example, you might see a question that looks like this: Leo, like most babies, drink lots of milk. This sentence is incorrect, because the subject, “Leo,” is a singular noun that requires the singular verb form “drinks.” A correct answer could be “babies, drinks lots of milk” or “babies, enjoys drinking milk.” Note that ACT will try to distract you by putting another noun or phrase between the subject and the verb so that you might think the plural noun “babies” is the subject of the sentence. Most people can catch errors of this sort pretty easily if the verb comes right after the subject, so the test writers employ a number of devices to complicate the subject–verb agreement: 1. Modifying phrases or clauses between the subject and the verb: “Leo, like most babies, drink lots of milk.” (should be drinks). 2. Placing the verb before the subject in the sentence: “Drinks lots of milk does Leo, like most babies.” (The verb error here is “Leo does drinks milk”; if it read “Drink lots of milk does Leo,” it could be grammatically correct although stylistically ugly.) 3. Subject joined by either . . . or or neither . . . nor; although there are two nouns named, the true subject is either or neither, both of which require a singular verb: “Neither Leo nor the twins drink much milk” (should be drinks). 4. Collective nouns such as audience, council, group, majority, or series. Generally speaking, the number of a verb with a collective noun as its subject depends on the sense of the sentence, but on the GMAT this type of noun is usually treated as a singular noun. ACT also frequently uses singular collective pronouns: each, everyone, everybody, nobody. Example: “Each of the babies drink lots of milk” (should be drinks). The key to handling this type of error is to determine what the subject is for each verb in the sentence.

Verb Tense
Tense errors are somewhat less common than subject–verb agreement errors on the GMAT, but they still appear often. The key to verb tenses is that they have to make sense. Actions that ended in the past cannot be happening in the present, and actions that are beginning in the present cannot be ongoing in the past. For most questions, all of the verbs in the sentence should be in the same tense: past with past, present with present, and future with future. This is a form of the principle of parallelism, which will be discussed later. If an underlined passage contains two different tenses, read it carefully to make sure that the chronology makes sense. Two verb tenses that the GMAT often uses in incorrect sentences are the conditional (used to describe actions that have not occurred but could occur) and the past perfect (used to describe actions in the past that ended in the past). Here is an example of a verb tense question: We dried off the car after it would stop raining.

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A. it would stop B. it will stop C. it stops D. it was stopping E. it stopped You should be able to tell quickly that A is incorrect, because it makes no sense to use the conditional tense for a past action. B is also incorrect because the future tense makes no sense here, nor does the present tense in C. The answer obviously needs to be in a past tense, but the past imperfect in D doesn’t make sense because the after in the sentence suggests that there was a definite point in time at which the rain stopped, so the ongoing past action of D is illogical. Only the past tense in E makes sense. Another kind of verb tense question could look like this: After it had stopped raining, we will dry off the car. A. it had stopped B. it will be stopping C. it stops D. it was stopping E. it stopped The underlined passage uses the past perfect tense, which applies to past actions that terminated in the past. In the context of this sentence, the past perfect makes no sense, because the sentence clearly implies that the drying will occur in the future after the ongoing rain stops; the past tenses in A, D, and E, therefore, cannot be right. B and C are the only sensible choices in the chronology of the sentence. Of the two, C is the superior choice, because “After it stops raining, we will dry off the car” clearly conveys the intended meaning of the sentence, and because “After it stops raining” is more idiomatic than B, “After it will be stopping raining.” Idiomatic expression errors will be discussed later, but the basic principle is that any verb form as awkward as “it will be stopping raining” is almost certainly not the right answer.

PRONOUNS: IN PLACE OF THE RIGHT ANSWER
A pronoun is a substitute word that takes the place of another noun. He, she, it, they, and them are all pronouns. ACT very frequently uses pronoun errors in Sentence Correction questions. The test writers introduce errors by using the wrong pronoun for the noun it replaces, or by using pronouns in such a way that it is not entirely clear to whom or what the pronoun is referring.

Pronoun Reference
The first type of pronoun error we are going to examine is called a pronoun reference error. In this type of error, a pronoun is used, but it is not perfectly clear to whom or what the pronoun refers. A pronoun reference error could look like this:

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According to Albert, Amy and Philip both wanted to take Ben shopping for hats, but he didn’t know which one of them to choose. The problems here are that he could refer to either Albert or Ben, and them could refer either to Amy and Philip or to the hats. A correct answer for this question might look like: According to Albert, Amy and Philip both wanted to take Ben shopping for hats, but Ben didn’t know which one of the hats to choose. A variant on the pronoun referent error could be called a missing referent error. In this type of error, the underlined passage contains a pronoun that does not have a noun elsewhere in the sentence to replace. This type of error could look like: Although Wellington feared a French naval invasion, he was confident that the coastal defenses could handle anything they could throw at them. The problem here is they; although you could infer that they refers to the French navy, there is no mention in the sentence of the French navy, the French, French ships, or any other plural noun that they could replace. Be on the lookout for any use of it, they, or them that lacks a referent.

Pronoun Number
Another common form of pronoun error is pronoun number errors, in which a plural pronoun replaces a singular subject, or vice versa. This type of error could look like this: Jim obviously loves his two hounds, Rose and Shasta, but they do not walk the dogs as often as the veterinarian recommends. The pronoun they in this context can refer only to the hounds, but the context of the sentence demands that Jim be the one who is not walking the dogs. The proper pronoun here should be he.

MISPLACED MODIFIERS
Like the pronoun reference error, the problem with the misplaced modifier is that it makes the sentence unclear. A modifier here is a phrase that modifies the subject of another phrase. In general, the modifier should be right next to the subject it is modifying. A misplaced modifier is one that, because of its position in the sentence, could lead a reader to misinterpret what noun is being modified. A misplaced modifier could look like this: Running on all four legs with startling speed, Sylvia quickly photographed the fleeing chimpanzee. Sylvia’s position in the sentence immediately after the modifying phrase makes her the obvious subject of the phrase, but the context of the sentence makes this reading ridiculous; even if Sylvia could run on all fours with startling speed, she certainly couldn’t photograph any fleeing chimps while doing so. A clearer version of this sentence might look like Sylvia quickly photographed the fleeing chimpanzee, running on all four legs with startling speed.
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Or, even better: Sylvia quickly photographed the chimpanzee as it fled on all four legs with startling speed. Why is the second correction better than the first? Because it simplifies the sentence, replaces a participle with a declarative verb, and removes any chance of ambiguity from the modifying clause. But for our purposes here, the important thing is to recognize what a misplaced modifier looks like. Here are some of the types of misplaced modifiers you might encounter: 1. A participial phrase (this means a phrase with an –ing word), such as Running on all fours, Sylvia quickly photographed the fleeing chimpanzee. 2. A participial phrase introduced by a preposition Upon returning to the mountain lake, the ice-cold water chilled Sylvia to the bone. (Sylvia is much more likely than the water to be returning to the mountain lake.) 3. Adjectives Wet and cold, the fire of the camp had never looked so inviting to Sylvia. (It is Sylvia who is wet and cold, not the fire.) 4. Adjectival phrases A photojournalist with an excellent international reputation, Sylvia’s photographs of wildlife always bring in top-dollar commissions. (Sylvia is the respected photojournalist, not her photographs.) How do you spot a misplaced modifier? Whenever you see a dependent clause (i.e., a clause that could not be a complete sentence on its own) set off by commas, identify which noun in the sentence it appears to modify. If it is unclear which noun is the subject of the clause, or if the apparent subject makes little sense in the context of the sentence, then you have a misplaced modifier on your hands. Read through the answer choices carefully to determine which choice offers the most logical reading.

PARALLELISM
One of the principles of standard English usage is that if a sentence presents multiple related items or phrases, then each of those items or phrases should be presented in parallel grammatical structures. There are a few ways in which this principle is tested on the GMAT. The most common way is when items are mentioned in a list, as in the following: Harold, a fervent environmentalist, is angry about the loss of wetlands, the decrease in biodiversity, and the destroying of the rainforest. The problem here is that the first two items in the list are nouns (loss and decrease), but the third item is a gerund (destroying). The parallel form would be destruction. A parallel construction error

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could also look like the following: Harold, a dedicated father, is always bringing the kids to soccer practice, attending piano concerts, and he reads stories to the children at night. For the final clause to be parallel with the previous two, it should take the participle form “and reading stories to the children at night.” Note that the nonparallel form could appear anywhere in the sentence, so whenever you see a list, be on the lookout for parallel constructions. The other common form of parallel construction tested on the GMAT is in a two-part sentence in which the grammatical construction of the first half creates an expectation that the second half will have a similar form. This sort of question could look like this: To say that Harold is a dedicated father is giving credit where credit is due. Since the first clause of the sentence (To say that Harold is a dedicated father) begins with an infinitive, it creates the expectation that the second clause will take the same grammatical form. The correct form of this sentence would be To say that Harold is a dedicated father is to give credit where credit is due. Parallel construction questions can be difficult for many test takers, because parallelism is one of the principles of formal grammar that people routinely violate in everyday speech. Don’t worry, though; with a little practice, you can quickly recognize the types of questions that ACT uses to test this principle. Just be on the lookout for (1) any kind of lists and (2) any two-part sentence.

IDIOMATIC EXPRESSIONS
Idiomatic expression refers to the way in which we generally match words together. Idiom errors are both the easiest and the hardest errors to spot on the GMAT. They are the easiest because, if you’ve been speaking English your whole life, the wrong answers should naturally look wrong and the right answers should naturally look right. They are also the hardest questions because there are thousands of idiomatic constructions in English, and if you are not familiar with the idiom in question, then you are pretty much out of luck. Fortunately, the GMAT generally tests only a limited set of idiomatic constructions with which most test takers are already familiar. After looking over the following list and working through the Sentence Correction questions in the practice tests, you should have a good idea of the types of constructions that appear on the test. With this type of question in particular, if an answer sounds awkward or overly wordy, it is probably wrong. An idiomatic expression question might look like: Since I don’t enjoy vegetables, I would like the mango rather with the broccoli. A. rather with B. rather than C. rather D. but not also E. but rather not

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The answer is B, because rather than is idiomatic and rather with and the other answers are not. Your ear alone may not always be a reliable test for Sentence Correction questions, but when you know that no one would say, “I would like the mango but rather with the broccoli,” you should trust your instincts. Here are some of the idiomatic expressions that have appeared in Sentence Correction questions in the past: according to appear to as great as as good as, or better than attributed to based on because of choose from conclude that contribute to a debate over defined as determined by a dispute over different from in danger of not only . . . but also prohibit from rather than regard as result of see . . . as subject to think of . . . as

FALSE COMPARISONS: APPLES AND ORANGES
The test writers often compose questions that incorrectly compare two things that are not comparable. A false comparison could look like this: The tomatoes in this bin are bigger than the other bin. The intended meaning, obviously, is that the tomatoes in one bin are bigger than the tomatoes in the other bin, but what the statement actually compares is the size of the tomatoes with the size of the other bin. Tomatoes should be compared to tomatoes, apples to apples, and oranges to oranges. A correct version of this sentence might read: The tomatoes in this bin are bigger than those in the other bin. Sentence Correction questions sometimes test this concept by falsely comparing two actions, or, rather, by comparing an action with a noun: After observing the race, we can all agree that greyhounds run faster than bulldogs. Although in everyday usage most people would find this sentence acceptable, it actually draws a false comparison between an action—the running of greyhounds—and a type of dog—bulldogs. The answers ACT would accept here would be “. . . greyhounds run faster than bulldogs run,” or “. . . greyhounds run faster than do bulldogs.” You should always be on the lookout for false comparisons when a Sentence Correction question contains words such as like, as, than, or similar to. Note that like can compare nouns or noun phrases, while as compares clauses (i.e. phrases containing verbs). This is a form of idiomatic expression: X is like Y, but X is to Y as Y is to Z.

QUANTITY
The test writers often throw in questions that test your knowledge of how standard English handles different quantities. These questions usually focus on the different terminology English uses to
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describe quantities of two and quantities of greater than two. For example, you choose among the five answer choices, but you choose between the two best choices, and the superior of two choices is the better choice, while the superior among five choices is the best choice. A GMAT quantity question might look like this: Although I cannot tell which one is better, Adam can always differentiate between the four flavors. Since this sentence is talking about four flavors, the proper wording would be: Although I cannot tell which one is best, Adam can always differentiate among the four flavors. The following table presents some of the quantity words that frequently appear on GMAT questions:
If Two Items Better Between Less More If More than Two Items Best Among Least Most

Another type of quantity question that sometimes pops up is the distinction between countable and noncountable items. If you are talking about a quantity to which you would normally assign a whole number, such as six cars or eight loaves of bread, then it is a countable item; if you instead would talk about the amount of something rather than its number, such as a lot of traffic or a little soup, then it is a noncountable item (but note that a cup of soup would be a countable item). The most common countable quantity question that appears on the GMAT involves the distinction between fewer and less: Mother gave me less biscuits than she gave Madeleine. This is the sort of error that people frequently make in everyday speech. Biscuits is a countable term, since they occur in discrete units that should be represented as a whole number, so the proper word to compare their quantity is not less but fewer. The sentence should read Mother gave me fewer biscuits than she gave Madeleine. Note that English is somewhat inconsistent on this point; if mother had given Madeleine a greater number of biscuits (countable) or a larger amount of soup (noncountable), in either case she would have gotten more than me. More is used with both countable and noncountable items. Here are some of the countable quantity words that show up on the GMAT:
Countable Fewer Many Number Noncountable Less Much Amount, Quantity

Another variant to watch out for is how you talk about the word number. Consider the following example: The number of orangutans was more than the gorillas.

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This sentence actually has two problems: first, it draws a false comparison by comparing a number (the number of orangutans) with a kind of animal (gorillas); second, while there were more orangutans than gorillas, the number of orangutans was greater than the number of gorillas. A number is not more, it is greater. The sentence should read The number of orangutans was greater than that of the gorillas. Any time you see numbers or quantities in a GMAT question, be on the lookout for the errors just described.

RARE ERRORS
The previous seven error types will encompass the majority of the errors you will see on the GMAT. Remember, though, that all grammatical rules are fair game, so ACT could always throw something uncommon at you. Reviewing grammar textbooks and working through many practice questions could help prepare you if ACT decides to do something unusual. Some grammar points that are occasionally seen on GMAT questions include the following: 1. The subjunctive mood. Almost all of the verbs we use are in the indicative mood, which indicates actions that have occurred, are occurring, or will occur. The subjunctive mood is used to express wishes or statements that are not actually true. Subjunctive verbs appear in the past tense or past perfect tense; were, the subjunctive verb you are most likely to encounter, is the subjunctive form of was. Here are some examples of the subjunctive in action: If she were tall, she could be a good basketball player. (The implication is that she is not tall.) I wish I had given you a present. (But I did not.) The rules for the subjunctive voice are complicated and it is rarely encountered on the GMAT, so your valuable study time would probably be better spent on other more common topics. If you’re gunning for a perfect score, though, and you have the time, check out a grammar book and familiarize yourself with the subjunctive. 2. Possessives. ACT sometimes tests whether you know how to form a possessive properly. Don’t confuse a possessive with a contraction: its is the possessive of it, it’s is the contraction of it is. Don’t accept a double possessive: “That friend of Larry’s is also a friend of mine.” (It should be either Larry’s friend or friend of Larry). 3. Split infinitives. Do not put a preposition between the “to” and the verb form when forming an infinitive: “to boldly go where no one has gone before” is stylistically incorrect. This principle will almost certainly not be the main error tested in any sentence, but if an answer choice includes a split infinitive, it is probably incorrect. 4. Terminal prepositions. Do not end a sentence with a preposition (i.e., to, with, about, and so on). This grammar point is also very unlikely to be the main error in any sentence, but if you see it in an answer choice, that choice is probably incorrect.

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THE MOST COMMON TYPE OF ERROR
The most common question type you are going to see is—no error at all. In about 20% of the Sentence Correction questions you encounter, which means probably about 3 of 15 on the computer-adaptive test, the underlined passage will be the best answer. These can sometimes be the most difficult questions, because the test format leads us to doubt all of the answers, and because ACT tries to make the wrong answers look right and vice versa. So how do you approach these questions? If the underlined passage does not contain any of the error types just listed, then choices B through E almost certainly will. Read through them slowly to seek out the errors in these choices. Once you have confirmed that all of the other choices are incorrect, go with answer A.

HOW TO APPROACH A HARD QUESTION
For each section of the GMAT, ACT has produced questions that most people will get right and that most people will get wrong. To break into the upper echelon of scores, you will need to be able to take difficult questions in stride. ACT can make Sentence Correction questions difficult in a number of ways: 1. Correct answers that look wrong 2. Incorrect answers that look right 3. Longer underlined passages with several possible errors in each one 4. Several choices that are grammatically correct, but with one choice more “standard” than the others If you’re working on a question and it appears that ACT is throwing one or more of these challenges at you, congratulations! If you are getting hard questions, then you probably have a good chance at a high score. If you have absorbed the information in this chapter and worked through the practice questions in the accompanying tests, you should be able to tackle these hard questions with at least a good shot at getting them right. We all get stumped sometimes, though. If that happens, here are some tips for improving your odds of choosing the right answer.

Not Necessarily Wrong, but Not Right Either
The test writers follow patterns when they write questions. There are certain verbal constructions that they frequently use to compose incorrect answers. Some markers of wrong answers include the following: \$ Any answer that includes being if it isn’t talking about a human being. Simple, declarative verbs are usually clearer and more direct than any verb form including being. \$ Unwieldy verb constructions like having been {verb}-ed or will have been {verb}-ing are usually wrong; for example, if a question gives you a choice between something like “the document having been read by Jack . . .” and “after Jack read the document . . .,” you should probably go with the simpler verb construction. \$ Passive verb forms when active verbs would work just as well; see the previous example. ACT, like English teachers everywhere, maintains that the active voice is more forceful than the passive voice, and therefore preferable. Passive verbs are very likely to be incorrect if there is no
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actor specified in the sentence (i.e., “the book was moved,” but the sentence doesn’t say who moved it). \$ Words ending in –ing when there are simpler choices. Be careful here, because gerunds and participles are often parts of the correct answer, but if you have a choice between the founding and the foundation, your odds are slightly better with the foundation. If you have a choice between founding or to found, you should probably go with to found. ACT generally prefers nouns and infinitives to gerunds and participles, so keep this in mind when sorting through the answer choices. Note that these are guidelines, not rules. The correct answer to a question could be: “The human being, having been read the document, opted for reading the document himself.” But it’s just not very likely. Try out these guidelines on some practice questions and try to get a feel for how ACT composes incorrect answers. Once you get a feel for the patterns ACT commonly uses, you will have a much easier time identifying the incorrect choices when you take the test.

If You Have to Guess
Hopefully, the information presented in this chapter and your own knowledge of English grammar will allow you to seek out and destroy the errors in all 15 or so Sentence Correction questions you will see on the GMAT. Unfortunately, tests don’t always go the way we plan, ACT sometimes throws curveballs, and some grammar points inexplicably disappear from our brains when we sit down in front of the computer. If these things happen, don’t panic. As with all the sections of the GMAT, the best strategy is to eliminate the answers you know are wrong and then choose the answer that looks best among the remaining choices. There are some strategies that you can use for guessing on Sentence Correction questions. Because of the way this type of question is written, there are two strategies that will substantially improve your chances of guessing the right answer, even if you cannot definitively eliminate a single choice.
1. Pick the Shortest Answer. GMAT English favors “effectiveness of expression,” and this often trans-

lates into “the most concise way of saying something.” This is a good principle to know for writing in general—that if you have two equally correct and clear ways of saying something, the shorter way is probably the better choice. Also, when the question writers think up their wrong answers, they often throw in unwieldy constructions that make the incorrect answers longer than the correct one. Remember, this is a guideline, not a rule. The shortest answer is often wrong, and the longest answer is sometimes right. But, if you look at many GMAT questions, the shortest answer is the correct one much more often than is the longest answer. Remember also that this strategy does not work on the other question types. Sorting answers by length is relevant only to Sentence Correction questions because of the specific way that ACT composes wrong answers. Do not use this strategy for Critical Reasoning questions.
2. Pick the “Most Common” Answer. What “most common” means in this context is the answer

with the most elements in common with the other answer choices. The reason this strategy is effective is that ACT has to compose incorrect answers that look like the correct answer, so the writers

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FURTHER STUDY
Working through practice tests is the best way to prepare for any GMAT question type, but you can also improve your performance on Sentence Correction questions by outside study. Any high school or college grammar text will present the same grammar rules that the test writers use when they compose questions. Some of the best books written on the subject of English usage are The Elements of Style by William Strunk, Jr., and E.B. White, and The Chicago Manual of Style by the staff of the University of Chicago Press. A little extra study on English usage will not be a waste of time in any event, because we can all improve our writing skills.

PRACTICE SENTENCES
The GMAT often complicates things by combining several types of errors in the same question. The following sentences provide some extreme examples of what the GMAT might throw at you. Read through the sentences, then (1) list as many types of error as you can identify in the sentence, and (2) rewrite the sentence in a correct and comprehensible form.

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1. Cottonseed oil, the cooking oil of choice within fried-food fanatics, burn with the higher temperature than corn oil. Errors:____________________________________________________________________________________ ____________________________________________________________________________________ __________________________________________ Rewrite:___________________________________________________________________________________ ____________________________________________________________________________________ __________________________________________ 2. If you had to say who was the greatest painter between the three greatest painters of the Renaissance, being Michelangelo, Leonardo, and Raphael, we would have to say that Leonardo is the better. Errors:____________________________________________________________________________________ ____________________________________________________________________________________ __________________________________________ Rewrite:___________________________________________________________________________________ ____________________________________________________________________________________ __________________________________________ 3. Colleen and Lauren, the daughters of Cindi, was at the mall when Cindi’s mother said hello to her, their grandmother. Errors:____________________________________________________________________________________ ____________________________________________________________________________________ __________________________________________ Rewrite:___________________________________________________________________________________ ____________________________________________________________________________________ __________________________________________ 4. After riding this bus for the last 15 years, I had been accustomed with the fumes of gas, the rudeness of fellow passengers, and to search in vain for a seat. Errors:____________________________________________________________________________________ ____________________________________________________________________________________ __________________________________________ Rewrite:___________________________________________________________________________________ ____________________________________________________________________________________ __________________________________________ 5. There was too many rats on the boats, so it was demanded for there to be less of them onboard before I board it. Errors:____________________________________________________________________________________ ____________________________________________________________________________________ __________________________________________ Rewrite:___________________________________________________________________________________ ____________________________________________________________________________________ __________________________________________

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Solutions
1. Errors: idiomatic expression (“cooking oil of choice within fried food fanatics” and “burn with the”); subject-verb agreement (“cottonseed oil ... burn”); false comparison (compares corn oil with the burning of cottonseed oil). A correct version could look like Cottonseed oil, the cooking oil of choice among fried-food fanatics, burns at a higher temperature than does corn oil. 2. Errors: verb tense (“was the greatest . . . is the better”); parallelism (“if you had to say . . ., we would have to say”); quantity (“between the three . . . Leonardo is the better”); idiomatic expression (“being Michelangelo . . .”; also, the general principle that you should avoid answers that contain “being”). A correct wording could be If you had to say who was the greatest painter among the three greatest painters of the Renaissance—Michelangelo, Leonardo, and Raphael—you would have to say that Leonardo was the best. 3. Errors: subject–verb agreement (“Colleen and Lauren . . . was”); pronoun reference or pronoun number (“Cindi’s mother said hello to her”); misplaced modifier (“when Cindi’s mother said hello to her, their grandmother”; Cindi’s mother is their grandmother). A correct wording could be Colleen and Lauren, the daughters of Cindi, were at the mall when Cindi’s mother, their grandmother, said hello to them. 4. Errors: verb tense (“after . . . the last 15 years, I had been accustomed”; the past perfect implies that this condition ended at a definite point in the past, but the logic of the sentence suggests that the author is still accustomed to these things); idiomatic expression (“accustomed with”); parallelism (“the fumes . . ., the rudeness . . ., and to search”). A correct wording might look like After riding this bus for the last 15 years, I have become accustomed to the fumes of gas, the rudeness of fellow passengers, and the vain search for a seat. 5. Errors: subject–verb agreement (“there was . . . rats”); passive verb (“it was demanded”; the sentence does not say who demanded, or what “it” is); countable quantity (“less of them”; this could apply only to “rats” or “boats,” both of which are countable); pronoun reference (“before I board it”; what is “it”?); idiomatic expression (“demanded for there to be”). A correct wording of this sentence might read There were too many rats on the boats, so I demanded that there be fewer rats onboard before I board a boat.

PRACTICE PROBLEMS
1. Belgrade is widely known as the capital city of Serbia, but it is also one of the oldest cities in

Europe and the largest in the territory formerly known as Yugoslavia. A. capital city of Serbia, but it is also one of the oldest

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B. capital city of Serbia, nevertheless also one of the oldest C. Serbia’s capital city, and it is also one of the older D. Serbia’s capital, but it is also one of the older E. capital city of Serbia, but it is also one of the older
2. Contrary to popular belief, not every snake with reddish or brownish scales is a copperhead; a

wide variety of perfectly harmless snakes that are frequently mistaken for copperheads. A. copperhead; a wide variety of perfectly harmless snakes that are frequently mistaken B. copperhead; a wide variety of perfectly harmless snakes that are frequently mistook C. copperhead; there is a wide variety of perfectly harmless snakes that people frequently mistook D. copperhead; there is a wide variety of perfectly harmless snakes that people frequently mistake E. copperhead; a wide variety of perfectly harmless snakes that people frequently mistake
3. The controversial amendment to generally accepted accounting principles will require companies

accounting for stock options as expenses at the time they are granted. A. accounting for stock options as expenses at the time they are granted B. accounting for stock options expenses at the time they are granted C. that accounted for stock options expenses when they are granted D. to account for stock options expenses at the point of time they are granted E. to account for stock options as expenses when they are granted
4. The structures designed by Ralph C. Harris were fifteen- and seventeen-story buildings, and for

their time, were some of the larger and more luxurious hotels and residences in existence. A. time, were some of the larger and more luxurious hotels and residences B. era, they were some of the larger and more luxurious hotels and residences C. era, were some of the largest and more luxurious hotels and residences D. time, they were some of the largest and most luxurious hotels and residences E. era, were some of the largely and more luxuriously hotels and residences
5. Weishan Liu, her being one of the world’s leading players of the guzheng instrument, has accu-

mulated a long list of honors, including recording soundtracks for movies such as Dim Sum and Indiana Jones and the Temple of Doom. A. Weishan Liu, her being one of the world’s leading players of the guzheng instrument B. Weishan Liu, one of the world’s leading players of a musical instrument called the guzheng C. Weishan Liu, the guzheng being a top instrument for her D. The guzheng, of which Weishan Liu is one of the top players in the world E. The guzheng, Weishan Liu being one of the top players in the world

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6. The cooperative announced last week that due to increasing sales in the tri-county area, it

would distribute a quarterly dividend of more than twice the usual amount to all of its members. A. The cooperative announced last week that due to increasing sales in the tri-county area B. The cooperative announced that due to increasing sales last week in the tri-county area C. Last week, the cooperative announced that due to sales increasing on a tri-county basis D. Last week, the cooperative, which announced increasing sales in the tri-county area E. Due to increasing sales in the tri-county area the cooperative announced last week
7. Farmers frequently plant a nurse crop such as oats to protect seedlings from overexposure to

the sun, prevent soil erosion, and it reduces growth of weeds. A. it reduces growth of weeds B. reduce weed growth C. reduction of weeds D. reduces weeds from growing E. reduce the growing of weeds
8. Chorioretinitis is an inflammation of the eye that normally effects only small children, and it

usually can be treated with antibiotics. A. effects only small children B. effects small children ordinarily C. affected small children D. affects small children E. affects only small children
9. Though most laypeople do not know the difference between classical and clinical homeopathy,

practitioners assert that clinical homeopathy is directed toward particular organs and tissues, and has contributed more to scientific research. A. has contributed more to scientific research B. contributed to more scientific research C. it contributes more scientific research D. contribute to most scientific research E. had more scientific contributions to research
10. Unlike the United States, the president of the Philippines are elected to a six-year term in office.

A. United States, the president of the Philippines are elected B. United States, the president of the Philippines is elected C. United States, the people of the Philippines elect a president D. the president of the United States, the people of the Philippines elect E. the president of the United States, the president of the Philippines is elected

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11. Recent improvements in technology, such as lighting that mimics the pattern and intensity of

natural sunlight, have made working night shifts much safer and more productive. A. have made working night shifts much safer and more productive B. have made those that work night shifts safer and more productive C. has made it safer and more productive to work at night D. has increased the productivity and safety of working at night E. had made working at night more safer and increased productivity
12. Though dentists recommend brushing one’s teeth three times a day, many adult Americans

brush just twice a day and floss hardly never. A. brush just twice a day and floss hardly never B. brush your teeth twice and never floss C. brush just twice but rarely floss at all D. brush twice daily but hardly ever floss E. only brush twice daily and rarely floss at all

Solutions
1. A.

A is grammatically correct as written and doesn’t introduce some of the awkward structure

found in B. C,D, and E are problematic because they use the word “older,” which clearly isn’t appropriate when discussing the cities of Europe, of which there are more than two.
2. D.

The part of the original sentence after the semicolon could not stand on its own, so

A could not be correct. B and E repeat the same problem; B and C also have the incorrectly structured “mistook.” Answer choice D has correct verb construction and sentence structure.
3. E.

The idiom “require to” dictates that A, B, and C are incorrect. D introduces the wordy

phrase “at the point of time,” which E says more simply as “when.”
4. D.

The sentence as it is written leaves out a subject to the verb “were,” as does C and E. The

main difference between the remaining answer choices is the use of the superlatives (largest/most) versus comparatives (larger/more), and because it is reasonable to assume that the buildings are being compared to multiple others, D is the best answer.
5. B.

“Her being” in the original sentence is awkward and an incorrect use of pronoun object

case. C is also awkwardly structured, and D and E put the guzheng as the subject of the sentence. Since the guzheng itself cannot win honors and record soundtracks, B is the best choice.
6. A.

Answer choices B and C are almost as good as A, but they change the meaning slightly and

are a bit awkward. D and E create fragments and comma splices, so are not the best answers.
7. B.

Items in a list must be phrased in a parallel way, so “reduce” must be the verb used, which

narrows the choices down to B and E. “Weed growth” is more direct than “the growing of weeds”, so B is the better choice.
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8. E.

One issue in this sentence is “affect” versus “effect.” Since “affect” is correct as a verb,

A and B are incorrect. C is in the past tense, which is not appropriate for this sentence, and D changes the meaning of the sentence.
9. A.

This sentence tests verb tense, so you need to determine which tense is needed. Since the

contribution is probably extending into the present, present perfect tense is most appropriate, making A the best choice.
10. E.

The original sentence compares the United States to the president of the Philippines,

which is not correct; a correct sentence would compare a president to a president or a country to a country. If you look at the remaining answer choices to see what is being compared, only E presents a proper comparison and is otherwise grammatically correct.
11. A.

Since the subject of the sentence is “recent improvements,” only A and B agree in number

and are in the proper tense. B changes the meaning of the sentence and doesn’t make much sense, so A is best.
12. E.

“Hardly never” is incorrect construction. B changes the pronoun from the “one” already

in the sentence to “you” and also changes the meaning of the last part with the word “never.” The exclusion of the word “daily” in C changes the meaning of the sentence significantly! The conjunction “but” in C and D is improper since the sentence has no change in the direction of meaning. E is the only choice that makes sense and is grammatically correct.

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CHAPTER 10

d

INTRODUCTION

157

PASSAGE TOPICS
Reading Comprehension passages have covered a wide array of topics in the past, but you can probably expect to see at least one passage dealing with science or technology, one passage dealing with business or economics, and one passage dealing with the social sciences (history, sociology, political science, and so on). Some people naturally feel more comfortable with some topics than with others, but you should approach them all in the same way: read fast for the big picture, focus on the information you need to answer the questions, and don’t bring in any outside knowledge that cannot be verified by the passage itself. You can also expect that at least one of the passages you see will deal with either women or a minority ethnic group. ACT includes these passages in part as a response to long-term criticism that the specific subject matter of its tests provides an advantage to white males. The question of whether these minority-themed passages rectify this historical imbalance is outside the scope of this book, but what is relevant to this book is that these reading passages invariably present minority groups in a positive light. If you see an answer choice that suggests something negative about a minority group, you can be sure that it is the wrong answer.

PASSAGE STRUCTURES
GMAT reading passages come in a variety of shapes, although they are all pretty close to the same size— approximately 250 to 350 words. Some present the views of the author in the first person, while others

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discuss ideas and facts from a strictly third-person perspective. Some start off with a hypothesis that they then go on to support, while others start with a hypothesis that they then attempt to refute. A very common type of passage compares two opposing arguments. Other passages explore topics without stating much of an argument at all. You should practice with many different reading passages in order to get a feel for the range of structures. Paragraphs in the passage will often have “structural signposts” near the beginning that signal how the paragraph fits into the structure of the passage. Some of these signal that the paragraph is going to continue the line of thought expressed in the preceding paragraph, while other words signal that the paragraph is going to express a different point of view. The structural signposts you are likely to encounter on GMAT passages are
Continuing a Line of Thought \$ In addition \$ By the same token \$ Likewise \$ Similarly \$ This argument \$ Therefore \$ Thus Changing the Line of Thought Although But Despite Even though Except However On the other hand Nevertheless Yet

\$ \$ \$ \$ \$ \$ \$ \$ \$

A very common type of passage will contrast a conventional viewpoint with a new viewpoint. Any passage that begins with a phrase like the conventional view, the commonly accepted belief, it has been widely accepted, or the majority of economists believe is probably going to compare a conventional viewpoint with a new line of thinking. Should you treat passages with different structures differently? Not really. But you will probably be more comfortable on the test day if all the passages you see have structures similar to passages that you’ve seen before. And once you’ve worked through several practice passages, you will get a feel for the kinds of words and phrases that signal whether the passage is going to explore a topic, advance a hypothesis, compare competing arguments, or do something else.

QUESTION TYPES
There are roughly six different types of Reading Comprehension questions that ACT composes. 1. Main idea. Main idea questions test your ability to capture the big picture. Main idea and supporting idea questions are the most common types of Reading Comprehension questions. Main idea questions are often the first question after the reading passage. A question of this type could have the following wording: \$ Which one of the following most accurately summarizes the main point of the passage? \$ Which of the following statements most accurately captures the central idea of the passage? \$ Of the following titles, which would be most appropriate for the contents of this passage? \$ The passage can best be described as which of the following?

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By now you should have a good idea of what you are going to face on the GMAT Reading Comprehension section. It’s time to start putting that knowledge into practice. Before you attempt to answer any of the questions, power-read the passage. Spend between one and two minutes reading over the passage very quickly to determine 1. What is the main idea of the passage? 2. What is the basic structure of the passage, and what role does each paragraph play? 3. What are the keywords—the handful of people, things, or ideas that the passage revolves around?

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THE ART OF THE WRONG ANSWER

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PRACTICE PROBLEMS
Since the 1994 introduction to supermarket shelves of Calgene’s Flavr Savr tomato, the first genetically modified food item to be offered to consumers, transgenic foods have made a quiet transformation of the food production system in America. The amount of farmland planted with transgenic crops exploded from barely over 10,000 acres in 1994 to approximately 200 million acres in 2004. The Grocery Manufacturers of America estimate that transgenic crops—primarily corn and soybeans—now appear in approximately 75 percent of all processed foods found in grocery stores. While many in the industry applaud this transformation as a beneficial use of technology that will improve products and profits, many observers are concerned that the long-term effects of these transgenic foods are still poorly understood. Humans have been modifying food since the dawn of agriculture. The difference between conventional selective breeding and biotechnology is that instead of relying on natural but targeted reproductive processes, biotechnology relies on the tools of recombinant DNA technology, primarily restriction endonucleases and ligase enzymes, to alter the genetic codes of organisms in ways that could not occur in nature. One transgenic food organism, the “Bt potato,” combines the genetic code of a regular potato with that of the Bacillus thuringiensis bacterium, resulting in a potato that is poisonous to many types of insect pests, but still edible by humans. Critics of bioengineering warn that we have no long-term studies on the effects of such manipulation of food organisms. Modified foods might have unintended consequences for the health of people who eat them. The modifications introduced into domesticated crops might spread into wild plant species, fundamentally altering the ecosystem. Many critics have argued that the introduction of bioengineered foods gives biotechnology companies

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undue power over the processes of food production, and thereby leaves small farmers and farmers in the developing world at the mercy of large corporations. Perhaps the most common criticism leveled at transgenic foods is that they are “not natural.” Despite these criticisms, the agricultural industry in America has continued to move ahead with further research into and planting of transgenic crops. Government regulatory agencies, such as the EPA, the FDA, and the Department of Agriculture, have essentially given biotechnology companies free rein as long as they can establish that transgenic crops are “substantially similar” to conventional crops, and biotechnology companies have so far successfully fought off all efforts to have transgenic foods labeled as such. To date, no confirmed case of harmful health effects from transgenic foods has been documented. American consumers, although they consistently voice doubts about transgenic foods when asked about them on surveys, are apparently unconcerned that they eat, on average, several genetically modified foods each week.

Questions 1–6 refer to the passage above.
1. Which of the following statements best summarizes the main idea of the passage?

A. The tools of recombinant DNA technology have spurred a fundamental transformation in the way in which food is engineered and grown. B. A majority of Americans now eat transgenic foods because of the benefits in nutrition and cost offered by these new products. C. Despite the fact that transgenic foods have been proven unsafe for human consumption, biotechnology companies have quietly achieved widespread distribution of these foods. D. Genetically modified foods, although they face criticism from those who doubt their safety, have become a significant part of the American food production system. E. Biotechnology offers a solution to the growing levels of hunger and malnutrition in the developing world, although critics worry that transgenic foods may have unintended health consequences.
2. The passage mentions each of the following as concerns raised by critics of transgenic foods

EXCEPT: A. Transgenic foods might affect the health of consumers in unforeseen ways. B. Transgenic foods may be more resistant to insect pests than conventional crops. C. An agricultural distribution system based on genetically modified food will leave small farmers dependent on biotechnology conglomerates. D. There is no data on what the health effects may be for humans who eat transgenic foods over a period of several decades. E. Plant species in the wild might become contaminated by genetically modified species.
3. Which of the following inferences drawn from the statements in the final paragraph, if

accurate, might best explain the apparently contradictory finding that Americans voice concerns over transgenic foods in polls but consume these foods on a regular basis?
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A. Government regulatory agencies have approved the sale of transgenic foods to consumers as long as the producers can establish that the transgenic foods are “substantially similar” to conventional foods. B. American farmers planted over 200 million acres with transgenic crops in 2004, a substantial increase from the acreage planted with transgenic crops a decade earlier. C. American consumers may be unaware that they are eating transgenic foods because of the biotechnology industry’s success in preventing the labeling of these foods. D. Critics of genetic engineering have been unsuccessful in their attempts to impose bans on transgenic food through the EPA and FDA. E. As of the writing of the passage, no deaths or other adverse health effects had been documented in connection with the consumption of transgenic foods.
4. The relationship between a conventional potato and a “Bt potato” is most similar to which of

the following? A. The relationship between a conventional automobile and one that has been equipped with a revolutionary new engine technology that allows it to fly. B. The relationship between a regular hamburger and one that has been made poisonous through the addition of bleach. C. The relationship between a laptop computer and a similar computer that is twice as fast as the first computer because it has a more powerful central processing unit. D. A wild chicken and a domesticated chicken that has been bred to gain weight three times faster than a wild chicken. E. A boiled potato and a baked potato with all the fixings.
5. The second paragraph plays what role in the passage?

A. It presents the first of two arguments discussed in the passage. B. It suggests that the hypothesis advanced in the first paragraph is incomplete. C. It refutes an argument and suggests an area for further study, which is discussed in the rest of the passage. D. It suggests a new way of looking at a topic that differs from the conventional view presented in the first paragraph. E. It provides background information relevant to the topic discussed in the following paragraphs.
6. The author’s attitude toward transgenic food can best be described as which of the following?

A. Angry and concerned. B. Accepting and optimistic. C. Enthusiastically ambivalent. D. Interested but uncommitted. E. Hopeful but suspicious.

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7. The main purpose of this passage is to

A. Trace the historical progression of tea from its origins to the present day. B. Give brief highlights from the history of the cultivation of tea. C. Provide an anecdotal account how tea became a drink. D. Highlight some important elements of the history of preparing and drinking tea. E. Argue against the notion of tea drinking as a valid social art.
8. The last sentence of the first paragraph serves to illustrate which of the following about tea?

A. The mistake that led to tea drinking’s ultimate elevation as a social grace B. The accidental and fortunate nature of how tea was discovered C. The spreading seeds of the habit of drinking tea D. The link between tea and Zen Buddhist practice of pilgrimage E. The unusually rapid way that tea was developed into a beverage
9. Which of the following inferences may be drawn from the discussion of Lu Yu’s work?

A. Before 800AD, it was largely unknown how to cultivate tea.
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B. Some people even today drink tea for reasons other than its physical benefits. C. Drinking tea was primarily a Zen Buddhist practice until the late 700s. D. The Ch’a Ching is one of the earliest works of Chinese origin that is concerned with agriculture. E. Lu Yu was interested in popularizing tea in countries other than China.
10. Based on the passage, Lafcadio Hearn would have agreed with which of the following state-

ments about Japanese Tea Ceremony? A. It is needlessly complex and intricate. B. It is important that students of the art spend many years mastering it. C. It is the pinnacle of Japanese taste and culture. D. It is both a simple act and one that is rich with cultural significance. E. It is an inextricable part of Japanese history and spirituality. Iguacu Falls, which sit on the border between Argentina and Brazil, are said to make Niagara look like a leaky faucet. The great cataracts stretch for two and a half miles across lushly foliaged rocky outcroppings before plunging a staggering two hundred and thirty feet into the river below. The falls region is densely forested, and is home to a wide variety of plants and animals, including a number of endangered ones. It is a paradise where parrots dive and swoop through the spray, butterflies cavort among the tropical plants and coatis, and giant otters and anteaters amble through the trees. The foliage itself varies between tropical and deciduous with orchids blushing in the shade of pines and ferns nodding gracefully in the shadow of fruit trees. Depending on rainfall and water flow, between 100 and 300 individual falls tumble over the cliffs creating a stunning panoply of churning water. Small wonder that this natural powerhouse attracted the attention of developers. At the top of the falls on the Parana River sits Itaipu Dam, the world’s largest operational hydroelectric power plant. The dam is often numbered among the wonders of the modern world. The falls’ superlatives don’t stop with technology. Many consider the cataract system itself one of the natural wonders of the world. In 1986, UNESCO (United Nations Educational, Scientific, and Cultural Organization) concurred when it declared the falls a World Heritage site in order to ensure its preservation. Questions 11–14 refer to the passage above.
11. The comparison in the first sentence is meant to emphasize the

A. Abundant beauty of Niagara Falls. B. Plumbing problems that can be caused by building in close proximity to a waterfall. C. Smallness of Niagara Falls in relation to Iguacu Falls. D. Distance of Iguacu Falls from civilization. E. Fact that Niagara Falls is a less popular tourist destination than Iguacu Falls.

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12. The author's attitude toward Iguacu Falls can best be described as which of the following?

A. Overweening pride. B. Positive appreciation. C. Mild acceptance. D. Apathetic objectivity. E. Cautious optimism.
13. What can most reasonably be inferred from the information in the final two paragraphs?

A. Iguacu Falls' success as a hydroelectric site could potentially cause a threat to its longevity. B. Conservationist efforts have made a tremendous impact in the maintenance of the Itaipu Dam hydroelectric power plant. C. Brazil and Argentina are two of the largest producers of hydroelectric power in the world. D. UNESCO considers the preservation of Iguacu Falls crucial to the balance of the world ecosystem. E. Developers consider any opportunity to invest in hydroelectric power a lucrative business venture.
14. The author of the passage is primarily concerned with

A. Exalting the beauties of a variety of waterfall sites. B. Outlining the history of Iguacu Falls since its discovery. C. Portraying the positive aesthetic and economic aspects of a natural phenomenon. D. Describing Iguacu Falls in terms that would make sense to an American audience. E. Discussing the tension between economic development and natural conservation.

Solutions
1. D.

This is a standard main idea question. The first paragraph contains the main ideas of the

passage, primarily in its last sentence: “While many in the industry applaud this transformation as a beneficial use of technology that will improve products and profits, many observers are concerned that the long-term effects of these transgenic foods are still poorly understood.” The passage is concerned with discussing the expansion of the transgenic food business in America, while also stating the concerns of those who oppose this development. Answer choice A makes a correct statement, but it focuses primarily on the second paragraph and ignores the entire question of criticism, so it does not provide a good summary for the passage as a whole. Answer choice B is also too limited, and it is probably inaccurate in stating that “a majority . . . eat transgenic foods because of the benefits,” when it is unclear that many Americans are aware that they are eating transgenic foods. Answer choice C is incorrect because it makes a statement “transgenic foods have been proven unsafe,” that is not supported by the passage. Answer choice D, the correct answer, addresses the main themes of the passage in a balanced tone that is characteristic of the passage itself. Answer choice E focuses on a topic—the developing world—that is not a major focus of the passage.

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2. B.

This is a supporting idea question. With an “all of the following EXCEPT” question, you

3. C.

This is an inference question that requires you to make a logical connection between two

4. A.

This is an applying information question. You have to determine what the relationship is

between a conventional potato and a “Bt potato,” and then see which of the answer choices presents a corresponding relationship. From the information in the second paragraph, we know that a Bt potato is a potato that has been modified through a new kind of technology so that it has a potentially useful attribute—it is poisonous to insect pests but not to humans—that is not normally found in potatoes. Answer choice A presents a parallel situation: a car has been modified by technology so that it possesses a potentially useful attribute—the ability to fly—that is not normally encountered in automobiles. This looks like a strong answer, but

you need to eliminate the other answer choices. Answer choice B presents a partially parallel situation—an item has been modified so that it is poisonous—but the addition of bleach does not correspond well to the modifying new technology of the Bt potato, and a bleached hamburger, unlike a Bt potato, is a completely useless item. Overall, B is a weaker choice than A. Answer choice C is partially parallel in that the second item may be more useful than the first, but there is no mention that the first was modified to produce the second, and the distinguishing attribute of the second computer, greater speed, is a difference in degree, and does not represent an entirely new attribute. Answer choice D is incorrect on similar grounds; a fatter chicken is just a variant on the old kind of chicken, rather than a chicken with an entirely new attribute. Also, it could be argued that selective breeding, since it is an old technology, is not a good match for the new technology that produced the Bt potato. Answer choice E is a poor choice because boiling and baking simply represent two different ways to prepare a potato; there is no mention of modifying technology or new attributes. Choices B, C, D, and E are all weaker than A, so A is the best choice.
5. E.

This is a standard logical structure question. In your initial reading of the passage, you may

have noticed that the second paragraph takes a step back from the controversy mentioned at the end of the first paragraph—which is the chief concern of the last two paragraphs—in order to provide information about how the genetic engineering of food works and to provide an example of a transgenic product. This paragraph cannot be said to present an argument (Answer choice A), suggest that the hypothesis of the first paragraph is incomplete (Answer choice B), refute an argument (Answer choice C), or suggest a new way of looking at something (Answer choice D). The only answer choice that provides a reasonable description of the role of the second paragraph is E; the technical terms and example provided in E are relevant background information for the discussion of transgenic foods in the following two paragraphs.
6. D.

This is a tone and style question. You can gauge an author’s attitude by the use of tone

words with strong positive or negative connotations. This passage, however, has very little in the way of tone words, so you have to gauge the author’s attitude by the choice of information presented. The lack of overt tone words means that there is no reason to suspect that the author is “angry,” as in answer choice A. On the other hand, the author presents several concerns voiced by critics without refuting them, so the unreservedly positive terms “Accepting and optimistic” in Answer choice B cannot be correct. Answer choice C, “Enthusiastically ambivalent,” may not even be possible; in any event, the author does not seem truly enthusiastic about either of the sides in the argument. Answer choice D, “Interested but uncommitted,” does appear to be an accurate description, because the author is clearly interested enough in the subject to have written the passage, but he or she does not explicitly commit to either side. The terms in answer choice E are too strong in both directions; the author seems somewhat accepting of the developments in agriculture, but does not make any statements that could be characterized as “hopeful.” The author’s decision to enumerate the concerns of critics without fully refuting them suggests that the author could be suspicious, but there is no clear evidence that the author is necessarily suspicious. Answer choice D is the best answer. Note that D is the most moderate of the answer choices; this is characteristic of tone questions. ACT rarely permits the authors of passages to express strong emotions. When you see emotional terms like angry or enthusiastic in answer choices for this type of question, those choices are usually wrong.
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7. D.

This is a primary purpose question, which is similar to a main idea question. It is testing

whether you can accurately determine the scope of the information presented and describe the way in which it was presented. Clearly the passage was about the origins of tea, but many of the answer choices contain that element, and it’s up to you to eliminate the ones that have extra, contradictory, or out-of-scope information. Answer choice A says that the passage “traces” tea’s history “to the present day,” which does not happen; the latest event in the passage takes place no later than 1899. Answer choice B concentrates on the cultivation of tea, which, though it is mentioned, is not the primary focus of the passage. Answer choice C is similarly mentioned, but it’s nowhere near the bulk of the passage. Answer choice E is incorrect based on the first word; the passage is not structured to argue against anything. Answer choice D matches the intent and scope of the passage, so it is the best answer.
8. B.

This is a logical structure question that asks what point a certain sentence illustrates in the

passage. The sentence has to do with how tea became a drink, so we would expect the correct answer to focus on that point. While answer choice A is tempting in that it mentions a “mistake,” it is off-base because its focus is on tea being elevated to a social grace, something not discussed at this point in the passage. Answer choice C is also not the focus of the sentence; it is about how the habit of drinking tea spread. Answer choice D is also not what the sentence was about, and in fact the words used are from a different part of the passage. Answer choice E also has the wrong focus. The sentence is not about speed. Only answer choice B focuses on how tea was accidentally discovered as a drink.
9. B.

This is an inference question that asks you to make a connection between the information

in one part of the passage and one of the answer choices. Answer choice A is tempting because Lu Yu wrote the first book on cultivating tea, but that does not imply that people didn’t know how to cultivate tea anyway. Answer choice C is simply not supported by the passage, and the same is true for D. E is reasonable, but not something that can be inferred from the information given. Answer choice B is the only one that is somewhat supported by the passage; the phrase “forever linking the drink to spirituality” supports the statement that people today may drink tea for other than physical reasons.
10. D.

This is an applying information question that asks you to make a decision based on

the information given in the passage. After reading the quote by Lafcadio Hearn, we can see that he sees the Japanese Tea Ceremony as something of a contrast, particularly by the use of the sentence “. . . yet the whole of this art . . . signifies nothing more than the making and serving of tea . . .” Answer choice A, however, is too extreme to be supported by the quote; Hearn is not strongly negative about the practice of tea ceremony. Answer choice B is perhaps something that is believed by members of Japanese society, but we have no support that Hearn believes it is “important.” Answer choice C is also extreme. It is a statement from elsewhere in the passage, but not an opinion expressed by Hearn. Answer choice E is somewhat supported by the passage, though the word “inextricably” is a little extreme; however, it is not necessarily Hearn’s opinion. Only answer choice D expresses the contradiction that Hearn saw in the practice of Japanese Tea Ceremony, and expresses it in a non-extreme, non-offensive way.

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11. C.

This is a logical structure question that asks what point is emphasized by the comparison

in the first sentence. The sentence says that Niagara Falls, which is commonly regarded as a huge series of waterfalls, looks like a leaky faucet when compared to Iguacu Falls. This is certainly a negative comparison for Niagara and one that makes a point of how small Niagara is (and, potentially, how unattractive). So answer choice A is not a possibility, and B and C have nothing to do with the purpose of the comparison that we've just stated. That leaves C and E, and while E may be true or reasonable, the passage doesn't give us support for it, certainly not in the first sentence. So C is the best possible answer.
12. B.

This is a style/tone question asking for the author's general attitude toward Iguacu Falls.

We can tell from the many positive things the author says about Iguacu in the passage that it is a positive attitude. C and E are not positive enough and D is not positive at all, so they should be eliminated. Answer choice A is strongly positive, but there is no indication that the author is proud of Iguacu; “pride” is not reasonable because we have no reason to think that the author had any responsibility for any of the events in the passage, so it can be eliminated. So though B is probably a little weaker than the tone of the passage, it is the best answer choice.
13. A.

This is an inference question focusing on the final two paragraphs. Answer choices B and

C are reasonable enough to assume, but the passage doesn’t give any support for them. Answer choice D is also reasonable, but it goes farther in scope than the passage supports by saying “crucial” and “world ecosystem.” Answer choice E is not supported by the passage and the word “any” makes this an extreme, and therefore bad, answer. Answer choice A is the only good inference; if UNESCO elected to declare the falls a World Heritage Site for its protection, it is reasonable to infer that there might be a potential threat to its survival, particularly because of the large hydroelectric power site mentioned in the next-to-last paragraph.
14. C.

This is a primary purpose/main idea question. Answer choice A is too broad in scope; the

only waterfall site the author could be said to exalt in this passage is Iguacu Falls. Answer choice B is not supported by the passage, as very little of Iguacu Falls’ history was discussed. Answer choice D is somewhat supported because of the comparison to Niagara Falls at the beginning, but ultimately it is not the focus of the whole passage. Similarly, answer choice E is tempting because of the information in the last paragraph, but it is not the focus of the passage as a whole. Answer choice C is the best supported, as the author does spend the whole passage extolling the virtues of a natural phenomenon, Iguacu Falls.

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CHAPTER 11

The Analytical Writing Assessment

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INTRODUCTION
You don’t have to be a great writer to be good at business. You do, however, have to be able to make a good argument and to communicate it effectively. These are the skills that the GMAT Analytical Writing Assessment aims to test. The Analytical Writing Assessment is composed of two parts: “Analysis of an Issue” and “Analysis of an Argument.” In each part, you will have 30 minutes to write a persuasive essay arguing a position on the topics the computer provides for you. You will type these essays using a simple word-processing program on the same computer on which you will take the computer-adaptive GMAT.

HOW THE ANALYTICAL WRITING ASSESSMENT IS USED

HOW TO APPROACH THE AWA
If you are not already a literary giant, there probably is not time between now and the test to turn yourself into one. Fortunately, that is not a problem. The AWA tests a very specific type of writing and grades it in a very specific way. As long as your writing is basically sound, you can

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prepare yourself to earn a good score on the AWA. The first step is to understand how ACT arrives at that 0 to 6 score.

HOW THE WRITING ASSESSMENT IS SCORED

Organization
The first thing your readers will notice is the structure of your essay. Do you have a clear thesis statement? Is the essay one long, rambling paragraph, or is it a clearly organized set of paragraphs with distinct roles in your argument? Does the essay’s structure make your argument easier or harder to follow? There is no secret to composing a well-organized essay. Follow this simple pattern, and your essay will, at the very least, have the appearance of organization: \$ Paragraph 1: Introduction x State your argument in a clear thesis statement. x Acknowledge that the opposite position has merits, but that for the following reasons (summarize your reasons), your position is the correct one. \$ Paragraph 2: Reason 1, with supporting evidence \$ Paragraph 3: Reason 2, with supporting evidence \$ Paragraph 4: Reason 3, with supporting evidence

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Logical Points
The main benefit of a well-crafted organizational structure is that it will showcase the points of your argument. The points you state will make or break your argument, so make them count. Before you type a word, decide what your argument is going to be. Choose between two and six main points that you are going to use to support your argument. For each point, develop an example/scenario/piece of evidence that supports the point, and present this supporting information along with your point. Your readers will see that you’ve made some logical points, they will observe that you have provided supporting evidence, and your score will go up.

Good Syntax

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your essay will appear dull. Note: Do not take this too far and use complicated words that you don’t normally use, or compose long and unwieldy sentences. The whole point is to make your essay more readable. If you have any doubt about a word or sentence, then stay on the safe side and keep it simple.

FACTORS THAT CAN HELP OR HURT YOUR SCORE
Your success in meeting the criteria just discussed will largely determine your score. There are, however, a few other issues that can push your score up or down.

Bonus Points

Recognizing the Arguments of the Other Side
Your conclusion will appear much stronger if it appears that you have considered the arguments on the other side of the argument or issue. You should address these arguments briefly as a counterpoint to your own argument. You should expose the weaknesses of these opposing arguments as a way to strengthen your own argument. You should not take both sides, because then you aren’t really making an argument. Show that you know what the other side is thinking, and then show why that view is wrong.

Length
ACT does not officially factor length into an essay’s score, but that does not mean that length is irrelevant. The fact is, essay length and essay scores show a high degree of correlation; very short essays tend to get
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lower scores, and essays with high scores tend to be longer than average. This does not mean, however, that the people who write the most will always get the best scores. A very long but sloppy essay that someone has thrown together without any clear argument or structure will get a low score, while a relatively short but persuasively argued essay could earn a high score. Your goal should be to write as much as you can while keeping your argument clear and structured. Another way of looking at it is that it doesn’t matter how many words you write, but it does matter how many good points you make and how well you make them. In general, the more lines of reasoning and evidence that you can bring to your essay, as long as they are consistent, the better your essay will be. In summary, write the longest good essay that you can.

Spelling
ACT does not factor spelling directly into the score, but the fact is that your human readers will probably be less impressed with your argument as a whole if they notice lots of misspellings. The situation with the computer reader is worse, because a misspelling could prevent it from understanding your argument and giving you credit for valid points. It is unlikely that spelling will affect your score either way, but to minimize the chances of misspellings hurting your score, you should: \$ Budget your time so that you can type at a comfortable pace. \$ Reserve a minute or two at the end to proofread your essay for obvious typos.

Typing

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ANALYSIS OF AN ISSUE

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For Making money is what businesses are for Shareholder value helps management focus on important goals If a company doesn’t make money for shareholders, it will go out of business and employees and customers will be out of luck

Against Definition of success is too restrictive Other groups make business success possible: employees, customers, society at large Focusing only on shareholder value encourages management decisions that may be bad for the company in the long run

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follow it (in the case of the computer). The essay also features good syntax as well as varied vocabulary and sentence structure. The essay is not perfect. It contains two typos: “esential” in the third paragraph and “rode” instead of “road” in the fourth paragraph. It also probably would be preferable to move the example of customers to the first supporting paragraph position if customers truly are “the most essential part of any successful business”; points in the middle paragraph tend to be overlooked in favor of those in the first and final supporting paragraphs. Finally, some of the sentences are a bit convoluted, and some of the supporting pieces of evidence could be stronger. But flaws of this nature are expected on a rough draft, and do not prohibit an essay from meeting ACT’s stated standards for a superior essay.

ANALYSIS OF AN ARGUMENT
Remember all the skills you learned for tackling Critical Reasoning questions? Good, because you need them here, too. When you write this essay, the computer will present you with an argument, which you will then be asked to analyze. Like most of the arguments in Critical Reasoning questions, the arguments on the AWA are wobbly. They make sense up to a point, but they invariably contain one or more flaws in reasoning. A question could look like this: The following is a transcript of a statement made by a recording industry executive at an industry conference: “The music recording industry is suffering grave economic losses due to the widespread piracy of digital music. This fate was an inevitable result of the industry’s misguided decision to switch from the analogue format of vinyl records to the digital formats used today on compact disks and computer files. Copying a vinyl record requires expensive and bulky machinery, whereas anyone with a computer and an Internet connection can start up a music piracy business. To boost music revenues, the recording industry should switch entirely back to the analogue format of vinyl records. Also, I can state with complete authority that music just sounds better on a vinyl record.” Discuss how well reasoned you find this argument. In your discussion, be sure to analyze the line of reasoning and the use of evidence in the argument. For example, you may need to consider what questionable assumptions underlie the thinking and what alternative examples or counterexamples might weaken the conclusion. You can also discuss what sort of evidence would strengthen or refute the argument, what changes in the argument would make it more logically sound, and what, if anything, would help you better evaluate its conclusion. All AWA arguments are followed by similar instructions—“Discuss how well reasoned” and so on—so read these instructions carefully now so that you will be familiar with them when you walk into the testing center. The first step in this type of question is to understand exactly what the argument is saying. Approach it with the same critical stance that you use for Critical Reasoning questions: what is the

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conclusion, what are the premises, and what are the unstated assumptions? For this argument, we have Premise 1: The music recording industry is suffering grave economic losses due to the widespread piracy of digital music. Premise 2: This fate was an inevitable result of the industry’s misguided decision to switch from analogue to digital, because copying a vinyl record requires expensive and bulky machinery, whereas anyone with a computer and an Internet connection can start up a music piracy business. Premise 3: Music sounds better on vinyl. Conclusion: To boost music revenues, the recording industry should switch entirely back to the analogue format of vinyl records. Note that the conclusion came in the second to last line, while the last line was actually a somewhat tangential premise. You cannot write an effective Analytical Writing essay if you fail to identify the correct conclusion, so determine the conclusion based on the sense of the passage, not on the position of sentences in the passage. The conclusion will probably come last, but this is not guaranteed. Okay, we know what the argument says, but is it persuasive? In order for the conclusion to be true, a number of assumptions would also have to be true: 1. The premises themselves are true. 2. Switching back to vinyl would actually solve the problem of digital music piracy. 3. Switching back to vinyl would not have other consequences that might hinder the goal of “boosting music revenues.” This argument is vulnerable on any of these grounds. Most AWA arguments are vulnerable to multiple lines of attack. Your job now is to write a cogent essay that assembles these lines of attack in a logical and persuasive way. You should begin by sketching an outline of what you are going to say. It could be something like this: Paragraph 1: Argument is flawed. Although digital piracy is an important issue, the conclusion is not properly drawn because of the following: P2: The premises are flawed. “grave economic losses” due to piracy questionable current situation not necessarily “inevitable result” of switch to digital statement that “vinyl sounds better” is unsupported P3: Stated solution won’t solve problem; people can still make digital files from records. P4: Conclusion is bad idea, because switching to vinyl will hurt record sales more than piracy does. P5: Summary—conclusion not properly drawn. New technology would provide better solution. Your outline could be less detailed than this one, or it could be more detailed, as long as you don’t spend more than five minutes or so writing it. The key is to plan out what you are going to say so that you can choose your best arguments and give your essay a logical structure. A good technique to use on Analysis of an Argument questions is to present a brief paraphrase of the argument’s key premise and conclusion at the beginning of your essay in order to show that you understand the argument. This technique forces you to distill the essence of the argument, it provides you with
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a good way to start the essay, and it allows you to frame the argument in a way that best suits your own argument. Here is what an essay on this argument might look like: The recording industry executive argues that in order to stem the tide of economic losses due to digital music piracy, the music recording industry should abandon the digital format entirely in favor of the old analogue format of vinyl records. While the executive does address a significant current problem for the music industry, the logic of his argument and the conclusion he reaches are both fundamentally flawed. Not only do the premises of his argument fail to support adequately his conclusion, but his conclusion would, if implemented, do more harm to the music industry than is currently inflicted by piracy. To begin with, his premises are flawed. It is inaccurate to characterize the effects of digital formats on the music industry as “grave economic losses” when in fact the music industry has reaped far higher revenues by selling music in digital format—primarily compact disks— than it ever earned in the old analogue days of vinyl. Also, his somewhat irrelevant statement that “music just sounds better on vinyl” is supported only by his personal authority, which in this context cannot reasonably be characterized as “complete.” Finally, his assumption that switching to vinyl records will halt music piracy due to technical complications is inherently flawed, because those vinyl records could very easily be recorded onto digital formats and then distributed over the Internet. His chosen solution does not actually solve his specified problem. The executive’s most fundamental error, however, is his failure to distinguish between stopping piracy and boosting revenue. Although his plan of reverting to an obsolete technology might, in a small way, impede the efforts of those who would use digital music unethically, it is more likely that it would result in far greater economic losses to the industry than are currently inflicted by piracy. The industry has switched overwhelmingly to digital formats because they offer a number of benefits both to the industry and to the consumer. For the industry, digital music is easier to produce and far less costly to distribute than bulky vinyl records. For consumers, digital formats such as compact disks and MP3s are far easier to store, sort through, and carry around than older analogue formats. For the whole industry to switch back to vinyl records would be like cutting off its nose to spite its face. For the reasons stated above, the executive’s argument simply does not hold up. If he were truly serious about addressing the problem of digital music piracy, his time would be better spent investigating technological ways to make digital formats more resistant to piracy. This essay would earn a high score in the 5 to 6 range. The writer shows that he understands the argument being presented, but is not convinced by it for a number of reasons. He goes on to point out a series of flaws in the argument, and then to suggest an alternative approach to the question. By pointing out two potentially fatal flaws—the executive’s plan will not necessarily stop piracy, and it may harm the industry more than it can help it—the author presents a compelling case that the executive’s argument is fundamentally flawed. Structurally, the essay is easy to follow. It states the author’s basic analysis at the very beginning, and then indicates the types of arguments that are going to follow: an attack both on the logic that
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was used to reach the conclusion and on the implications of the conclusion itself. The final paragraph summarizes the argument and suggests an alternative solution. The essay follows the basic pattern of Paragraph 1: The argument says this, but it is flawed for the following reasons. Paragraph 2: Reason 1, and supporting evidence. Paragraph 3: Reason 2, and supporting evidence. Paragraph 4: For the reasons above, the argument is clearly flawed. A better argument would have ______________. The essay also uses some structural words that help the reader follow the argument: “While,” “Not only . . . but,” “To begin with,” “For the reasons stated above . . .” These kinds of words signal to the human and computer readers that the argument flows, regardless of what it actually says. The writing is easy to understand and is generally free of grammatical and spelling errors. The varied vocabulary and sentence structure make the essay relatively painless to read.

PRACTICE ESSAYS
You will definitely improve your chances of earning a high score on the AWA by running through a few practice essays before you take the test. Writing is a skill that can be improved through practice, and writing for the GMAT is a very specific skill that can be greatly improved through practice. Pacing is a crucial component of the AWA, so use the following essay topics to get a feel for how you will pace yourself on the test day.

Sample Issues
For the issues that follow, take five minutes for each topic to digest the issue and to sketch an outline of how you would address the topic in a thirty-minute GMAT essay. For at least one of the topics, type an essay under timed conditions. It is important that you practice under the most authentic conditions possible, so use a word processor and stick to the time limit. For each of the issues statements, your assignment is to Discuss the extent to which you agree or disagree with the opinion stated above. Support your views with reasons and/or examples from your own experiences, observations, or reading. 1. The producers of movies and television programs have a responsibility to provide entertainment that educates the public and upholds societal standards. 2. Issues that affect many nations, such as drug trafficking or acid rain, are best addressed at a multinational level. 3. Although people today have substantially more material things than people did fifty years ago, real quality of life has not improved in that time. 4. Colleges and universities should view their students as customers, just as businesses do. 5. The busiest people are the happiest people.

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Sample Argument

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PART THREE

Beyond the GMAT

CHAPTER 12

Choosing the Right Program

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INTRODUCTION
Preparing to take the GMAT is an important—no, a critical—step toward the pursuit of the MBA, but it is only the start of the battle. In the next several chapters, we’ll help you determine where to apply, how to get in, what to do once you’re there, and how to go about looking for a job.

CHOOSING A SCHOOL: CONSIDERING YOUR OBJECTIVES

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expected of them. So, they’re generally worth what people pay for them. As a side note, you are also getting paid that much for a reason—you’ll work hard for the money you earn. \$ You want to teach business administration. This is a less common, but still obvious reason for attending graduate business school. The leading Ph.D. programs, however, are not necessarily the leading MBA programs—there is a big difference between teaching Master’s candidates and grooming those who will teach them in the future. The Tuck School at Dartmouth, for example, does not even offer a Ph.D. in business. So, if you’re interested in something a bit more advanced than the MBA, you’ll need to reach beyond the rankings; it’s best to look at who is getting hired where. Finally, remember that the teaching of business is the most lucrative academic job one can get these days. Not many other university professors can earn in the low six figures as relatively junior faculty.

A BRIEF TAXONOMY OF MBA PROGRAM TYPES
The next question is, what sort of program to attend. Broadly speaking, there are two options.

The Full-Time Option
The pursuit of the traditional two-year, full-time program is probably why most people would buy a book like this. A full-time MBA program is like none other. While leading part-time MBA programs (discussed next) offer many of the academic attributes of their full-time equivalents, the full-time program is, for most ranked programs, the flagship program for the school and the focus of the school’s administration and budget. What full-time MBA programs offer through this total immersion process is unparalleled access to a wide range of faculty, speakers, contacts, recruiters, and alumni on a weekly, and even daily, basis. If you can afford to quit your day job (more on that later in this chapter), the experience, both academic and social, is worth it.

Part-Time, Evening, and Weekend Programs
For those who have jobs that they either can’t or don’t want to surrender, there are other excellent options. Part-time programs generally allow students three to five years to complete the course work that a full-time program expects to cover in just two. Some schools, however, insist that their evening or weekend programs are not part-time at all; while they may stretch out the length of schooling, they may also allow less flexibility in what courses are taken when. For details, you simply must check with every school in which you are interested. Also check access to key faculty for both core courses and your intended electives. The best professors do not always pull double duty for day and evening programs. The perceived detractor in this case is quality. There is a widespread perception that degrees attained in evening and weekend programs are somehow not the equal of those attained during the conventional full-time programs. This is hard to assert convincingly. At many schools, the faculty that teaches core courses and popular electives teaches for both full-time and part-time programs. What is often true, however, is that the evening, weekend, and part-time programs have slightly lower admission standards, at least in the quantitative aspects of an application. Excellent job experience in a mid-career professional can often make up for a less-than-stellar GMAT score or undergraduate GPA.
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That can help if you find yourself in that category, but many recruiters know the difference, and some shy away from relying too heavily on the résumé books of the evening classes. Executive programs are a further twist on the MBA concept. These are usually shortened versions of the standard MBA courses that gloss over some of the more quantitatively challenging course work and focus instead on high-level case work. The objective is not just to suck in senior managers with money to spend but rusty calculators. At a certain point, most business managers shift from being producers of analysis to being consumers of analysis, so the focus of their graduate education should shift as well. On the other hand, career services assistance is often less impressive for part-timers. At one time, many executive and part-time students were sponsored by large corporations, and many universities did not want to irritate these corporations by offering their employees avenues of escape. This, however, is changing as well. Check the school’s policy on this matter. You will specifically want to know what level of access to campus recruiting and career services assistance is available relative to that for full-time students.

A BRIEF BIBLIOGRAPHY OF SCHOOL RATINGS LISTS
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\$ The Financial Times (FT) issues its survey annually, in January. If you’ve not read London’s FT, you should know that it’s probably the second most important English-language business newspaper in the world (after, of course, the Wall Street Journal). The FT survey pays rather more attention to schools outside the United States, which is a nice feature for those considering shipping out to overseas destinations for school. \$ The Economist ranks schools according to more or less the same criteria as the FT. The Economist Intelligence Unit, the magazine’s affiliated research group, also publishes Which MBA?, an annual book-length expansion of the survey. As a publication based in London, it too pays rather more attention to schools outside of North America. The Economist’s editorial staff is particularly well regarded by the schools that it surveys, so its opinions might be given some weight. \$ The Wall Street Journal (WSJ) has a narrow but deep approach, surveying corporate recruiters for their opinions about, and satisfaction with, recruiting at various schools. The downside of this approach is that it focuses on a single attribute of the schools: the recent experience of the companies that have recruited there. The upside is that this is one of the most important attributes to measure—graduate business schools are professional schools, so you probably wouldn’t be going except for the job. Besides, if you want data on other aspects of the schools, there are plenty of other publications that rate those. The WSJ also divides schools by their regional and national recruiting strength. If you have a geographic focus to your full-time employment aspirations, you should pay attention to which schools place their graduates where. The WSJ’s survey is released annually, and it is absolutely worth picking up. By now, you may have caught one of the major flaws in all these approaches, except for that of the Wall Street Journal. Current students may have important opinions about individual schools, but they are the last group whom one should survey systematically. MBA students have a financial incentive to overstate how much they like their school: if its rank rises in the next survey released, each student stands a better chance of prizing higher compensation out of his next employer or client.

SELECTING A PORTFOLIO OF SCHOOLS
So, we’ve demonstrated that you should be interested in what journalists think are the world’s best schools, but that you also shouldn’t get too hung up on their lists. MBAs among new Fortune 1000 CEOs in 2004 and early 2005, and the 2004 BusinessWeek rankings of the schools attended.
MBA Program The University of Chicago Northwestern University (Kellogg) The University of Pennsylvania (Wharton) Harvard University Dartmouth College (Tuck) The University of California-Berkeley (Haas) University of Texas (McCombs) Washington University (Olin) CEOs 3 2 2 2 1 1 1 1 Rank 2 1 3 5 10 17 19 23
Continued

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MBA Program American Graduate School of International Management (Thunderbird) Michigan State University (Broad) Lake Forest Graduate School of Management Northwestern State University of Louisiana Drexel University (LeBow) La Salle University Georgia State University (Robinson) Lehigh University No MBA at all Total

CEOs 1 1 1 1 1 1 1 1 70 91

Rank — — — — — — — — —

Geography Matters
First, consider where the school is located. The preceding example of Michigan State illustrates this point perfectly. If you are primarily interested in the automotive industry, then Michigan State, the
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University of Michigan, and Carnegie Mellon should absolutely be on your list. They all have excellent reputations in that business, and they are all close to Detroit, the undeniable center of the industry in North America. If running an index fund is your next desired gig, MIT ought to be on your list: you’ll be raked over the statistical coals in the classroom, and Boston is pretty much the North American center of fund management. You should also be thinking about where you want to live when you graduate. Columbia University has an excellent school, particularly if you want to work on Wall Street, but looking for a job in southern California while studying in New York City is a difficult task. UCLA’s Anderson School is probably worth a long look at that point. Most schools do place people worldwide, but nearly all have regional strength. In the world of recruiting, proximity and convenience matter—for both the employer and the employee. It just isn’t cost efficient to recruit remotely if you can find great talent in your own backyard. Despite its national and international reputation, Stanford places almost two-thirds of its graduates in northern California. After two years in Palo Alto, leaving can be a hard thing. So, before placing a school high on your list, you may want to consider just how geographically flexible you can be.

Size Matters
Size matters, but we can’t say exactly how it matters for you, since it matters in both directions. The intimate environment of a small school like Emory’s Goizueta Business School or the University of North Carolina’s Kenan-Flagler School can make for a rewarding and collegial experience. If you crave personal attention and small class sizes, and you don’t need five electives in options pricing from which to choose, then you won’t need a class of over 700 peers. On the other hand, recruiters have a slight tendency to gravitate disproportionately toward larger programs. Recruiting takes time (and therefore money), and small schools offer fewer choices of potential hires for them. Thus, if you are picking a small school, consider the location. Emory has a built-in advantage over UNC: Atlanta is a much larger city than even the metropolitan Raleigh–Durham–Chapel Hill area. On the other hand, it’s easy to patrol the Research Triangle from UNC, and there’s a good possibility that someone you will know on the faculty or get to know through an alumnus will have the right contact to get you in the door. (See how this gets back to location?)

Every school has a particular focus and relative academic strengths—even those that tout general management. That’s easy to see in the finance departments of places like the University of Chicago and the University of Pennsylvania’s Wharton School. But while case-intensive programs like the University of Virginia’s Darden School aim to train general managers who can tackle a wide range of problems, this is also a focus. Many of the surveying organizations release not just Top 10 lists, but Top 10 lists for individual disciplines—say, the best schools for finance, marketing, or entrepreneurship. All the same, you will need to dig down a layer below what the lists reveal. The McCombs School at the University of Texas has an excellent finance department, but it is arguably the leading place in the world to study energy finance. If you’re looking to work in Houston for BP or want a finance job with ExxonMobil in northern Virginia, it’s worth a look.
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More specifically, have a look at who teaches what. At many institutions your first year will mostly be consumed by core classes. (There are exceptions; the University of Chicago is particularly renowned for its laissez-faire, sink yourself if you so choose approach.) If those core classes are typically handed off to the junior faculty on the “least impressive instructor” list, think twice. Use your on-site visits to sit in on multiple core class lectures so that you can evaluate teaching methods, instructions, and the classroom exchanges among students to see if these classes match your expectations and your needs.

Recruiters Matter
Before applying anywhere, scrutinize the list of companies that have hired students in the past few years, and especially the last year. (Many recruiting lists are a composite over several years, so it’s better to investigate who really hired recently.) Check to see which companies hired more than one student (several surveys list top hiring firms). It’s fine to want to work for Goldman Sachs, but if the bank does not recruit formally at the school you’re thinking of attending, then working for that outfit will be considerably less likely. It can be done, but it may also require a great deal of work on your part. Next, consider whether you are laser-focused on a single industry, or whether you’d like the opportunity to explore more than one thing in school. The breadth of the recruiting population is then important. If you’re convinced that you want to work in banking in New York City, then the Stern School of Business at New York University is an excellent choice. Wall Street is not the first destination for graduates of the W. P. Carey School at Arizona State University, but the school has a widely regarded reputation for producing logistics managers. Generally speaking, however, the better ranked the school is on more lists, the better will be your access to the wider pool of recruiters. Then again, this is an easy matter to test by querying the school in question as well as the current students.

Alumni Matter
You should absolutely investigate who the school has placed into what sorts of jobs, and where they have gone since then. The rankings lists of prominent alumni are not necessarily the place to start. Jon Corzine, the governor of New Jersey (and formerly U.S. senator and managing director of Goldman Sachs), is arguably one of the most visible alumni of the University of Chicago’s Graduate School of Business, but you’re not likely to get much time on his calendar. More important would be the names of the recent mid-career and less exalted senior alumni who have important positions in the industries you are considering. Every school tracks this information for recruiting and development purposes, so you should feel free to ask how deep the alumni pool is for the companies you are targeting.

Career Management Matters
Finally, built into that hefty tuition you’ll be paying will be the services of a professional career services staff. Ask how many people are on the staff, what their respective roles are, and how long they have
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been in their jobs. Expect some turnover—career services is a tough business, with demanding clients (MBA students on one side and corporate recruiters on the other), so the burnout rate is high. Ask what programs the school runs throughout the year for students to prepare them for the job search and interviews. Also inquire as to what trips the school conducts to destinations as part of its outreach strategy or as student trips.

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CHAPTER 13

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THE IMPORTANCE OF THE GMAT IN ADMISSIONS
Since you’re reading this book, you’re probably already aware that the GMAT is a big deal in MBA admissions, at least for the leading schools. There are two reasons for this, one good and one not-so-good.

GMATs Matter, so GMATs Matter
The not-so-good reason is that the schools are ranked in part by the average GMAT scores of their incoming classes. Every year, most of the major rankings bodies—basically the editorial staffs of BusinessWeek, The Economist, The Financial Times, and US News & World Report— latch onto quantitative factors to a greater or lesser extent, because, well, they’re quantitative. Actually, BusinessWeek releases its figures only every other year, which is probably just fine, since graduate school reputations and rankings should not shift radically in a year unless something truly exceptional (like a new building) or catastrophic (like a really bad recruiting year) happens. As for the publications, The Wall Street Journal is alone among this group in simply polling recruiters, which produces a quite different list. GMAT scores are an easy figure for prospective applicants to grasp, so everyone wants to know the averages. How smart your classmates will be is an important consideration, since a great deal of one’s graduate school education is provided by one’s peers. Admissions staffs know this, so they watch (or, perhaps more accurately, chase) the average GMAT scores of the incoming class. That applicant may have worked in the West Wing of the White House, but the National Security Advisor’s endorsement on his recommendation may not be enough to make up for a 520 score. That would tank the average, and the school (horrors) could fall a point or two.

GMATs Are a Hygiene Factor
Rankings pressure aside, there is a perfectly valid reason that admissions staffs care about GMAT scores. Contrary to the conspiracy theorists and those who are trying to sell you books of test-taking tricks, standardized tests are reasonably reliable, at least in one respect (keep reading). On the one hand, several internal business school studies we have seen indicate that

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THE IMPORTANCE OF YOUR PAST UNIVERSITY TRANSCRIPTS
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know that partial differential equations will look better on your transcript than basket weaving. Prestige matters here, too, so an art history major from Rice University may still look better than an electrical engineer from Cornfield State College. However, don’t expect the admissions staff to have special knowledge of what works in the real world. Engineering majors usually thrive in finance classes—after all, what is the Black-Scholes model but a heat transfer equation in disguise? Those students, however, do not necessarily profit from that ability economically. One recent study from a leading MBA program in the United States indicates that those with liberal arts and social science bachelor’s degrees actually outearn their engineeringtrained classmates in their first jobs. Why? Qualitative feedback indicates that they are better interviewees, which indicates better social skills, which mean a lot in this world and for your future earnings potential. So, if you studied circuit design in college, lose the attitude about the liberal arts and figure out fast which one is the salad fork.

RESEARCHING THE PROGRAMS

You will need a résumé for your application, so you might as well write a decent one now. Even if you don’t, you will need one by September of your first year: recruiting doesn’t wait. Résumé books need to be published, and basic résumés need to be put into the school’s campus recruiting system. Presentations for second-year recruiting generally start in October, and you may just meet someone into whose hands you’d like to thrust a business card or résumé, even if you’re a lowly first-year. Fall career fairs, both on and off campus, typically take place in the mid-September to mid-October time frame to target second-year students and make early assessments of first-years for intern recruiting. So before writing your résumé, you must understand the purpose of the document. In most contexts, it has but one: to land you an interview with the organization that employs the person reading it. Since each reader will have a different set of criteria in mind, you should ideally customize your résumé for every submission. As that can be very time-consuming, you may consider maintaining a set of slightly different résumés for every type of application that you are making (whether for

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1. Identification
Use your common name, unless you are from the Far East and specifically wish to use an English-style name. In this case, list both your given name and your English nickname, such as Qiongyi (Jane) Wang

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For an address, consider including your permanent address for holiday communications or to illustrate geographic interest. Include a telephone number and a school or personal e-mail address. In general, the school’s e-mail address is preferred.

2. Education

Experience
List your experience in reverse chronological order. For graduate students, this is generally better than the alternative, the functional résumé. In each case, start with the name of the company, the division (if applicable), the location, your title, and the dates of employment (month/year is generally accepted). If you desire and have the room, you may want to include a general overview statement, particularly if the company is not a household name in the industry in which you are seeking a position. After that, you can provide an overview (if needed) of your basic job responsibilities, including their scale and scope, but make sure to put the description of the company before the description of your job. The most important part of your experience, however, is your list of accomplishments. Use bullets (left justified only), and include at least two per job (a single bullet is a logically inconsistent concept, and it shows). You may omit this format with less recent jobs in order to conserve space. Keep most of

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Quality Teamwork and coordination Sample Bullet Point \$ Led a cross-functional team of 12 from marketing, sales, engineering, and finance to resolve successfully our secondlargest customer’s most significant quality issue. \$ Developed a new production cost reduction method for the firm, and successfully tested it in four client engagements. \$ Wrote six speeches for Deputy Secretary of Defense Paul Wolfowitz. \$ Ranked among the top three sales associates (in a region with over 100) three years out of four. \$ Surveyed the automated widget market for potential acquisition candidates, and recommended the two that the firm subsequently acquired. \$ Negotiated long-lead supply contracts with Brazilian aircraft parts manufacturers (in Portuguese).

Analytical and quantitative rigor Communication skills Pattern of accomplishments Strategic thinking and planning Global orientation (cross-cultural)

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\$ Managed purchasing division that procured \$15M in parts for Ford Motor Co. \$ I managed a purchasing division that procured approximately \$15 million in automobile parts for the Ford Motor Company. Finally, remember that accuracy in grammar and spelling is even more important. Anything that signals an inattention to detail tells the reader (the person who might be offering you a job) that you just don’t care that much. Worse, it can be confusing. For more on this, read Lynne Truss’s Eats, Shoots and Leaves (Gotham, 2004), but for now, these are a few random tips.

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REQUESTING AN INTERVIEW

WRITING SOME COMPELLING ESSAYS
The essay-writing process provides an important opportunity to reflect on why you want that MBA. In one sense, the essays are just the written long form of the interview questions that you will encounter. In the interview, your answers are expected to be well thought out, compelling, and hopefully original, but also a bit off the cuff. In the case of the essays, they really need to be polished as well as original— there’s just too much time available not to get it right. First, try to think of some way to make your essay creative—you really should try to take pity on the admissions staffs, which read hundreds of these essays every week for months during the admissions cycle. More to your interest, an also-ran essay will not stick out in anyone’s mind when the admissions people meet to decide whether to admit you or the gal who just got back from that stint setting up microcredit lending institutions in Nepal.

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Remember, while it all starts with the GMAT, it all gets back to the job. We will discuss the job hunt in greater detail in Chapter 15, but we must briefly mention it now. In the past few years, the relationship between admissions and career services within business schools has gotten closer. At many leading institutions, the former now routinely asks the latter for opinions regarding candidates. Are his career goals realistic? Will she be difficult to place into an internship? What sort of recruiters will be interested in his profile, and does that match those that we expect to have on campus? Could a negative answer mean that she might turn out to be a previously unrecognized admissions error? The school will be assessing not just your past performance, but your future marketability, and the latter is arguably more important. Career changers will face the most scrutiny on this dimension. Top-flight MBA programs are often destinations for career changers. During the long economic expansion of the 1990s, many recruiters were flocking to the leading programs to hire anyone they could, so many twenty-somethings who were dissatisfied with their current situation saw the MBA as a way out. Indeed, for many it was. The problem today is that recruiting has tightened a bit, and past work experience is now relatively

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more valued. So, if you are a career changer, you will have to explain what you want to do, and why you don’t want to continue on your current path. If you’re an accountant, you will need to explain why you want to be a marketer, but without saying too many negative things about accounting. You really don’t want to come across as a malcontent. You will also need to show how your progression through your previous activities has prepared you for the shift that you are looking to make. That said, as long as you have a backup plan, don’t be afraid to make the switch, and to make the MBA the hinge that you rely on in the process. It’s a fabulous and edifying experience, and there is no other place in the world where so many recruiters, from so many different industries, will pay so much attention to you in such a short period of time.

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CHAPTER 14

d

CONCEPTS TO REMEMBER FROM YOUR GMAT PREPARATION

MATH CAMP
“Math camp” is the affectionate MBA term for the mathematics review course that many schools offer in July or August for students who, well, haven’t really thought about algebra, statistics, or calculus since high school. It’s a relatively embarrassment-free reintroduction to all of the math that you once knew, then forgot, but really need to know again, fast. Expect to cover everything in Chapters 3 and 4 of this book in less than a day. At that point, you’ll probably move on to more sophisticated algebra, and cover a considerable amount of probability and statistics as well. Math camp may go further than that. In Chapters 3 and 4, we stressed the importance of algebra. That’s not quite all the mathematics you’ll need for an MBA program, as you’ll need to understand statistics very well before you finish. Depending on where you go to school, you may need to brush up on your calculus as well. If you’re not concentrating in finance, then there aren’t that many situations in which you will need to use or understand more than basic calculus. The only one that is certain to arise is the monopoly-pricing problem in microeconomics. That is the question of what price

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ESSENTIAL TOOLS FOR THE MBA STUDENT
So suppose you’ve posted an excellent score on the GMAT, you’ve written some fabulous essays (that are even mostly true), you’ve been accepted to an outstanding MBA program, you’ve mailed in your deposit, you’ve secured some gigantic student loans, and you’ve loaded up the truck to move to Philadelphia, Chicago, Palo Alto, or elsewhere. Wait—that cramped student apartment that you’ve secured for two years won’t hold half your stuff, so you sold most of it on eBay. Given the impending impoverishment of your lifestyle, are there any things that you can’t do without? Absolutely. Every MBA student needs, at a minimum, the same four essential pieces of gear: 1. The laptop computer. Don’t even think about a desktop; the lack of portability will hugely cramp your mobility when working in groups. Furthermore, pay no attention to what the kid at Circuit City tells you are the performance differences between the two types of machine at the same price point. A three-year-old laptop has more than enough processing power and memory for what you will need to do. The only thing driving improvements in the personal computers marketed to individuals these days is the need to see greater resolution in the blood pools in Quake III. That’s a fine way to make a living in software (we suppose), but there’s no need for that in an MBA program. Sure, it will run your regression analyses faster, but a few

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4. The Wall Street Journal subscription. This is absolutely indispensable if you are headed to a career in investment banking, but it’s almost as important for everyone else. Our sniffy European friends tell us that The Financial Times (the “pink pages,” because of the salmon color of the paper) is a most acceptable substitute. Whatever. Reading The Wall Street Journal every day gives you a ground-level reminder about the way things really function, and a daily short course in the lexicon of commerce. One of the worst interviewing experiences one of us had (as an interviewer) involved an MBA student who kept referring to the European Union’s currency as the “Eurodollar.” (For reference, Eurodollars are not units of currency; they are bonds issued in Europe but denominated in U.S. dollars. They’re not as popular as they once were, and the EU’s currency is the euro.) He probably wouldn’t have made such a careerlimiting move if he had read the Journal daily.

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CHAPTER 15

Recruiting and Career Management

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INTRODUCTION
This chapter marks the end of our story, and just the beginning of yours. As we noted in Chapter 12, the job that you will land after school is probably the main reason that you are thinking about pursuing an MBA. Before we get there, however, we need to warn you about one frightening fact: You may have finished your school search, but the GMAT is not finished with you. Ponder the unfairness of that for a moment, and then, like any good capitalist, pull yourself up by your own bootstraps and stop complaining about what’s not fair. You’ll have plenty of time to change the world—right now, just deal with it.

THE IMPORTANCE OF THE GMAT TO RECRUITERS
The GMAT was developed and is maintained to tell admissions staffs how well prospective students are likely to do in their introductory masters-level business classes. That doesn’t mean that the GMAT is used only for that. Many of the larger investment banks and management consultancies crave the quantified objectivity of a test like the GMAT, and ask their prospective hires to forward them copies of their scores along with their transcripts. If the MBA programs can use the numbers, they reason, there is no reason that they cannot as well. (Kurt Salmon Associates, a consultancy that is well known for its retailing and supply-chain management skills, even has job candidates take its own exam, which irritated MBA students have long termed the KSAT. Procter & Gamble’s similar test is affectionately known as the P&GMAT.)

In fact, at the leading MBA programs, you stand a good chance of being asked about your GMAT score within a few weeks of your arrival. Full-time recruiting for second-year students begins at most schools by October, and the talent scouts generally don’t overlook the first-years who look promising. Some second-years who interned at McKinsey, and whom the Firm has deputized to look for talent, may ask that question at the end of a conversation, saying something like, “You know, I should introduce you to Bob, the managing partner for global whatever . . . and by the way, what was your GMAT?”

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Management consultants have a deservedly bad reputation for being at least that competitive, so don’t be surprised. In fact, seize the opportunity to showcase your talent with any firm in which you are even slightly interested. The quality of your internship will have a significant effect on the outcome of your full-time job search, so getting an early start on mapping out your strategy—even before you arrive at school—is a good idea. Things will begin in earnest almost immediately upon your arrival:
Typical schedule for first-year MBA recruiting September October November Self-assessment, résumé development, marketing plans Career fairs, company research, cover letters, networking and interview skills Mock interviews, case interview training, trips to Wall Street for investment banking, first résumé submissions for campus recruiting Informational interviews with alumni; refining job search strategies Additional mock interviews, start of on-campus interviews for first-years

December January–February

What’s a trek? That’s a fair question, but you’ll be very familiar with the concept by the end of your first term. As an example, consider the McDonough School of Business at Georgetown University. It’s an excellent school, but it’s a long way from San Francisco. If working in northern California’s software industry is your bag, but you have your heart set on Georgetown, you might face a very difficult recruiting problem. Three thousand miles and three time-zone changes are a lot to overcome when trying to do business on a personal level. That’s where the treks come in. The career services offices of many schools organize several day- to week-long group trips to cities that would otherwise be long hauls for individuals to make alone. These treks often include opportunities to network with local alumni and act like mini-hiring conferences, giving the employers a detailed look at an intimate group of students (typically no more than 30). Conversely, this gives students an opportunity to see the company’s employees in their natural environment. A lot can be learned about a company’s culture on site, so take advantage of these trips to learn more about a company than you might in the standard hour-long campus presentation.

TOOLS FOR CAREER MANAGEMENT
Whether you’re headed to California or New Jersey, there are only a few things that you will need to manage your MBA career search. While this list may seem obvious, you really will need to pay solid attention to each item on it. \$ A few good suits. Wearing a plaid sport coat to the Merrill Lynch interview seems like an obviously stupid idea, but we’ve seen it happen. Get yourself several new suits that fit perfectly (this includes appropriate hems on skirts or cuffs on pants, and tailoring the length of the jacket sleeves). This will be easy to do, since custom tailors patrol the better MBA programs like ticket scalpers outside a Yankees game. If you are buying retail, don’t go to the cheapest place; a good interview suit is just as much an investment as the degree is. First impressions count. Go for classic styles, good material, and the best tailoring you can get. One final note for men: wear a white shirt to the interview. Beige shirts look uniformly bad on everyone, and blue shirts can be
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There are times when a naked résumé will suffice with a recruiter: a New York investment bank (these places are usually not long on grace) may request stacks of one-page this-is-my-life summaries from MBA programs, and specifically ask that cover letters not be sent. For all other contacts, however, a cover letter is an essential element of the conveyance of a résumé. There is nothing less impressive than a résumé shoved in an envelope and mailed to a recruiter. Sending out a thousand of those is so easy that sending one in that generic format is never notable, no matter how stellar the content. It shows that you cared only enough to be expeditious. Therefore, always include a cover letter in a mailing (e-mail or hard copy) to a potential employer, even if the company or institution states that it is optional. It indicates that you can write intelligently, and that you care to do so. This is not to say that you will be engaging in some perfunctory exercise. The cover letter has but two purposes: to illustrate your fit with the organization, and to induce the reader to pay close attention to your résumé. The cover letter is an opportunity to communicate your story—how you came to this point in your career, and why you’d like to talk to the organization about taking things further. The letter should highlight accomplishments, relevant work experience, and skills specific to the organization, without simply repeating the content of the résumé. That may seem difficult, but that is part of the value of the writing assignment.

Content
The most important thing that you can convey in your cover letter is how your skills are transferable— that is, how they will enable you to move from industry to industry or career to career. The cover letter illustrates how you have done the sort of work that the organization in question requires at some point in the past, or how your past experiences have prepared you for what lies ahead (whether that is a job or a seat in the program). Your cover letters must indicate your transferable skills derived from accomplishments, work experience, at-work training, and education. This includes skills in areas such as managing people, projects, and budgets; leading teams; improving work processes; communicating to large groups; implementing technical advances; closing sales; analyzing complex data; hiring; firing; and training your eventual replacement.

Formats
While we can’t spoon-feed you the content, we can definitely help with the format, as there are some rules that you can follow. To start with, there is at least one classic three-paragraph format for cover letters that can serve as a basic template. Other approaches are perfectly valid, but this works if you need a welltested guide. Again, we phrase this in terms of answers to the questions that any good recruiter would ask: Paragraph 1: Who am I and why am I writing? There’s a good chance that your name won’t be immediately recognizable. Even if you think that it will be, a brief and casual introduction (“you may remember . . . ”) may be worth the trouble. In general, most cover letters will begin with a framing statement about where you come from (your school and year) and lead quickly into more personal information about your specific interest in the firm and any people you have spoken with or research you have done to validate that interest.
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RECRUITING AND CAREER MANAGEMENT

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\$ Use simple stationery. Blue paper is eye-catching, but that effect wears off quickly, leaving the reader to wonder whether you actually thought that you’d gain an advantage that way. \$ Send it to the right person. That may be an MBA recruiter, a decision maker within a particular functional area, a decision maker in another functional area who may refer you to the right person, or even a non-decision maker who might be sufficiently taken with your cause to champion your candidacy (this is especially true of alumni). Whatever you say, remember that the addressee will be one of the first people to learn about your interest in the organization. You would do well to make a good first impression, whether on a company or a school.

Review
Finally, as we noted about your résumé in Chapter 13, you must not send out any cover letter without a thorough review. This is aimed at eliminating poor grammar and punctuation, misspelled words, and (in this case) direct repetition of the résumé. As before, check the visual appeal of the letter, and exercise care in using industry-specific jargon. Try to avoid being cute or clever, as this often backfires by giving an unprofessional appearance.

THANK-YOU NOTES
A brief discussion of thank-you notes is in order, if only because they’re something that you should get accustomed to writing during your application process. Whether they’re sent to a potential recruiter or an influential alumnus of a targeted school, thank-you notes have several valuable uses. They reaffirm your interest in an institution, remind the interviewer or contact of who you are, offer the opportunity to mention something you might have omitted during the interview, and demonstrate the followthrough that is expected of MBA graduates. When are thank-you notes appropriate? Frequently—as in after every job interview, after every informational interview, and on any occasion when someone has done a favor for you (e.g., referred your résumé to someone else or given you a name to call). They should be sent as quickly as possible, preferably within 24 hours of the interview or meeting. Today, electronic mail is absolutely acceptable as a means of delivery, especially when the decision is time-critical, as in the interview process. If anyone tells you otherwise, check whether he is wearing wing-tips and a three-piece suit. If, however, the thank-you is not time sensitive, a handwritten note has a warm and personal touch that is a welcome change from e-mail. What should the thank-you note contain? Not much. Thank-you letters should be short and to the point, thanking the interviewer for meeting with you, mentioning some things that you discussed in the interview that are of particular interest to you, possibly adding something that you may not have mentioned in the interview that you feel is relevant, and reaffirming your interest in the position and the company. The usual point about thoroughly reviewing the letter for transgressions against rules of grammar, style, punctuation, and spelling applies, so we’ll not repeat it in detail. There is, however, one other important point to make: do not send the same letter to everyone in the same organization. Sooner rather than later, recipients are bound to compare notes, if only inadvertently. This will not go well for you.
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INTERVIEWS
Since you’ll be interviewing for a spot in an MBA program (or at least trying to land an interview for one), you should start preparing now. Thinking about job interviews will help you get ready for school interviews, so we’ll focus on those. There is a long list of good books on the topic, and you should definitely consider reading a few of them. For now, we’ll cover the basics. The typical interview lasts 30 to 45 minutes. Most firms that conduct campus recruiting programs provide two interviews. The first round is most often a screening interview to gauge interest, background, skills, and fit with the organization. Second-round interviews can involve greater depth of questioning, and are often focused on specific industry knowledge. The second round is frequently off-campus (either at the firm’s local office or in a suitable hotel), and may consist of a series of interviews with various staff members at different levels within the organization. Most interviews contain a combination of what are basically three types of interview questions. From the perspective of the uninitiated, these are the Good, the Bad, and the Ugly.

The Good—the Résumé Walk-Through
Sample Points for Marketing Interview Advertising Brand management Competitive analysis Consumer research Customer relations Product management

Public relations and communication Sales

Ability to Highlight in Each Functional Area Determining a promotional message and a channel to reach target customers Managing all aspects of marketing for a product, typically consumer packaged goods Benchmarking the price, positioning, market share, or other metric against that of your competition Determining the characteristics, trends, and needs of a given market Developing and managing a relationship with customers by ensuring that their needs are met Managing all aspects of marketing and development for a product category, typically high-tech consumer products, content, or software Determining overall brand positioning and managing communications channels to generate publicity and influence public perceptions Generating transactions

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creating a winning response to these questions so that your answer is more thoughtful than what may come to mind under stress. If you cannot speak intelligently about every item on your résumé for at least two to three minutes, then either (1) it shouldn’t be on your résumé, or (2) you should get a new monologue. This includes the additional section at the end.

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The Ugly—Case Interviews
These are the interviews that uninitiated MBA candidates dread. In actuality, preparing for them is not so difficult, since succeeding at them is mostly a matter of practice. There is a great deal to say about case interviews, and there is a small library of trade books and crib notes about how to deal with them. Since you are not likely to face this sort of interview during your admissions interviews, we will cover only the basics here.
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What sort of questions might you face? The following table shows some examples; again, we use examples compiled from marketing interviews, just to stick with our theme. At one time, questions of this type were the exclusive province of consultancies, but today, you’re increasingly likely to get them from packaged goods companies, so it’s good to know what your consulting-bound classmates will be facing. Additionally, we find that finance and marketing firms are increasingly using case or mini-case questions as a part of the interview process, so it is important to add this to your skill set. The key to case interviewing is being interactive: you must ask questions, take notes, and act as though you’re actually solving a client’s question. The interviewer will be trying to determine how well you think under pressure and how well you manage that intellectual workload on the fly. If you’re working what’s normally a 60-hour per week job, being intellectually inefficient could leave you with an 80-hour-per-week job, and that is just not sustainable over the long haul.
Lines of Case Interview Questioning in Marketing Market segmentation Share of market Branding

Price strategy

Channels of distribution

Product or services mix

Product development Positioning

Product launch Promotions Customer acquisition and retention

Potential Questions How would you determine the target market for this product? How would you go about trying to increase the number of customers for this product? How would you enhance the way customers perceive this brand? How would you increase brand awareness? At what price would you sell this product? What discount would you grant this large customer? What channel would be most profitable for bringing this product to its ultimate customers? What conflicts might this entail in the channel, or with other channels? Within this multiproduct company, what is the best way to organize your mix of products and service offerings? What are the key attributes that this product should offer consumers? What are the most logical means of advertising for influencing how your product is perceived by target customers? How do you want them to perceive it? How would you go about determining whether this new product will be profitable? What communications and offers would you use to increase interest in this special event? What does this company need to do to shore up declining interest in this particular product?

How do you deal with these questions? There are plenty of ways to tackle them, but broadly speaking, case interviewing involves six steps: \$ Listening. The interviewer will generally start by providing some general background information on the case. He probably will not give you all the information you need in order to answer the question at the start, and he may throw in a few red herrings just to make your life difficult
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FINISHING UP AND LOOKING BACK
At the end of an interview, you’ll often hear one of two final questions: \$ “What questions do you have?” Anticipating this, always keep something in reserve. Actually, keep a list of these questions in reserve, since you never know when some character will think
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NETWORKING
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SELECTING THE RIGHT OFFER
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\$ At the right compensation \$ With the right lifestyle \$ With the right coworkers \$ In the right industry \$ In the right location, and \$ With the right upward trajectory That’s a lot to get right, and it will naturally involve trade-offs. So, as you are planning your admissions strategy, consider which of those criteria are relatively more important to you, and which you can relatively sacrifice now for the right possibilities later.

WILL THE GMAT EVER HAUNT YOU AGAIN?
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In the end, your success in getting into business school should be closely correlated with your projected success in business. Much of your success in both venues will be determined by your skill in communication. A skilled business communicator can spin a tale, persuade an audience, write a brief, deliver a speech, give a slide presentation, promote an idea, and above all sell himself. Business school is a safe place in which to further develop these skills, but it helps if you can demonstrate some promise in advance.

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PART FOUR

The Practice Tests

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Instructions for the GMAT Practice Tests

T

he following six practice tests recreate the range of questions you are likely to encounter when you take the GMAT Computer-Adaptive Test. Working through these practice tests, as well as those on

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Practice Test 1
ANALYTICAL WRITING 1

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Analysis of an Issue
TIME—30 MINUTES

The success of a company correlates directly with the average job satisfaction of its employees. Discuss the extent to which you agree or disagree with the opinion stated above. Support your views with reasons and/or examples from your own experiences, observations, or reading.

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ANALYTICAL WRITING 2

Analysis of an Argument
TIME—30 MINUTES

directions: In this section, you will be asked to write a critique of the argument presented below. You may, for example, consider what questionable assumptions underlie the thinking, what alternative explanations or counterexamples might weaken the conclusion, or what sort of evidence could help strengthen or refute the argument. Read the argument and the instructions that follow it, and then make any notes that will help you plan your response. Write your response on a separate sheet of paper. If possible, type your essay on a word processor. Observe the 30-minute time limit.

The following letter was printed in a medical journal: Many nonprescription drugs can cause serious side effects, particularly when taken in conjunction with other drugs or in large quantities. If these potentially harmful nonprescription drugs were sold only by prescription, then a doctor or pharmacist would be able to explain the possible side effects of the drug and would also be able to monitor the quantity of the drug purchased, thereby decreasing the chance that a person would take too much of the drug. Therefore, any drug with potentially serious side effects should be sold only by prescription. Discuss how well reasoned you find this argument. In your discussion, be sure to analyze the line of reasoning and the use of evidence in the argument. For example, you may need to consider what questionable assumptions underlie the thinking and what alternative examples or counterexamples might weaken the conclusion. You can also discuss what sort of evidence would strengthen or refute the argument, what changes in the argument would make it more logically sound, and what, if anything, would help you better evaluate its conclusion.

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37 QUESTIONS

Quantitative
TIME—75 MINUTES

Solve the problem and indicate the best of the answer choices given. numbers: All numbers used are real numbers. figures: A figure accompanying a problem-solving question is intended to provide information useful in solving the problem. Figures are drawn as accurately as possible EXCEPT when it is stated in a specific problem that its figure is not drawn to scale. Straight lines may sometimes appear jagged. All figures lie in a plane unless otherwise indicated.

1. Greg sells gaskets. On three sales, Greg has received commissions of \$385, \$70, and \$190, and he has one additional sale pending. If Greg is to receive an average (arithmetic mean) commission of exactly \$220 on the four sales, then the fourth commission must be: A. B. C. D. E. \$135 \$155 \$220 \$235 \$645

3. What is the value of 3x2 − 1.8x + 0.3 for x = 0.6? A. B. C. D. E. −0.3 0 0.3 1.08 2.46

2. In an effort to plan out expenses, the Roberts family is representing its annual budget as a circle graph. Each sector of the graph is proportional to the amount of the budget it represents. If “clothes and shoes” takes up 54° of the chart, how much of the Roberts’s \$20,000 annual budget is dedicated to clothes and shoes? A. B. C. D. E. \$1,500 \$3,000 \$4,500 \$5,000 \$5,400

4. Over a three-week period, the price of an ounce of gold increased by 25% in the first week, decreased by 20% in the following week, and increased by 5% in the third week. If the price of gold was G dollars per ounce at the beginning of the three weeks, what was the price, in terms of G, at the end of the three weeks? A. B. C. D. E. 0.95G G 1.05G 1.1G 1.15G

5. If a cube has a total surface area of 96, what is its volume? A. B. C. D. E. 16 36 64 81 96

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6. The table below shows the enrollment in various classes at a certain college. Class Biology Physics Calculus Number of Students 50 35 40

NUMBERS: All

numbers used are real numbers.

Although no student is enrolled in all three classes, 15 are enrolled in both Biology and Physics, 10 are enrolled in both Biology and Calculus, and 12 are enrolled in both Physics and Calculus. How many different students are in the three classes? A. B. C. D. E. 51 88 90 125 162

FIGURES: A figure accompanying a data sufficiency problem will conform to the information given in the question, but will not necessarily conform to the additional information given in statements (1) and (2). Lines shown as straight can be assumed to be straight, and lines that appear jagged can also be assumed to be straight. You may assume that the position of points, angles, regions, etc., exist in the order shown and that angle measures are greater than zero. All figures lie in a plane unless otherwise indicated. NOTE: In data sufficiency problems that ask for the value of a quantity, the data given in the statements are sufficient only when it is possible to determine exactly one numerical value for the quantity.

7. In a nationwide poll, P people were asked 2 2 questions. If – answered “yes” to question 1, 5 1 and of those – also answered “yes” to 3 question 2, which of the following represents the number of people polled who did not answer “yes” to both questions? 2 A. –– P 15 B. 3 P – 5 C. 3 P – 4 D. 5 P – 6 13 P E. –– 15
The following data sufficiency problems consist of a question and two statements, labeled (1) and (2), in which certain data are given. You have to decide whether the data given in the statements are sufficient for answering the question. Using the data given in the statements plus your knowledge of mathematics and everyday facts (such as the number of days in July or the meaning of counterclockwise), you must indicate whether A. B. C. D. E. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. EACH statement ALONE is sufficient. Statements (1) and (2) TOGETHER are NOT sufficient.

8. A certain salad dressing made only of oil and vinegar is premixed and sold in the grocery store. What is the ratio of oil to vinegar in the mix? (1) An 18.6-ounce bottle of the salad dressing contains 12.4 ounces of vinegar. (2) In a 32-ounce bottle of the salad dressing, there is half as much oil as there is vinegar. 9. At a certain pancake festival with 600 attendees in which every attendee ate at least 1 pancake, how many people had only 1 pancake? (1) At the festival there were 1,200 pancakes served, and no person had more than 3 pancakes. (2) Seventy-two percent of the attendees at the festival had 2 or more pancakes. 10. A rectangle is equal in area to a square with sides of length 12. Is the diagonal of the rectangle greater in length than 20? (1) The rectangle has a length of 16. (2) The rectangle has a width of 9.

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11. A type of candy comes in two flavors, sweet and sour, and in two colors, yellow and green. The color and flavor of the individual pieces of candy are not related. If in a certain 1 box of this candy – of the yellow pieces and 4 5 of the green pieces are sour, what is the – 7 ratio of the number of yellow pieces to the number of green pieces in the box? (1) In the box, the number of sweet yellow pieces is equal to the number of sour green pieces. (2) In the box, the number of green pieces is two less than the number of yellow pieces. 12. In isosceles triangle ABC, what is the value of ∠C ? (1) The measure of ∠B is 47° (2) The measure of ∠A is 96° Solve the problem and indicate the best of the answer choices given.

15. To be considered grade AA, an egg must weigh between 75 and 90 grams, including the shell. Shells of grade AA eggs weigh between 3 and 5 grams. What is the smallest possible mass, in grams, of a 12-egg omelet, assuming that only grade AA eggs are used, the shells are all discarded, and no mass is lost in the cooking process? A. B. C. D. E. 800 840 864 900 1,080

8 16. (0.2) = ( 0.2 )5

A. B. C. D. E.

0.0008 0.001 0.008 0.04 0.08
2 4

17. What is the ratio of ⎛ 1 ⎞ to ⎛ 1 ⎞ ? ⎜ ⎟ ⎜ ⎟ ⎝ 3⎠ ⎝ 3⎠ A. 9 B. 3 C. 1 D. 1:3 E. 1:27 18. A group of 7 fishermen chartered a boat for a day to fish for flounder. The boat costs x dollars per day to rent. If the group can find 3 more fishermen on the docks who are willing to come aboard and share the rental costs, how much less will the rental cost be per person in terms of x? A. B. C. D. E. x/70 x/35 3x/70 3x/10 3x/7

13. In the rectangular quadrant system shown above, which quadrant, if any, contains no point (x, y) that satisfies the equation 3x + 5y = −2? A. B. C. D. E. none I II III IV

14. If a copier makes 3 copies every 4 seconds, then continues at this rate, how many minutes will it take to make 9,000 copies? A. B. C. D. E. 60 100 120 200 3,000

19. The size of a flat-screen television is given as the length of the screen’s diagonal. How many square inches greater is the screen of a square 34-inch flat-screen television than a square 27-inch flat-screen television? A. B. C. D. E. 106.75 213.5 427 729 1,156

PRACTICE TEST 1

\$239

The following data sufficiency problems consist of a question and two statements, labeled (1) and (2), in which certain data are given. You have to decide whether the data given in the statements are sufficient for answering the question. Using the data given in the statements plus your knowledge of mathematics and everyday facts (such as the number of days in July or the meaning of counterclockwise), you must indicate whether A. B. C. D. E. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. EACH statement ALONE is sufficient. Statements (1) and (2) TOGETHER are NOT sufficient.

24. Is integer y > 0? (1) –(2 + y) > 0 (2) (2 + y)2 > 0
Solve the problem and indicate the best of the answer choices given.

25. If 4 and 11 are the lengths of two sides of a triangular region, which of the following can be the length of the third side? I. 5 II. 13 III. 15 A. B. C. D. E. I only II only I and II only II and III only I, II, and III

20. What is the value of n? (1) n4 = 256 (2) n3 > n2 21. An employee at a company was given the task of making a large number of copies. He spent the first 45 minutes making copies at a constant rate on copier A, but copier A broke down before the task was completed. He then spent the next 30 minutes finishing the task on copier B, which also produced copies at a constant rate. How many total minutes would the task have taken had copier A not broken down? (1) Copier A produced twice as many copies in its first 5 minutes of operation as copier B produced in its first 15 minutes. (2) Copier B produces 10 copies per minute. 22. If ab 0 0, is c an integer? (1) c = 5a – 2b (2) a = 2b 23. x = 0.57y 9. If y denotes the thousandth digit in the decimal representation of x above, what digit is y? (1) If x were rounded to the nearest tenth, the result would be 0.6. (2) If x were rounded to the nearest hundredth, the result would be 0.58.

26. A certain truck uses 18 gallons of diesel fuel in traveling 270 miles. In order for the truck to travel the same distance using 10 gallons of diesel fuel, by how many miles per gallon must the truck’s fuel mileage be increased? A. B. C. D. E. 8 9 12 15 27

27. The figure above represents a window, with the shaded regions representing openings for glass and the pale regions representing the wood panels between and around the glass. If the window is 4.5 feet high by 2.5 feet wide, and if each of the wooden panels is exactly 4 inches thick, what is the total surface area, in square inches, of glass in the window? (1 foot = 12 inches; figure not drawn to scale) A. B. C. D. E. 189 378 448 756 1,620

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THE PRACTICE TESTS

28. If 3( x 2 + x ) − 7 = x 2 + 2( 4 + x 2 ), then x = A. B. C. D. E. 5 6 9 15 25

32. Chauncy, an English bulldog, received 1,618 votes in the Mr. Bulldog USA competition, giving him approximately 20 percent of the vote. Approximately what percent of the remaining votes would he have needed to receive in order to win 30 percent of the total votes? A. B. C. D. E. 10% 12.5% 15% 17.5% 20%

29. Suzie’s Discount Footwear sells all pairs of shoes for one price and all pairs of boots for another price. On Monday the store sold 22 pairs of shoes and 16 pairs of boots for \$650. On Tuesday the store sold 8 pairs of shoes and 32 pairs of boots for \$760. How much more do pairs of boots cost than pairs of shoes at Suzie’s Discount Footwear? A. B. C. D. E. \$2.50 \$5.00 \$5.50 \$7.50 \$15.00

30. For any 3 given numbers, which of the following is always equivalent to adding the 3 numbers together and then dividing the sum by 3? I. Ordering the 3 numbers numerically, from highest to lowest, and then selecting the middle number. II. Dividing each of the numbers by 3 and then adding the results together. III. Multiplying each number by 6, adding the resulting products together, and then dividing the sum by 9. A. B. C. D. E. I only II only I and II only II and III only None of the above

The following data sufficiency problems consist of a question and two statements, labeled (1) and (2), in which certain data are given. You have to decide whether the data given in the statements are sufficient for answering the question. Using the data given in the statements plus your knowledge of mathematics and everyday facts (such as the number of days in July or the meaning of counterclockwise), you must indicate whether A. B. C. D. E. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. EACH statement ALONE is sufficient. Statements (1) and (2) TOGETHER are NOT sufficient.

33. If 8 skiers raced down a course multiple times in one day, and each skier used a different pair of skis on each run, what is the total number of different skis used by the 8 skiers during the day? (1) No skier shared any skis with any other skier. (2) Each skier made exactly 12 runs during the day. 34. The symbol ⊗ represents one of the following operations: addition, subtraction, multiplication, or division. What is the value of 7 ⊗ 4? (1) 4 ⊗ 7 < 1 (2) 4 ⊗ 3 > 1

31. A hat company ships its hats, individually wrapped, in 8-inch by 10-inch by 12-inch boxes. Each hat is valued at \$7.50. If the company’s latest order required a truck with at least 288,000 cubic inches of storage space in which to ship the hats in their boxes, what was the minimum value of the order? A. B. C. D. E. \$960 \$1,350 \$1,725 \$2,050 \$2,250

PRACTICE TEST 1

\$241

35. Salespeople at a certain car dealership are paid a \$250 commission on every car they sell up to their monthly quota, and \$500 for every car they sell over the quota. What is the monthly sales quota at this dealership? (1) One salesperson exceeded the quota by 8 cars and received a total monthly commission of \$7,500. (2) One salesperson achieved only half of the quota; he received a commission of \$1,750 and a warning that he will be fired unless he meets the next month’s quota. 36. If a ≠ −b , is a − b < 1? b +a (1) b 2 > a 2 (2) a − b > 1

37. The hold of a fishing boat contains only cod, haddock, and halibut. If a fish is selected at random from the hold, what is the probability that it will be a halibut or a haddock? (1) There are twice as many halibut as cod in the hold, and twice as many haddock as halibut. (2) Cod account for 1/7 of the fish by number in the hold.

242#

THE PRACTICE TESTS

41 QUESTIONS

Verbal
TIME—75 MINUTES

For the following questions, select the best of the answer choices given.

1. Studies have shown that companies that present seminars on workplace safety to their employees actually have higher rates of workplace accidents than do companies that do not present such seminars to their employees. Despite this finding, it is still in the best interests of companies and their employees for companies to present these seminars. Which of the following, if true, provides the strongest support for the argument that the companies should continue to present these seminars? A. Companies that present workplace safety seminars to their employees are likely to be in manufacturing industries or segments of the service sector that present more opportunities for workplace accidents than the average company. B. A fast-food chain determined that the rate of workplace accidents remained the same at its franchises after all employees had viewed a 30-minute workplace safety video. C. Workers are ultimately responsible for their own safety, and no amount of workplace education can alter their behavior. D. A business research institute determined that workplace accidents reduce the productivity of manufacturing businesses by as much as 8 percent per year. E. Many companies mistakenly believe that presenting workplace safety seminars to their employees relieves the company of legal liability in the event that employees are injured on the job.

2. For hundreds of years, pearl divers have gathered pearls directly from mollusks on the sea floor. This is an extremely risky profession, exposing the divers to risks of drowning, air embolism, and shark attacks. Still, as long as society demands authentic cultured pearls, these brave divers must continue to risk their lives. Which of the following statements, if true, most seriously weakens the conclusion above? A. Shark attacks on pearl divers have decreased steadily over the last three decades because of declining shark populations. B. Cultured pearls are generally considered more beautiful than those made by artificial means. C. Robotic pearl harvesters can gather pearls faster and at less cost than human divers, although they may disturb aquatic communities. D. Part of the value of cultured pearls derives from the exotic way in which they are obtained. E. With the proper equipment and training, a diver employing scuba gear can harvest three times as many pearls per hour as can a free air diver.

PRACTICE TEST 1

\$243

3. An electronics company’s two divisions showed consistent performance over the last two years. In each year, the audiovisual department accounted for roughly 30 percent of the company’s sales and 70 percent of the company’s profits over the period, while the home appliance division accounted for the balance. Which of the following statements regarding the last two years can be inferred from the statement above? A. The audiovisual market is growing faster than is the home appliance division. B. The home appliance division has realized lower profits per dollar of sales than has the audiovisual division. C. Total dollar sales for each division has remained roughly constant for the last five years. D. The company has devoted more money to research and development efforts in the audiovisual division than in the home appliance division. E. To maximize profitability, the company should focus its resources on the home appliance division. 4. Gastric bypass surgery has been shown to be effective at helping extremely obese people lose weight. Some patients have lost as much as 300 pounds after undergoing the surgery, thereby substantially prolonging their lives. Despite the success of the treatment, most doctors have not embraced the surgery as a weight loss option. Which of the following statements, if true, best accounts for the lukewarm reaction of the medical community to gastric bypass surgery? A. Gastric bypass surgery carries a high risk of serious complications, including death. B. Obesity is one of the leading contributors to heart disease and hypertension, two leading causes of death. C. Obesity rates among the American population have been increasing consistently for the last three decades. D. Many patients report that losing weight through diets is ineffective, since they

usually gain the weight back within six months. E. Most health insurance plans will cover the cost of gastric bypass surgery for morbidly obese patients at high risk of heart disease.
The questions in this group are based on the content of a passage. After reading the passage, choose the best answer to each question. Answer all questions following the passage on the basis of what is stated or implied in the passage.

244#

THE PRACTICE TESTS

5. This passage is primarily interested in which of the following? A. Investigating the factors that brought about the Marvel revolution and the Silver Age of comic books B. Reviewing the factors that brought about the end of the Golden Age of comic books C. Comparing and contrasting two eras in the history of comic books D. Condemning the horror comic book for its corrupting influence on the nation’s youth E. Evaluating the historical legacy of William Gaines’s EC Comics 6. According to the passage, which of the following was true of the creators of superhero comic books in the postwar years? A. They sought to head off the censorship of the Comics Code Authority by voluntarily prohibiting stories dealing with sexuality, drugs, or criminal behavior. B. They introduced characters such as Superman and The Spirit. C. They unintentionally laid the groundwork for the transition from the Golden Age of comic books to the Silver Age. D. They focused increasingly on flashy artwork and less on well-developed stories. E. They responded to the competitive pressure from horror comic books by increasing the amount of violence in their stories. 7. According to the passage, what can we infer to be the central message of Fredric Wertham’s The Seduction of the Innocent? A. Adults reading violent comic books were as likely to be corrupted by them as young people were. B. The horror comic books of the late 1940s were inferior to the superhero comic books that gained popularity during World War II. C. Comic books were leading the nation’s youth into crime, violence, and drug abuse. D. Creating a regulatory board to censor the comic book industry would drive the worst offenders out of the business. E. Comic books would never be able to convey stories of any serious literary merit.

8. According to the final paragraph of the passage, what may we infer about the comic book companies of the Silver Age? A. They were able to create popular comic books despite the regulations of the Comics Code Authority. B. They achieved commercial success because of the popularity of characters such as Spider-Man, the Hulk, and the Fantastic Four. C. They repeated the same mistakes as the comic book companies of the Golden Age. D. They failed to succeed because of the numbing effect of the Comics Code Authority regulations. E. Marvel Comics was the only major comic book company to survive from the Golden Age into the Silver Age. 9. In what light does the passage depict the efforts by Fredric Wertham to bring about regulation of the comic book industry? A. As a fanatical crusade brought about by Wertham’s inner demons B. As a witch-hunt roughly analogous to the concurrent anti-Communist hearings by the House Committee on Un-American Activities C. As a reasonable response to an industry that had gone too far D. As an angry response to a trend in the subject matter of the comic book industry E. As an inappropriate response to a phenomenon that was not actually hurting anyone 10. According to the passage, which of the following statements can be made about the content of Weird Tales and The Crypt of Terror? A. Their adult-oriented content was not suitable for young readers. B. Their grim and gritty content was a market response to the demands of soldiers home from World War II. C. They frequently depicted violence and criminal behavior, but shied away from sexuality or drug abuse. D. Their sales surpassed those of previous best-selling titles such as Superman or Batman. E. The publication of Weird Tales #1 coincided with the end of the Golden Age of comic books.

PRACTICE TEST 1

\$245

The following questions present a sentence, part of which or all of which is underlined. Beneath the sentence, you will find five ways of phrasing the underlined part. The first of these repeats the original; the other four are different. If you think the original is best, choose the first answer; otherwise choose one of the others. These questions test correctness and effectiveness of expression. In choosing your answer, follow the requirements of standard written English; that is, pay attention to grammar, choice of words, and sentence construction. Choose the answer that produces the most effective sentence; this answer should be clear and exact, without awkwardness, ambiguity, redundancy, or grammatical error.

13. The stock market collapse of 1929 had far-reaching consequences for the national economy, causing a nationwide collapse in home values, putting millions out of work, and by erasing the investment savings of one-fifth of the population. A. B. C. D. E. and by erasing and erasing and having erased and erased by erasing

14. No less remarkable than the invention of nuclear power has been the way the technology has prompted governments to reevaluate the nature of international relations. A. No less remarkable than the invention of nuclear power B. What was as remarkable as the invention of nuclear power C. Inventing nuclear power has been none the less remarkable than D. The invention of nuclear power has been no less remarkable as E. The thing that was as remarkable as inventing nuclear power 15. Unlike the recognition of ethical lapses in others, many people are disinclined to perceive the same flaws in themselves. A. Unlike the recognition of ethical lapses in others, many people are disinclined to perceive the same flaws in themselves. B. Unlike the perception of ethical flaws in themselves, many people are willing to recognize these same flaws in others. C. Many people, willing to recognize ethical lapses in others, are disinclined to perceive the same flaws in themselves. D. Many people are disinclined to perceive the same flaws in themselves, but are willing to perceive ethical lapses in others. E. Although willing to recognize ethical lapses in others, many people in themselves are disinclined to perceive the same flaws.

11. The way in which the mighty blue whale and the other baleen whales—the finback, gray, humpback, and right whales—eats was discovered by careful observation by biologists. A. B. C. D. E. eats was discovered by eat was discovered through eats were discovered by means of eat were discovered by eat was discovered resulting from

12. The eighteenth-century author Jonathan Swift once suggested in a satiric essay Irish farmers could eat their children to address the twin problems of overpopulation and lack of food. A. Irish farmers could eat their children to address the twin problems of overpopulation and lack of food B. that the twin problems of overpopulation and lacking food could be addressed by the eating of children by Irish farmers C. of the twin problems of Irish farmers, overpopulation and a lack of food, could be addressed by the eating of their children D. that Irish farmers could address the twin problems of overpopulation and lack of food by eating their children E. that Irish farmers, facing overpopulation and lacking food, could address the twin problems through eating their children

246#

THE PRACTICE TESTS

For the following questions, select the best of the answer choices given.

B.

C.

D.

E.

provide basic components of the modern computer and electronics industries. The missile defense system in question will not require the development of any new technologies. Space-based missile defense programs may be the only way to defend civilian populations against preemptive nuclear attacks. Space-based missile defense programs, although more expensive than traditional land-based systems, are theoretically more effective than traditional land-based systems. The scientists employed on the project could make extraordinary advances in the capabilities of intercontinental ballistic missiles used by the army.

18. The commissioner of a professional sports league dictated that teams could not put players on the field who had a greater than 20 percent chance of suffering a careerending spinal injury during competition. The commissioner justified this decision as a way to protect players from injury while protecting the league from lawsuits. Which of the following, if true, would most undermine the effectiveness of the commissioner’s new policy? A. Spinal injuries can result in paralysis, loss of fine motor skills, and even death. B. The previous year, more than seven players in the league suffered careerending spinal injuries. C. The players’ union agrees that the risk of injury is an inevitable part of playing the game at a professional level. D. There is no scientifically valid method for determining the likelihood of any player suffering a career-ending spinal injury at any given time. E. Players barred from playing because of this new regulation will be entitled to compensation for lost wages at a level determined by the commissioner’s office.

PRACTICE TEST 1

\$247

19. There are few things worse for a new parent than listening to a baby scream in hunger while a bottle of formula slowly warms up in a bowl of hot water. So why not just pop the bottle in the microwave and zap it in 20 seconds? Because microwaves heat fluids unevenly, and a hot pocket in the formula could seriously injure the baby. Which of the following is presupposed in the argument against heating formula in the microwave? A. Babies generally refuse to eat formula that has been heated in a microwave. B. Microwave radiation might break down some of the proteins in formula that are vital to a baby’s health. C. Different microwaves use different amounts of power, and consequently some models could heat a bottle to scalding temperature faster than others. D. Parents cannot be expected to consistently even out the temperature of a microwaved bottle by shaking it vigorously before giving it to the baby. E. Once formula has been heated, any leftover formula should be discarded, because otherwise the formula could spoil between feedings and make the baby sick. 20. Charlie’s Chainsaw Company has reason to believe that one of its models of saw is defective. A recall of all of the saws would cost more than \$5 million, and would probably result in a loss in market share over the next quarter because of bad publicity. Still, a recall is the right economic decision. Which of the following, if true, most supports the conclusion above? A. Defective chainsaws can seriously injure or even kill the people who use them. B. Charlie’s chief rival has recalled two of its products within the past year. C. Product recalls often result in a perception by customers that a given product is permanently defective, even after the defect has been remedied. D. The stocks of publicly traded companies that announce product recalls often drop upon the announcement, but they generally return to the pre-announcement level within 12 months.

E. Three years ago a rival company went out of business because of large punitive damages awarded to a plaintiff who had been injured by a defective chainsaw. 21. A dog enthusiast took home two puppies from the dog shelter. He fed one of the puppies super-premium canned dog food, while he fed the other a generic brand from the grocery store. The dog fed on the generic brand gained weight twice as fast as the dog fed the super-premium brand. Because of the difference in these results, the dog enthusiast concluded that the generic brand actually provided nutrition superior to that of the super-premium brand. Each of the following, if true, would weaken the evidence for the dog enthusiast’s conclusion except for which of the following? A. A dog will sometimes gain more weight when eating inferior-quality food because he must eat more of it to obtain the nutrients he needs. B. The dogs were of mixed breeds and appeared to be descended from dogs of different sizes. C. Both dogs ate all of the food given to them at each serving. D. The dog enthusiast did not give the two dogs equal amounts of their respective foods. E. The dog who received the super-premium dog food suffered from a digestive system disorder that hindered his growth.
The following questions present a sentence, part of which or all of which is underlined. Beneath the sentence, you will find five ways of phrasing the underlined part. The first of these repeats the original; the other four are different. If you think the original is best, choose the first answer; otherwise choose one of the others. These questions test correctness and effectiveness of expression. In choosing your answer, follow the requirements of standard written English; that is, pay attention to grammar, choice of words, and sentence construction. Choose the answer that produces the most effective sentence; this answer should be clear and exact, without awkwardness, ambiguity, redundancy, or grammatical error.

248#

THE PRACTICE TESTS

22. A council of ecologists in Hawaii have concluded that much of the currently uncontrolled invasive species on the island chain were arriving in the holds of cargo ships. A. have concluded that much of the currently uncontrolled invasive species on the island chain were arriving B. has concluded that many of the currently uncontrolled invasive species on the island chain arrived C. have concluded that many of the currently uncontrolled invasive species on the island chain have arrived D. concluded that many of the currently uncontrolled invasive species on the island chain would arrive E. has concluded that much of the currently uncontrolled invasive species on the island chain had arrived 23. Some people say that the answer to crime is to build more prisons, but more sensitive observers argue that instead we should address the sources of crime through reduced poverty, a cut off supply of illicit drugs, and by focusing on keeping kids in school. A. through reduced poverty, a cut off supply of illicit drugs, and by focusing on keeping kids in school B. by the reduction of poverty, cutting off the supply of illicit drugs, and to focus on keeping kids in school C. by reducing poverty, cutting off the supply of illicit drugs, and focusing on keeping kids in school D. by means of reducing poverty, cutting off the supply of illicit drugs, and through focusing on keeping kids in school E. to reduce poverty, cut off the supply of illicit drugs, and to focus on keeping kids in school 24. As automobiles replaced horses as the primary means of transportation, it was widely anticipated that the time spent in transit by the average traveler would decrease. A. As automobiles replaced horses as the primary means of transportation, it was widely anticipated that B. Insofar as automobiles replaced horses as the primary means of transportation, it was anticipated widely

C. With horses being replaced by automobiles as the primary means of transportation, there was wide anticipation that D. As the primary means of transportation replaced horses with automobiles, many anticipated that E. Automobiles replacing horses as the primary means of transportation produced anticipation widely that 25. Intrigued by the new rules that favored quickness over strength, the decision of the coach was to give more playing time to the team’s smaller athletes. A. the decision of the coach was to give more playing time to the team’s smaller athletes B. the coach decided to give the team’s smaller athletes more playing time C. it was decided by the coach to give the team’s smaller athletes more playing time D. the team’s smaller athletes were given more playing time by the coach E. more playing time was given to the team’s smaller athletes by the coach 26. At ground level, nitrous oxides are bad enough, but when up high, atmospherically they bond with free ions to create dangerous smog particles. A. but when up high, atmospherically they B. however, it is in the upper atmosphere in which it may C. but in the upper atmosphere, they D. however, but once in the upper atmosphere it is known to E. as in the upper atmosphere they

PRACTICE TEST 1

\$249

For the following questions, select the best of the answer choices given.

27. Paleontologists hypothesize that modern birds evolved from the family of dinosaurs that included Tyrannosaurus rex. This hypothesis would be strongly supported if evidence that dinosaurs from this family had a body covering resembling feathers could be found, but so far no such evidence has been found. Which of the following, if true, would most help the paleontologists explain why no evidence of feathered dinosaurs has yet been found? A. Fossilized dinosaurs have shown many birdlike characteristics, such as bone structure and winglike arms. B. If birds are in fact the descendants of dinosaurs, then it can be argued that the dinosaurs never really died out. C. Flying dinosaurs such as the Pteranodon, which is not thought to have been related to modern birds, do not appear to have had feathers. D. Soft tissues such as skin and feathers do not fossilize like bones, and therefore are far less likely to have left permanent evidence in the fossil record. E. The thousands of dinosaur fossils excavated by paleontologists represent only a tiny fraction of the billions of dinosaurs that once lived. 28. Bob and Linda are tired of the freezing cold days in Glenmont, so they are considering retiring to either Sunny Glen or Buena Vista. Bob points out that Sunny Glen has an average annual temperature 8 degrees Fahrenheit higher than that of Buena Vista. Linda insists, however, that Buena Vista would be the better choice. Which of the following, if true, best accounts for Linda’s preference for Buena Vista? A. Different people experience cold in different ways, so what seems cold to Linda may seem pleasantly cool to Bob. B. Sunny Glen has a somewhat higher risk of hurricanes than does Glenmont. C. Buena Vista has a range of cultural offerings, including an opera, a ballet, and three jazz clubs.

D. Living in a place that gets very hot, such as Sunny Glen, can have as many health risks as living in a place that gets very cold. E. While Sunny Glen is warmer than Buena Vista in the summer, it also has more freezing cold days in the winter. 29. Although many people would not believe it, the mosquito is actually the most dangerous animal in Africa. While the bite of the black mamba is invariably lethal when untreated, this dreaded snake kills only a few dozen people per year. Hippopotami, with their immense strength and foul dispositions, kill hundreds of people per year in rivers and lakes, but the mosquito is still more dangerous. Mosquitoes bite hundreds of millions of people in Africa every year, and they infect over a million each year with malaria, a disease that is often fatal. Which of the following questions would be most useful in evaluating the claim made above regarding the mosquito? A. Could a person survive an attack by a black mamba if that person received prompt medical attention? B. What criteria are used to determine which animal is the “most dangerous” animal? C. Could the incidence of mosquito bites be decreased through the judicious use of pesticides and insect repellent? D. Does malaria kill more people per year in Africa than tuberculosis? E. How does the percentage of people who survive hippopotamus attacks in Africa each year compare with the percentage of people who survive mosquito bites?
The questions in this group are based on the content of a passage. After reading the passage, choose the best answer to each question. Answer all questions following the passage on the basis of what is stated or implied in the passage.

Although hard statistics are difficult to come by, there is substantial anecdotal evidence that use of performance-enhancing drugs, or doping, is rampant in professional sports. Of perhaps greater significance to society are the estimated 1.5 million amateur athletes who use steroids, either to improve their appearance or to emulate the performance of their favorite professional athletes. This chemical epidemic is a pernicious threat to both the nation’s health and our collective sense of “fair play.”

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Nonprescription anabolic steroids have been illegal in the United States since 1991, and most professional sports leagues have banned them since the 1980s. These bans are partly a matter of fairness—a talented athlete trained to the peak of her ability simply cannot compete with an equivalent athlete using steroids—but also based on issues of health. Anabolic androgenic steroids (“anabolic” means that they build tissues; “androgenic” means that they increase masculine traits) have been linked to liver damage, kidney tumors, high blood pressure, balding, and acne. They function by increasing the body’s level of testosterone, the primary male sex hormone. In men, this dramatic increase in testosterone can lead to the shrinking of testicles, infertility, and the development of breasts; in women, it can lead to the growth of facial hair and permanent damage to the reproductive system. Steroids have also been linked to a range of psychological problems, including depression and psychotic rage. The punishments for getting caught using steroids are severe, and the serious health consequences are well documented. Despite this, millions of professional and amateur athletes continue to use performance-enhancing drugs. Why is this? One clear pattern is that many athletes will do whatever it takes to get an edge on the competition. Since the 1950s, Olympic athletes have played a catand-mouse game with Olympic Committee officials to get away with doping, because the drugs really do work. Athletes who dope are simply stronger and faster than their competitors who play fair. Professional athletes in football and baseball have found that steroids and human growth hormone can give them the edge to score that extra touchdown or home run, and in the modern sports market, those results can translate into millions of dollars in salary. For the millions of less talented athletes in gyms and playing fields across the country, drugs seem like the only way to approach the abilities of their heroes in professional sports. The other clear pattern, unfortunately, is that it has been all too easy for abusers to get away with it. Steroid abuse is often regarded as a “victimless crime.” One of the favored ways to trick the testers is to use “designer” steroids. There are thousands of permutations of testosterone, such as THG, that can be produced in a lab. Chemists have discovered that they can create new drugs that produce androgenic effects but do not set off the standard doping tests. Other methods have been to use the steroids but stop a few weeks before testing, to use other chemicals to mask the traces of steroids, or to switch

in a “clean” sample of urine at the testing site. Other athletes use steroid precursors, such as androstenedione, that have androgenic effects similar to those of steroids but are not illegal because they are not technically steroids. The sad fact is that unless the government and professional sports organizations are willing to get tough on the steroid problem, the use of performance-enhancing drugs in sports is not going to end. 30. What appears to be the primary purpose of this passage? A. To educate readers about the health threats involved in the use of performance-enhancing drugs B. To analyze the ways in which professional athletes have eluded attempts to screen for performance-enhancing drugs C. To discuss the reasons why performanceenhancing drugs are a dangerous and persistent problem for society D. To complain about the inadequate efforts by government and professional sports organizations to eliminate the problem of performance-enhancing drugs E. To argue that athletes, both professional and amateur, should not use performance-enhancing drugs on the grounds that they are both dangerous and unfair 31. According to the passage, all of the following are known potential consequences of steroid use except for which of the following? A. B. C. D. E. Damage to reproductive organs Decreased blood pressure Increases in the user’s strength and speed Kidney tumors Increased risk of depression

32. The author’s attitude toward the problem of steroid abuse is best described as which of the following? A. B. C. D. E. Cautious but optimistic Judgmental but supportive Ambivalent but resigned Curious but subjective Concerned but pessimistic

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33. Which of the following can be inferred about a long-distance race in which both athletes who use performance-enhancing drugs and those who do not use these drugs compete? A. The athletes using the drugs will be caught by the proper authorities and ejected from the race. B. The athletes using the drugs will have a better chance of winning the race. C. The athletes using the drugs will use steroid precursors that produce effects similar to those of androgenic drugs but are not technically steroids. D. The athletes using the drugs are more likely to be professionals in their sport than the athletes who do not use such drugs. E. The athletes using the drugs will be more likely to use any means possible to win the race, including intentional sabotage of the other racers’ equipment. 34. The relationship of an athlete who does not use performance-enhancing drugs to an athlete who does use such drugs is most similar to which of the following? A. The relationship of a farmer selling milk from cows that have been given bovine growth hormone, a legal drug that promotes greater than normal milk production, to a farmer selling milk from cows that have not been given bovine growth hormone B. The relationship of a chess player to a competitor who uses psychological tricks in order to gain an advantage C. The relationship of a boxer in the lightweight class to a boxer in the heavyweight class D. The relationship of a person taking a standardized test according to the rules to a person taking the same test while using an illegal hidden calculator E. The relationship of a person entering a pig in an agricultural contest to a person entering a guinea pig in the same contest 35. According to the passage, which of the following can be inferred about the “designer” steroid THG? A. It can increase masculine traits in users without setting off standard doping tests.

B. It does not cause the health problems associated with traditional anabolic steroids. C. Even if professional sports organizations could detect THG, they would take no action against those who use it. D. It is a chemical permutation of progesterone, a hormone that has powerful effects on the human body. E. Because it is a “designer” steroid, it is more expensive than generic steroids. 36. Which of the following best expresses the role of the third paragraph in the overall structure of the passage? A. It redirects the theme of the passage from presenting a problem to explaining the reasons for the problem’s severity. B. It introduces a new concept that defines the rest of the passage. C. It provides an answer to a question posed in the first two paragraphs. D. It refutes the central hypothesis of the second paragraph and poses a question that is answered in the following paragraphs. E. It narrows the focus of the passage from the general themes of the first two paragraphs to the more specific themes of the last two paragraphs.
The following questions present a sentence, part of which or all of which is underlined. Beneath the sentence you will find five ways of phrasing the underlined part. The first of these repeats the original; the other four are different. If you think the original is best, choose the first answer; otherwise choose one of the others. These questions test correctness and effectiveness of expression. In choosing your answer, follow the requirements of standard written English; that is, pay attention to grammar, choice of words, and sentence construction. Choose the answer that produces the most effective sentence; this answer should be clear and exact, without awkwardness, ambiguity, redundancy, or grammatical error.

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37. His opponent having sprained his wrist, Andrew could have won by exploiting this weakness, but he chose not to do it. A. His opponent having sprained his wrist, Andrew could have won by exploiting this weakness, but he chose not to do it. B. Andrew could have won by exploiting this weakness after his opponent sprained his wrist, but he chose not to do so. C. Choosing not to do so, Andrew could have won after his opponent sprained his wrist by exploiting this weakness. D. After his opponent sprained his wrist, Andrew could have won by exploiting this weakness, but he chose not to do so. E. After his opponent sprained his wrist, Andrew could have, but chose not to do it, won by exploiting this weakness. 38. Since the average test score of students enrolled in charter schools were rising 7.5 percent in the spring, many educators concluded that the system was working. A. Since the average test score of students enrolled in charter schools were rising 7.5 percent in the spring, many educators concluded B. As the average test score of students enrolled in charter schools rose 7.5 percent in the spring, with many educators concluding C. Because the average test score of students enrolled in charter schools rose 7.5 percent in the spring, many educators concluded D. Because the average test score of students enrolled in charter schools were up 7.5 percent in the spring, many educators concluded E. With average test scores rising by 7.5 percent among students enrolled in charter schools, and many educators concluded 39. The police chief argued that first-time offenders who have no high school diploma but who have families with a record of crime will probably break the law again. A. who have no high school diploma but who have families with a record of crime

PRACTICE TEST 1

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Practice Test 2
ANALYTICAL WRITING 1

d

Analysis of an Issue
TIME—30 MINUTES

Because of research priorities at the national and academic levels, we know more about the surface of the moon than we do about the ocean floor of our own planet, despite the central role the oceans play in global transportation, food production, and climate. It would be more sensible to reallocate those resources dedicated to space research to the exploration of our oceans. Discuss the extent to which you agree or disagree with the opinion stated above. Support your views with reasons and/or examples from your own experiences, observations, or reading.

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Analysis of an Argument
TIME—30 MINUTES

directions: In this section, you will be asked to write a critique of the argument presented below. You may, for example, consider what questionable assumptions underlie the thinking, what alternative explanations or counterexamples might weaken the conclusion, or what sort of evidence could help strengthen or refute the argument. Read the argument and the instructions that follow it, and then make any notes that will help you plan your response. Write your response on a separate sheet of paper. If possible, type your essay on a word processor. Observe the 30-minute time limit.

A spokesman for a dairy company issued the following statement: Many consumers buy organic milk because they are concerned about the consequences of the widespread use of recombinant bovine growth hormone and antibiotics in the conventional dairy industry. These concerns, however, are unfounded. While bovine growth hormone has been shown to produce significant developmental effects in cattle, no study has ever shown that its presence in commercial milk has had any developmental effects on human consumers. Regarding antibiotics, while it has been argued that large-scale, preemptive use of antibiotics in cattle feed can interfere with the animals’ immune systems and can lead to the proliferation of antibiotic-resistant strains of bacteria, neither of these effects affect the quality of the milk produced by cattle that are fed antibiotics. Therefore, there is no reasonable justification for a consumer to pay \$5 for a gallon of organic milk when a perfectly good gallon of conventional milk can be had for half the price. Discuss how well reasoned you find this argument. In your discussion, be sure to analyze the line of reasoning and the use of evidence in the argument. For example, you may need to consider what questionable assumptions underlie the thinking and what alternative examples or counterexamples might weaken the conclusion. You can also discuss what sort of evidence would strengthen or refute the argument, what changes in the argument would make it more logically sound, and what, if anything, would help you better evaluate its conclusion.

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37 QUESTIONS

Quantitative
TIME—75 MINUTES

Solve the problem and indicate the best of the answer choices given. numbers: All numbers used are real numbers. figures: A figure accompanying a problem-solving question is intended to provide information useful in solving the problem. Figures are drawn as accurately as possible EXCEPT when it is stated in a specific problem that its figure is not drawn to scale. Straight lines may sometimes appear jagged. All figures lie in a plane unless otherwise indicated.

1. Jim’s Taxi Service charges an initial fee of \$2.25 at the beginning of a trip and an additional charge of \$0.35 for each 2/5 of a mile traveled. What is the total charge for a trip of 3.6 miles? A. B. C. D. E. \$3.15 \$4.45 \$4.80 \$5.05 \$5.40

2. If the area of a square with sides of length 8 centimeters is equal to the area of a rectangle with a width of 4 centimeters, what is the length of the rectangle, in centimeters? A. B. C. D. E. 4 8 12 16 18

a b c 4. If x = + 2 + 3 , where a, b, and c are each 3 3 3 equal to 0 or 1, then x could be each of the following EXCEPT: A. 1 27 1 B. 9 4 C. 27 2 D. 9 4 E. 9 Score 5 4 3 2 1 Number of Applicants 2 12 21 7 8

3. A certain lab experiments with white and brown mice only. In one experiment, 2/3 of the mice are white. If there are 13 brown mice in the experiment, how many mice in total are in the experiment? A. B. C. D. E. 39 33 26 21 10

5. Fifty applicants for a job were given scores from 1 to 5 on their interview performance. Their scores are shown in the table above. What was the average score for the group? A. B. C. D. E. 2.79 2.86 2.91 2.99 3.03

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The following data sufficiency problems consist of a question and two statements, labeled (1) and (2), in which certain data are given. You have to decide whether the data given in the statements are sufficient for answering the question. Using the data given in the statements plus your knowledge of mathematics and everyday facts (such as the number of days in July or the meaning of counterclockwise), you must indicate whether A. B. C. D. E. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. EACH statement ALONE is sufficient. Statements (1) and (2) TOGETHER are NOT sufficient.

8. What is the area of the rectangular region depicted above with sides A and B and diagonal C ? (1) C 2 = 9 + A2 (2) A + B = 7 9. Do at least 20 percent of the people in country X who are over the age of 25 possess a college diploma? (1) In country X, among the population over the age of 25, 26 percent of the male population and 16 percent of the female population possess college diplomas. (2) In country X, women account for 55 percent of the total population. 10. If C = 5r and s 0 0, what is the value of C? 2s (1) r = 4s 2 (2) r = 5
Solve the problem and indicate the best of the answer choices given.

numbers: All numbers used are real numbers. figures: A figure accompanying a data sufficiency problem will conform to the information given in the question, but will not necessarily conform to the additional information given in statements (1) and (2). Lines shown as straight can be assumed to be straight, and lines that appear jagged can also be assumed to be straight. You may assume that the position of points, angles, regions, etc., exist in the order shown and that angle measures are greater than zero. All figures lie in a plane unless otherwise indicated. note: In data sufficiency problems that ask for the value of a quantity, the data given in the statements are sufficient only when it is possible to determine exactly one numerical value for the quantity. 6. Carrie, Lisa, and Betty all make purchases at a music store that sells all records for a certain price and all CDs for a certain price. How much does Carrie pay for 1 record and 2 CDs? (1) Lisa bought 3 records for \$22.50. (2) Betty bought 2 records and 4 CDs for \$55.00. 7. N and P are points on the number line below 20. Is P closer to 10 than N is? (1) P is greater than the average of 10 and N. P (2) –– = 3 N

11. If 8a = 9b and ab 0 0, what is the ratio of a – to b ? – 9 8 A. 64 –– 81 8 B. – 9 C. 1 D. 9 – 8 E. 81 –– 64 12. Two hundred multiples of seven are chosen at random, and 300 multiples of eight are chosen at random. Approximately what percentage of the 500 selected numbers are odd? A. B. C. D. E. 20% 25% 40% 50% 80%

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13. In triangle ABC above, if ∠BAD and ∠ADB have measures of 4n°, ∠ACB has a measure of n°, and ∠DBC has a measure of 45°, what is the measure of ∠ABC ? (Figure not necessarily drawn to scale.) A. B. C. D. E. 45° 60° 90° 105° 120°

A. 3xw 3w B. x w C. 3x xw D. 3 x E. 3w ⎛ 1 1⎞ 17. ⎜ − ⎟ – 1 = ⎝ 3 2⎠ A. B. C. D. E. −7 6 −5 6 −1 6 5 6 7 6

14. A coed soccer team has W women and M men on the team. If 4 women and 2 men are added to the team roster, and if one person on the team is selected at random to serve as team captain, then the probability that the team captain will be a woman can be represented as W +4 A. W + M + 6 W +4 B. W +M +2 W +4 C. M +2 W +4 D. W +M E. W M 15. What is the twenty-third decimal to the right in the fraction 23 ? 24 A. 1 B. 2 C. 3 D. 4 E. 5 16. If Scott has earned x dollars by working 3 days a week at a constant daily rate for w weeks, which of the following represents his daily wage?

18. In a certain conservative mutual fund, 70 percent of the money is invested in bonds, and of that portion, 40 percent is invested in highly rated corporate bonds. If at least \$1.4 million in this fund is invested in highly rated corporate bonds, what is the smallest possible total value for the mutual fund? A. B. C. D. E. \$4 million \$5 million \$6 million \$7 million \$8 million

19. If the diameter of a circle is 14, then the area of the circle is A. B. C. D. E. 7π 14π 28π 49π 196π

The following data sufficiency problems consist of a question and two statements, labeled (1) and (2), in which certain data are given. You have to decide whether the data given in the statements are sufficient for answering the question. Using the data given in the statements plus your knowledge of mathematics and everyday facts (such as the number of days in July or the meaning of counterclockwise), you must indicate whether

PRACTICE TEST 2

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A. B. C. D. E.

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. EACH statement ALONE is sufficient. Statements (1) and (2) TOGETHER are NOT sufficient.

(1) The average (arithmetic mean) age of UltraCorp employees is 32.8, while the average age of MegaTech employees is 27.2. (2) If the merger goes through and all employees from both companies remain employed, the average (arithmetic mean) age of the MegaUltraTech employees will be 31.4.
Solve the problem and indicate the best of the answer choices given.

20. If a is an integer, is b an integer? (1) The average (arithmetic mean) of a and b is an integer. (2) The average (arithmetic mean) of a, b, and b + 4 is a. 21. Did Alberto pay more than N dollars for his new stereo, excluding the sales tax? (1) The price Alberto paid for the stereo was 1.05N, including the sales tax. (2) Alberto paid \$35 in sales tax on the purchase of his new stereo. 22. Is r < 1? (1) r > 0 (2) r 2 < 0

26. In a sample of 800 high school students in which all students are either freshmen, sophomores, juniors, or seniors, 22 percent are juniors and 74 percent are not sophomores. If there are 160 seniors, how many more freshmen than sophomores are there among the sample of students? A. B. C. D. E. 42 48 56 208 256

27. The time it took car P to travel 600 miles was 2 hours less than the time it took car R to travel the same distance. If car P’s average speed was 10 miles per hour greater than that of car R, what was car R’s average speed, in miles per hour? A. B. C. D. E. 40 50 60 70 80

23. In the figure above, with B a point on the line AC, what is the measure of ∠XBZ ? (Figure not necessarily drawn to scale.) (1) BX bisects ∠ABY, which is a right angle, and BZ bisects ∠YBC. (2) ∠ABX = ∠XBY = ∠YBZ = ∠ZBC 24. If P and Q are both positive, what is the value of P ? (1) PQ is a positive multiple of 5. (2) 300 percent of P equals 500 percent of Q. 25. MegaTech and UltraCorp are considering a merger to form the MegaUltraTech Corporation. Does MegaTech have more employees than UltraCorp?

28. For any numbers a and b, a •b = ab(3 − b). If a and a • b both represent positive numbers, which of the following could be a value of b? A. B. C. D. E. −5 −2 2 4 7

29. Marcella has 25 pairs of shoes. If she loses 9 individual shoes, what is the greatest number of matching pairs she could have left?

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A. B. C. D. E.

21 20 19 16 15

30. If Finn was 18 months old one year ago, how old was he, in months, x months ago? A. B. C. D. E. x − 30 x − 12 18 − x 24 − x 30 − x

The following data sufficiency problems consist of a question and two statements, labeled (1) and (2), in which certain data are given. You have to decide whether the data given in the statements are sufficient for answering the question. Using the data given in the statements plus your knowledge of mathematics and everyday facts (such as the number of days in July or the meaning of counterclockwise), you must indicate whether A. B. C. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. EACH statement ALONE is sufficient. Statements (1) and (2) TOGETHER are NOT sufficient.

31. A restaurant orders 150 kg of pumpkins from the farmer’s market. The farmer fills the order with 23 pumpkins. The average mass of the first 20 pumpkins is 6.5 kg. What must be the minimum average mass of the remaining 3 pumpkins to fill the order? A. B. C. D. E. 5.5 kg 5.67 kg 6.67 kg 7 kg 11.5 kg

D. E.

34. If 5a = 9b = 15c, what is the value of a + b + c? (1) 3c − a = 5c − 3b (2) 6cb = 10a 35. Stanley has gained 8 pounds a year ever since he turned 18. How much weight has Stanley gained since he turned 18? (1) Stanley now weighs twice what he weighed when he turned 18. (2) Stanley is now twice the age he was when he turned 18. 36. What is the value of the greater of two numbers if one of the numbers is three times the smaller number? (1) One of the numbers is 12. (2) The sum of the two numbers is 16. 37. If r is a positive integer, what is the value of r ? (1) r < 70 (2) r > 7

32. The square root of 636 is between which set of integers? A. B. C. D. E. 24 and 25 25 and 26 26 and 27 27 and 28 28 and 29

33. In a forest 150 deer were caught, tagged with electronic markers, then released. A week later, 50 deer were captured in the same forest. Of these 50 deer, it was found that 5 had been tagged with the electronic markers. If the percentage of tagged deer in the second sample approximates the percentage of tagged deer in the forest, and if no deer had either left or entered the forest over the preceding week, what is the approximate number of deer in the forest? A. B. C. D. E. 150 750 1,250 1,500 2,500

PRACTICE TEST 2

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41 QUESTIONS

Verbal
TIME—75 MINUTES

The following questions present a sentence, part of which or all of which is underlined. Beneath the sentence, you will find five ways of phrasing the underlined part. The first of these repeats the original; the other four are different. If you think the original is best, choose the first answer; otherwise choose one of the others. These questions test correctness and effectiveness of expression. In choosing your answer, follow the requirements of standard written English; that is, pay attention to grammar, choice of words, and sentence construction. Choose the answer that produces the most effective sentence; this answer should be clear and exact, without awkwardness, ambiguity, redundancy, or grammatical error.

1. The gap in the ozone hole over the North Pole can expand each summer enough that it exposes regions as far south as Sweden by heightened UV radiation, also increasing rates of skin cancer in the northern regions by as much as 50 percent. A. that it exposes regions as far south as Sweden by heightened UV radiation, also increasing B. that regions as far south as Sweden have been exposed to heightened UV radiation, as well as having increased C. to expose regions as far south as Sweden to heightened UV radiation, increased D. to expose regions as far south as Sweden to heightened UV radiation and increase E. that exposure to heightened UV radiation in regions as far south as Sweden, as well as increasing 2. In winning the 1998 Kentucky Derby, Swiftilocks showed a burst of speed as that of Man o’War, who won 20 of 21 races in 1919 and 1920. A. B. C. D. E. as that of Man o’War, who won not unlike that of Man o’War, who won not unlike Man o’War, who won like that of Man o’War for winning like Man o’War and his winning

3. Rising tides of unemployment claims across the state has led the governor to declare the economy to be in a state of emergency. A. B. C. D. E. Rising tides Because the rising tide The tide is rising The rising tide The rising of the tide

4. Seeking to decrease the incidence of tooth decay, the American Dental Association is to spend \$45 million over the next seven years promoting good dental hygiene. A. the American Dental Association is to spend \$45 million over the next seven years promoting good dental hygiene B. the American Dental Association will spend \$45 million over the next seven years to promote good dental hygiene C. over the next seven years the American Dental Association is to spend \$45 million promoting good dental hygiene D. good dental hygiene will be promoted by the American Dental Association, which is spending \$45 million over the next seven years E. \$45 million will be spent by the American Dental Association over the next seven years on the promotion of good dental hygiene

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5. Some paleontologists claim that the discovery of what appear to be feathers in the fossil of an Archosaur could force a revision of current theories on the phylogeny of Archosaurs, alter conceptions of dinosaur skin surfaces, and require scholars to credit birds with a far earlier origin than previously thought. A. require scholars to credit birds with a far earlier origin than previously thought B. scholars may be required to credit birds with a far earlier origin than previously thought C. require a crediting by scholars of birds with a far earlier origin than previously thought D. , compared to what was previously thought, require scholars to credit birds with a far earlier origin E. crediting birds with a far earlier origin than scholars had previously thought
For the following questions, select the best of the answer choices given.

7. A pharmaceutical company tested a new diet drug over a two-month period. The test group of 100 dieters lost an average of five pounds per person during the first month, but gained an average of two pounds per person in the second month. All of the following could help explain the results of the experiment except: A. The second month of the test occurred during a holiday season, when people are more likely to gain weight. B. The diet drug has unpleasant side effects, causing many of the subjects to stop using the drug after the first month. C. The pharmaceutical company provided low-calorie diets to the test subjects in the first month, but let the dieters choose their own food in the second month. D. The pharmaceutical company selected for the test people who were 20 to 40 pounds over their ideal weights. E. The diet drug relies on a metabolic effect that loses efficacy the longer a person takes the drug. 8. The Tricounty Bridge was supposed to relieve traffic in East Countway County. Although the bridge was opened last year, traffic in the county has gotten worse over the last year. To relieve the traffic situation in East Countway, therefore, the traffic commission should order the Tricounty Bridge closed. Which of the following, if true, gives the most support to the conclusion of the passage above? A. The increased traffic seen in East Countway over the last year is largely attributable to a large casino and resort hotel that opened for business shortly after the opening of the Tricounty Bridge. B. The Tricounty Bridge allows inhabitants of heavily populated West Countway County to reach East Countway in less than a halfhour, as opposed to the two hours the trip required before the opening of the bridge. C. The bridge is only open for the periods 7–9 a.m. and 3–5 p.m. on weekdays. D. Ship captains on the Countway River have complained that the bridge disrupts shipping on the river, thereby hurting the local economy. E. The bridge is unlikely ever to pay for itself with the current low toll payment.
PRACTICE TEST 2 \$263

6. Covington College has four full-time Classics professors, but only 12 Classics majors. This three-to-one student-to-professor ratio is the lowest in the college. Since the college is facing financial difficulties, and since the tuition from just 12 students is not sufficient to pay the salaries of 4 full-time professors, the college should cancel the Classics program to reduce expenses. Which of the following, if true, most weakens the conclusion above? A. Professors in the Classics department teach popular language and literature classes that are attended by hundreds of students who are not Classics majors. B. Students at Covington College pay, on average, \$22,500 per year in tuition and fees, while the average professor of humanities receives a salary of \$61,500 per year. C. A well-regarded Classics program adds prestige to a college or university. D. The Classics department has already decreased in size from six full-time professors 10 years ago. E. The study of classical literature and languages is increasingly irrelevant to the high-tech workplace of today.

9. Alcohol-control advocates argue that television advertising plays a large role in leading teenagers to drink. In Hungary, however, where television advertising of alcoholic beverages has been prohibited since 1980, teenage alcohol use is higher than in some other European countries where such advertising is allowed. Which of the following statements draws the most reliable conclusion from the information given above? A. Hungarian culture, in general, views alcohol use more positively than do most other European cultures. B. Television advertising is the most effective way to encourage consumers to try a new alcoholic beverage. C. Television advertising cannot be the only factor that affects the prevalence of teenage drinking. D. Alcohol use among Hungarian teenagers has increased in recent years. E. Alcohol abuse is the greatest threat facing Hungarian teenagers.
The questions in this group are based on the content of a passage. After reading the passage, choose the best answer to each question. Answer all questions following the passage on the basis of what is stated or implied in the passage.

The complex life cycle of the Plasmodium protozoan, the causative agent of malaria, has contributed to the difficulty of devising effective public health measures to combat the disease. It took scientists centuries to deconstruct the basic relationship between protozoan, mosquito vector, and human host. Modern physiologists and epidemiologists are still working out the intricacies of malarial infection. The disease is transmitted by the bite of a female Anopheles mosquito infected with the Plasmodium parasite. Only Anopheles mosquitoes are capable of transmitting the disease, and only females take blood meals from humans. To become infected with Plasmodium, the female mosquito takes a blood meal from a human carrying the parasite in his or her blood. Once ingested, the parasite matures in the mosquito’s gut for approximately a week, after which it migrates to the insect’s salivary glands. By mixing with the mosquito’s saliva, the parasite

facilitates its transmission to a human host when the mosquito bites that human. Once in a human’s bloodstream, the parasite travels to the human’s liver. At this initial stage, the Plasmodium parasite is called a sporozoite. Within the liver, the sporozoite can form 30,000 to 40,000 daughter cells, called merozoites, which are released into the host’s bloodstream at a later date, sometimes within a week of the initial infection and sometimes as much as several months later. The merozoites seek out and attach themselves to red blood cells, in which they incubate 8 to 24 daughter cells over the next two days. When the daughter cells are mature, the red blood cell ruptures and the new parasites are released into the bloodstream to seek out red blood cells of their own. Some of the new merozoites become male and female gametocytes; if these gametocytes are ingested by a mosquito feeding on the host’s blood, they will fertilize in the mosquito’s gut to produce new sporozoites, and the cycle will continue. The symptoms that we associate with malaria—a high, recurring fever; joint pain; a swollen spleen— are caused by toxins released from the red blood cells ruptured by merozoites. The human spleen can destroy these infected blood cells, but the Plasmodium parasite counters this effect by increasing the stickiness of proteins on the blood cells’ surfaces so that the cells stick to the walls of blood vessels. If the sticky surface proteins affect a particularly large number of cells, the malaria can transform into a hemorrhagic fever, the most deadly form of malaria. A further complicating factor in the natural history of malaria is the many variants of the Plasmodium protozoan. Scientists now recognize that malaria is caused by at least six different species: P falciparum, P vivax, P ovale, P malariae, . . . . P knowesli, and P semiovale. Of these species, . . P falciparum accounts for the majority of infections . and approximately 90 percent of malarial deaths in the world.

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10. The passage is primarily concerned with which of the following? A. Describing the life cycle of the Plasmodium protozoan as it relates to the disease malaria B. Comparing and contrasting the life cycles of the six variants of the Plasmodium protozoan known to cause malaria C. Addressing the public health implications of the life cycle of the Plasmodium parasite D. Providing information on how a person can avoid infection with malaria E. Describing the life cycle of the Anopheles mosquito as it relates to the transmission of the Plasmodium protozoan to humans 11. Which of the following most accurately states the role of the first paragraph in relation to the passage as a whole? A. It summarizes two theories, the relative merits of which are debated in the passage. B. It puts forth an argument that the rest of the passage is devoted to refuting. C. It introduces a new concept that the rest of the passage expands upon. D. It frames the background and relevance of the material to follow. E. It outlines the major themes of each of the four paragraphs to follow. 12. If a mosquito were to bite a person, and that person were later to develop malaria and die of the disease, it is most likely that the person was infected with which of the following? A. B. C. D. E. Anopheles gambiae Anopheles semiovale Plasmodium malariae Plasmodium vivax Plasmodium falciparum

14. Based on the information given in the passage, which of the following would be most effective in preventing a person infected with malaria from developing a hemorrhagic fever? A. Surgical removal of the spleen B. A medicine that prevents changes to the surface proteins of red blood cells C. An effective vaccine against malaria D. A potent pesticide that reliably kills the Anopheles mosquito without producing any negative consequences for the environment or for human health E. A small infusion of a weaker variant of the Plasmodium protozoan that will then compete with the existing parasitic infection
For the following questions, select the best of the answer choices given.

15. In fisheries in general, when a large harvest is taken one year, there will be fewer fish available to be harvested in the following year, leading to decreasing yields of most fish species over time. The Maine lobster is an anomaly, however. Even though the vast number of lobster traps covering the New England coast pull in more lobsters every year, the number of lobsters in the water has shown no signs of decreasing. Which of the following, if true, most helps to explain the apparent anomaly concerning the number of Maine lobsters? A. The decline of other fish species in the region has deprived the lobster of its natural food source of scavenged fish. B. The bait in lobster traps provides abundant food for young lobsters, which are still small enough to swim out of the traps, leading to much higher survival rates among young lobsters than would be expected in nature. C. As global warming heats the waters of the Atlantic coastline, the Maine lobster has extended its northern range to well past Nova Scotia. D. The ever-increasing demand for lobsters in seafood restaurants and steakhouses across the country has driven a corresponding increase in the supply of the product. E. The increased lobster harvest has resulted in many juvenile lobsters but very few breeding-age lobsters, which could result in a crash in lobster numbers in the near future.

13. The relationship of a merozoite to a sporozoite is most like which of the following? A. A mother to a daughter B. A brother to a sister C. One of several subsidiaries spun off from a large corporation D. A computer program to a computer E. Orange juice to an orange tree

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16. Federal tax evasion is a serious crime that places an unfair tax burden on those members of society who pay their fair share. To reduce the incidence of tax evasion, the government needs to prosecute a few high-profile individuals whose cases will receive substantial media attention. The argument above relies on which of the following assumptions? A. The tax system is so complicated that even people who try to comply with it may inadvertently not pay some of their taxes. B. The average citizen will be less likely to evade taxes after he or she sees a high-profile individual prosecuted for tax evasion. C. Tax revenues collected from high-profile tax evaders will help to alleviate the unfair tax burden on honest citizens. D. Although it is difficult to secure a conviction on a charge of tax evasion, if the government focuses its efforts on a small number of high-profile individuals, the odds of obtaining a conviction will increase. E. While there is no universal measure for determining whether a taxation system is “fair” or “unfair,” the current system was constructed by Congress to represent the societal priorities and values of the American people. 17. Adam’s dog, a golden retriever named Hans, can respond to over 150 different commands. Adam cites this fact as evidence for his claim that Hans can understand the English language. Which of the following, if true, casts the most doubt on Adam’s claim that Hans can understand the English language? A. Each of the 150 commands to which Hans responds involves both a spoken word in English and a distinctive hand sign. B. Hans does not respond to the same commands when spoken to him by Adam’s French and Italian friends in their own languages. C. Scientists have demonstrated conclusively that canine vocal chords are incapable of

replicating many of the sounds used in the English language. D. Animal behaviorists have demonstrated that even very young dogs surpass both wolves and chimpanzees—animals that are thought to be more intelligent than dogs—in the ability to understand human nonverbal communication. E. The golden retriever is widely considered to be less intelligent than the border collie, and no border collie has ever been shown to truly understand the English language. 18. The Comfocar company manufactures a sedan that can drive comfortably at 80 miles per hour. A rival company, Turbocar, recently introduced a comparably equipped sedan that can drive comfortably at up to 110 miles per hour. Turbocar claims that its sedan will outsell Comfocar’s sedan because the Turbocar sedan can get customers to their destinations in comfort much faster than can the Comfocar sedan. Which of the following, if true, casts the most doubt on Turbocar’s claims? A. Customers in surveys consistently rank comfort among the most important criteria in purchasing a car. B. Many road surfaces are engineered to allow comfortable driving at speeds up to 120 miles per hour. C. Automotive safety experts state that it is not safe for any car to be driven faster than 100 miles per hour. D. Comprehensive research has determined that while the Turbocar model has faster acceleration and a higher top speed than the Comfocar sedan, both cars show approximately the same fuel efficiency. E. Nowhere in the main marketing areas for these two car companies is it legal or practical to drive faster than 70 miles per hour.
The following questions present a sentence, part of which or all of which is underlined. Beneath the sentence, you will find five ways of phrasing the underlined part. The first of these repeats the original; the other four are different. If you think the original is best, choose the first answer; otherwise choose one of the others.

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These questions test correctness and effectiveness of expression. In choosing your answer, follow the requirements of standard written English; that is, pay attention to grammar, choice of words, and sentence construction. Choose the answer that produces the most effective sentence; this answer should be clear and exact, without awkwardness, ambiguity, redundancy, or grammatical error.

has the same appeal to an illiterate shepherd wandering the steppes of Kazakhstan as to a professional musician sipping her latte in Paris. A. B. C. D. E. Kazakhstan as to Kazakhstan, just as to Kazakhstan; just as it would to a Kazakhstan, as it would to a Kazakhstan as a

19. Blues musician Paul “Poboy” Smith, born in Tupelo, Mississippi, in 1936, has since 1958 been a fixture on the southern blues scene after the release of his debut album in that year. A. Blues musician Paul “Poboy” Smith, born in Tupelo, Mississippi, in 1936, has since 1958 been a fixture on the southern blues scene after the release of his debut album in that year. B. Being born in 1936 in Tupelo, Mississippi, blues musician Paul “Poboy” Smith released his debut album in 1958 and has been a fixture on the southern blues scene since then. C. Born in Tupelo, Mississippi, in 1936, blues musician Paul “Poboy” Smith has been a fixture on the southern blues scene since the release of his debut album in 1958. D. Having been a fixture on the southern blues scene since 1958 when he released his debut album, Paul “Poboy” Smith is a blues musician who was born in 1936 in Tupelo, Mississippi. E. Since the release of his debut album in 1958, blues musician Paul “Poboy” Smith has been a fixture on the southern blues scene; he was born in Tupelo, Mississippi in 1936. 20. SEC regulations require that a public company disclose to their potential investors any legal, technological, or financial complications that could endanger their investments. A. B. C. D. E. a public company disclose to their a public company discloses to its a public company disclose to its public companies disclose to its public companies have disclosed to their

22. Mary, just as did the other students, objected to the squash casserole. A. Mary, just as did the other students, objected to B. Like the other students, Mary was objectionable to C. Mary, like the other students, objected to D. Mary objected, in the manner of the other students, to E. Mary, as the other students, objected 23. At the MegaTek Corporation, an inexperienced financial analyst mistook the rising cost of semiconductors as a seasonal fluctuation in the market. A. the rising cost of semiconductors as a seasonal fluctuation B. rise in price of semiconductors as a seasonal fluctuation C. rising cost of semiconductors for a seasonal fluctuation D. rising of the cost of semiconductors for a fluctuation by season E. rise of semiconductors in price to a seasonal fluctuation
The questions in this group are based on the content of a passage. After reading the passage, choose the best answer to each question. Answer all questions following the passage on the basis of what is stated or implied in the passage.

21. The genius of Beethoven can be seen in the widely observed phenomenon that his music

The collapse of the stock “bubble” of Internetrelated companies in 2000–2001 has resulted in more than its fair share of analysis, hand-wringing, and finger-pointing. A panel discussion at a recent Technology Today conference in Santa Monica produced a heated debate between two former luminaries of the dot.com world: investment banker Pat Verhofen and Sue Mickelson, founder and CEO of Internet retailer Frizbeez.com. Verhofen fired the opening shot by placing blame for the collapse of Internet stocks on the

PRACTICE TEST 2

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shoulders of Internet entrepreneurs who aggressively promoted ideas without viable business models. These entrepreneurs were both irresponsible and deceptive, Verhofen argued, to take investors’ money to fund operations that could not reasonably turn a profit, such as giving computers away for free or selling bulky objects, such as dog food or furniture, over the Internet. Many of these companies, he suggested, were little more than arrangements of smoke and mirrors designed to separate investors from their money. Mickelson responded that Verhofen was like a fox in a henhouse blaming the rooster for all the dead chickens. Entrepreneurs cannot be blamed, she argued, for trying to make money for themselves and other people, because that is what entrepreneurs do. She also stated that you cannot know what ideas will or will not work until you try them; contemporaries of the Wright brothers said that a heavier-than-air aircraft could never work, and look at the skies today. Mickelson instead placed the blame on the unscrupulous bankers and fund managers who hyped Internet stocks in order to cash in on fees from IPOs and trades. In contrast to entrepreneurs, these financial types actually do have a responsibility to offer only sound financial advice to their clients. If anyone should bear the blame, she argued, it should be people like Pat Verhofen. Indigo Smith, the moderator of the panel, responded that perhaps the true fault lay with the common investors, who should not have invested in technology stocks in the first place if they lacked the knowledge to do so properly. While she expressed sympathy for those elderly investors who lost substantial portions of their retirement savings on flimsy Internet stocks, she observed that no one forced them to invest in those stocks. 24. Which of the following best describes the structure of the passage? A. It mentions a puzzling situation, and then describes three approaches people have taken to help understand that situation. B. It presents an argument for why something took place, and then offers a refutation of that argument. C. It introduces a past phenomenon and then presents three explanations for why the phenomenon took place.

D. It describes a problem, offers a solution to the problem, and then offers reasons why the solution could not work. E. It offers three explanations for a phenomenon and then summarizes what all three have in common. 25. Which of the following statements presents the strongest conclusion one could draw based on the information given in the passage? A. The collapse of the Internet stock “bubble” drove thousands of investors into bankruptcy. B. People involved with the Internet do not all agree on which party bears the most responsibility for the collapse of the Internet stock “bubble.” C. Of all parties involved with the Internet, financial professionals such as investment bankers and fund managers derived the most profits from the stock “bubble.” D. The Internet stock “bubble” could not have occurred if entrepreneurs had been honest about the true financial prospects of their companies. E. The average investor has no one to blame but himself or herself if he or she invested in an Internet stock without adequately understanding the true financial prospects of the companies in question. 26. Which of the following best captures the meaning of the simile attributed to Mickelson that Verhofen “was like a fox in a henhouse blaming the rooster for all the dead chickens”? A. As an entrepreneur, Mickelson understands that similes and other figures of speech can help convey complex ideas to audiences. B. Verhofen, as an investment banker, was personally responsible for promoting businesses that he knew were not viable from a long-term perspective. C. Foxes, unlike roosters, have no legitimate business in henhouses, and are far more likely than roosters to kill chickens. D. As an investment banker, Verhofen was more likely to be the culprit of the crime than those he identified as responsible. E. Entrepreneurs cannot be blamed for trying to make money for themselves and other people because that is what they do.

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27. If Mickelson had not used the example of the Wright brothers in her argument, what other example might have illustrated her point as well? A. Despite widespread public opinion that the sun revolves around the earth, Galileo Galilei published findings showing that the earth revolved around the sun; he later retracted this assertion as a result of pressure from the Church. B. A tobacco company chose to market cigarettes to children despite widespread public opinion that such marketing is unethical; over the following decade, the company expanded its share of the tobacco market. C. A home electronics company devoted substantial development resources to eight-track audio technology despite widespread industry opinion that cassette tapes were the wave of the future; eighttracks were soon replaced by cassette tapes, which in turn were replaced by compact disks. D. A newspaper chose to publish a story that government lawyers said it could not print; the newspaper won its case against the government lawyers in a federal court, and the writer of the story won a Pulitzer Prize. E. A computer company initiated research into manufacturing a computer for home use when widespread public opinion held that computers could be useful only for large corporations or government agencies; personal home computers became a multibillion-dollar market. 28. If Verhofen’s arguments and statements are all correct, which of the following statements can accurately be inferred? A. Biotechnology executives who aggressively raise investment capital for bioengineered products with no conceivable market should be held responsible if biotechnology stocks crash. B. Investors should make financial decisions only with the advice of qualified financial advisors, such as investment bankers or fund managers.

C. If people lose money on investments that they inadequately researched, they have only themselves to blame. D. If insurance companies provide home insurance for homes built in a hurricane zone and those homes are subsequently all destroyed by a major hurricane, the insurance company should be blamed for any investment losses suffered by its shareholders. E. The collapse of Internet stocks would not have occurred if companies had not attempted to sell bulky items, like dog food, over the Internet.
The following questions present a sentence, part of which or all of which is underlined. Beneath the sentence, you will find five ways of phrasing the underlined part. The first of these repeats the original; the other four are different. If you think the original is best, choose the first answer; otherwise choose one of the others. These questions test correctness and effectiveness of expression. In choosing your answer, follow the requirements of standard written English; that is, pay attention to grammar, choice of words, and sentence construction. Choose the answer that produces the most effective sentence; this answer should be clear and exact, without awkwardness, ambiguity, redundancy, or grammatical error.

29. While some military planners claimed that it would be possible to win a war fought with nuclear weapons, many scientists argued that such a war could not truly be won, because the fallout from nuclear warfare would create a nuclear winter and it also would be rendering the earth uninhabitable. A. it also would be rendering the earth uninhabitable B. rendering the earth uninhabitable C. might have uninhabitably rendered the earth D. render the earth uninhabitable E. would also have rendered the earth uninhabitable

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30. Providing adequate public health-care facilities is a crucial task in a county like Travis, where more than 60 percent of household incomes are below the poverty line. A. where more than 60 percent of household incomes are B. where more than 60 percent of household income is C. which has more than 60 percent of the household incomes D. where they have more than 60 percent of household income E. where more than 60 percent of them have household incomes 31. Noted for its tenacity and courage, the English bulldog, having originally been bred for the brutal sport of bull-baiting, but now is cherished as a loyal animal companion. A. the English bulldog, having originally been bred for the brutal sport of bull-baiting, but now is cherished B. English bulldogs were originally bred for the brutal sport of bull-baiting, but they are now cherished C. English bulldogs were originally bred to bait bulls in a brutal sport, but it is now cherished D. the English bulldog was originally bred for the brutal sport of bull-baiting, but it is now cherished E. the English bulldog, originally bred to bait bulls for a brutal sport, is now being cherished 32. Advanced market research for the MegaTek Corporation predicts that launching a MegaTek Superstore in a given city would only succeed should the density of repeat customers have been greater than 200 per square mile. A. would only succeed should the density of repeat customers have been greater than B. will succeed only should the density of repeat customers be more numerous than C. will succeed only if the density of repeat customers is greater than D. should only succeed with a repeat customer density of greater than E. will succeed only with repeat customer density being greater than
For the following questions, select the best of the answer choices given.
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33. In order to increase revenues, a cell-phone company has decided to change its fee structure. Instead of charging a flat rate of \$20 per month and \$0.05 for every minute over 200 minutes, the company will now charge \$50 per month for unlimited usage. Which of the following is a consideration that, if true, suggests that the new plan will not actually increase the company’s revenues? A. A rival company, which charges no start-up fee, offers an unlimited calling plan for \$40 per month. B. Two-thirds of the company’s customers use less than 500 minutes per month. C. Studies have shown that customers using unlimited calling plans will increase their monthly usage of minutes by over 50 percent. D. One-fifth of the company’s customers use in excess of 1,000 minutes per month. E. In recent months the company has received several complaints of insufficient signal strength and poor customer service. 34. A real estate developer in Florida, desiring to protect his high-rise apartment building on the beach from hurricane damage, has planted sea oats in two rows in front of his building in order to encourage the development of sand dunes between the water and his building. Which of the following, if true, casts the most doubt on the probable effectiveness of the developer’s plan? A. Sand dunes provide little protection for tall buildings against the wind, which is sufficiently powerful even in minor hurricanes to cause serious damage to buildings. B. Sand dunes have been shown to provide effective protection against the storm surge, the pounding waves driven by hurricane-force winds onto dry land. C. Although sea oats will lead to the growth of sand dunes over many years, it would be far faster to build concrete bunkers between the building and the water. D. Hurricane insurance has become so expensive that many owners of beachfront property choose not to buy it. E. The developer has invested in reinforced steel girders and shatterproof glass as a way of minimizing damage to his building in the event that a hurricane hits the area.

35. According to local tradition, Sultan Abu ibn al-Hasan founded the East African trading state of Kilwa in the mid-tenth century. Professor Ascalon, however, argues that Sultan al-Hasan did not rule in Kilwa until at least a century later. Which of the following, if true, provides the strongest support for Professor Ascalon’s position? A. The Hunsu Kubwa Palace, the largest stone structure in sub-Saharan Africa prior to the eighteenth century, dates to the rule of Sultan Sulaiman in the fourteenth century. B. The oldest mosque on the island, which has traditionally been attributed to the reign of Abu ibn al-Hasan, has a foundation dating to ca. 800 C.E. C. The Kilwa Chronicle, a document based on Kilwa oral history that has been shown to be unreliable on matters of chronology, dates the rise to power of Sultan al-Hasan to the year 957 C.E. D. Silver and copper coins bearing the name of Abu ibn al-Hasan have been found in archeological sites dating from the late eleventh to the fourteenth centuries, but none have been found in sites dating earlier than the late eleventh century. E. Archeological records suggest that the island of Kilwa enjoyed a period of economic prosperity beginning in the mid-eleventh century. 36. In theory, Ecuador could be a major exporter of shrimp. In actuality, it is not. The explanation is that 80 percent of the country’s rich estuaries are owned by the government. This hurts Ecuador’s shrimp production, because the government does not have the flexibility necessary for efficient shrimp farming that private industry possesses. The answer to which of the following questions would be most relevant to evaluating the adequacy of the explanation given above? A. Who owns the 20 percent of estuaries that are not owned by the government? B. What percentage of Ecuador’s production of shrimp is consumed domestically? C. Has the government stated any plans to sell any of its estuaries to private industry, provided that the price is sufficient?

D. Is Peru, Ecuador’s neighbor to the south, actually better suited for commercial shrimp farming than Ecuador, which is a substantially smaller country? E. How does Ecuador’s shrimp production on government-owned estuaries compare to that on comparable land owned by private industry?
The questions in this group are based on the content of a passage. After reading the passage, choose the best answer to each question. Answer all questions following the passage on the basis of what is stated or implied in the passage.

One of the best sources modern scholars have for learning about Hellenistic Egypt is the large supply of papyrus fragments that have turned up in the Egyptian desert over the last century. Papyrus is a thick type of paper made from a reedy plant found in Egypt. Papyrus is much tougher than the wood-pulp paper used in modern society; whereas a book produced today will most likely fall apart within a century, there are papyrus fragments that are still legible over 2,000 years after scribes wrote on them. It is primarily by accident that any of these fragments have survived. Most of the surviving fragments have been found in ancient garbage dumps that were covered over by the desert and preserved in the dry heat. The benefit of this type of archeological find is that these discarded scraps often give us a more accurate picture of the daily lives of ancient Egyptians—their business affairs, personal correspondence, and religious pleas—than the stone engravings and recorded texts that were intended to be passed down to later generations. One of the most important papyrus discoveries of recent years was the revelation in 2001 that a scrap of papyrus that had been discarded and used to wrap a mummy contained 110 previously unknown epigrams (short, witty poems) by the Hellenistic poet Posidippus (ca. 280–240 B.C.). Posidippus lived in Alexandria and benefited from the support of King Ptolemy II Philadelphos (ruled 284–246 B.C.). These new epigrams have yielded fascinating insight into the court culture and literary sensibilities of early Hellenistic Egypt. King Ptolemy, of course, was also a sponsor of the famous library of Alexandria, the greatest depository of knowledge in the ancient world. According to the twelfth-century Byzantine writer John Tzetzes, the ancient library contained nearly half a million papyrus scrolls. If that library had not burned down, maybe archeologists today would not have
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to spend so much of their time sorting through ancient trash! 37. The author’s primary intention in this passage appears to be which of the following? A. To shed light on the underappreciated work of the Hellenistic poet Posidippus B. To compare the relative merits of papyrus and wood-pulp paper as media for recording information C. To discuss the ways in which papyrus fragments help scholars learn about Hellenistic Egypt D. To answer the questions regarding the burning of the library of Alexandria, one of the great mysteries of the ancient world E. To suggest possibly fruitful paths for future archeological research into Hellenistic Egypt 38. Which of the following would best illustrate how a discarded fragment of papyrus might give us a more accurate picture of the daily lives of ancient Egyptians than a record intended to be permanent? A. A poet such as Posidippus may have composed rough drafts of his epigrams on papyrus fragments prior to writing them in their final form. B. Grocery lists, which give insights into the diets of ancient people, would never be included in stone inscriptions but could be scribbled on scraps of papyrus. C. The Hellenistic monarchs employed some of the finest historians of the Greek world to provide chronicles of their reigns. D. Some papyrus fragments may have been used for purposes other than writing, such as binding wounds or wrapping small packages. E. Stone inscriptions describing military events often embellish the truth to favor whoever is paying for the inscription.

39. The mention of the discovery of 110 previously unknown epigrams by the poet Posidippus serves what purpose in the passage? A. Revealing insights into the nuances of court culture in Hellenistic Egypt B. Demonstrating how durable a material papyrus can be C. Arguing for a greater appreciation of this little-known Hellenistic poet D. Highlighting the importance of royal patronage in the development of arts and literature in the Hellenistic world E. Illustrating the kind of discovery that can be made from researching papyrus fragments 40. According to information given in the passage, which of the following locations would probably yield the highest probability of finding a previously undiscovered papyrus fragment? A. The ship of a royal messenger that sank off the Egyptian coast of the Mediterranean Sea in the third century B.C. B. The charred remnants of an ancient Egyptian palace that was burned by Roman troops in the first century B.C. C. The refuse heap of an ancient Egyptian town that was buried in the desert in the fifth century A.D. D. The private collections of French and British explorers from the nineteenth century A.D. who first uncovered many of the principal sites of Egyptian archeology E. The library of a Hellenistic fishing village that sank into the marshes of the Nile Delta in the third century A.D.

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41. What does the author imply by the final statement: “If that library had not burned down, maybe archeologists today would not have to spend so much of their time sorting through ancient trash!”? A. The author implies that if the library had not burned down, archeologists would be able to appreciate the full cultural legacy of King Ptolemy II Philadelphos. B. The author implies that if the library had not burned down, scholars today would have not only the full works of Posidippus, but also those of Aeschylus, Sophocles, and Euripides. C. The author implies that if the library had not burned down, the scrolls contained

within the library would have decomposed before modern times in any event, because they would not have been preserved in the dry heat of the desert. D. The author implies that if the library had not burned down, it might have contained more complete details about the life and culture of Hellenistic Egypt than can be found in the papyrus fragments from ancient refuse dumps. E. The author implies that if the library had not burned down, the cultural awakening of the Renaissance might have occurred centuries earlier.

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Practice Test 3
ANALYTICAL WRITING 1

f

Analysis of an Issue
TIME—30 MINUTES

People value things more when they have suffered for them. Discuss the extent to which you agree or disagree with the opinion stated above. Support your views with reasons and/or examples from your own experiences, observations, or reading.

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ANALYTICAL WRITING 2

Analysis of an Argument
TIME—30 MINUTES

directions: In this section, you will be asked to write a critique of the argument presented below. You may, for example, consider what questionable assumptions underlie the thinking, what alternative explanations or counterexamples might weaken the conclusion, or what sort of evidence could help strengthen or refute the argument. Read the argument and the instructions that follow it, and then make any notes that will help you plan your response. Write your response on a separate sheet of paper. If possible, type your essay on a word processor. Observe the 30-minute time limit.

A speaker at an electronic entertainment conference made the following statement: Video games have been widely criticized for having a negative effect on the nation’s youth. If one looks at the facts, however, over the last 25 years, the period in which the use of video games became common among the nation’s youth, math scores on the most commonly used college aptitude test have risen consistently, and entry-level salaries for college graduates have also risen significantly. This evidence suggests that video games are actually providing young people with the skills they need to succeed in college and in the workplace. Discuss how well reasoned you find this argument. In your discussion, be sure to analyze the line of reasoning and the use of evidence in the argument. For example, you may need to consider what questionable assumptions underlie the thinking and what alternative examples or counterexamples might weaken the conclusion. You can also discuss what sort of evidence would strengthen or refute the argument, what changes in the argument would make it more logically sound, and what, if anything, would help you better evaluate its conclusion.

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37 QUESTIONS

Quantitative
TIME—75 MINUTES

The following data sufficiency problems consist of a question and two statements, labeled (1) and (2), in which certain data are given. You have to decide whether the data given in the statements are sufficient for answering the question. Using the data given in the statements plus your knowledge of mathematics and everyday facts (such as the number of days in July or the meaning of counterclockwise), you must indicate whether

NOTE: In data sufficiency problems that ask for the value of a quantity, the data given in the statements are sufficient only when it is possible to determine exactly one numerical value for the quantity.

1. If x is an integer, is 18 + 54 an integer? x (1) 18 < x < 54 (2) x is a multiple of 18 2. If a > 0 and b > 0, is a > b ? b a (1) a = b − 2 (2) a = 1 4b 5

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. D. EACH statement ALONE is sufficient. E. Statements (1) and (2) TOGETHER are NOT sufficient. numbers: All numbers used are real numbers.
A figure accompanying a data sufficiency problem will conform to the information given in the question, but will not necessarily conform to the additional information given in statements (1) and (2). Lines shown as straight can be assumed to be straight, and lines that appear jagged can also be assumed to be straight. You may assume that the position of points, angles, regions, etc., exist in the order shown and that angle measures are greater than zero. All figures lie in a plane unless otherwise indicated.
FIGURES:

3. The figure above shows the shape of a flowerbed. If arcs WZ and XY are semicircles and WXYZ is a square, what is the area of the flowerbed? (1) The perimeter of square WXYZ is 24. (2) The diagonal WY = 6 2. 4. A total of 72 passengers are on a ship, and they go out on an excursion in boats R and Q. How many of the ship’s passengers are female? (1) There are 13 females on boat Q. (2) There are equal numbers of women on boats R and Q.

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5. In the xy plane, is the point (4, −2) on the line l ? (1) Point (1, 1) is on line l. (2) The equation x = 2 − y describes line l. Solve the problem and indicate the best of the answer choices given. numbers: All numbers used are real numbers. figures: A figure accompanying a problem-solving question is intended to provide information useful in solving the problem. Figures are drawn as accurately as possible EXCEPT when it is stated in a specific problem that its figure is not drawn to scale. Straight lines may sometimes appear jagged. All figures lie in a plane unless otherwise indicated.

9. In an animal behavior experiment, 50 tagged white pigeons and 200 tagged gray pigeons were released from a laboratory. Within one week, 88 percent of the white pigeons and 80.5 percent of the gray pigeons had returned to the laboratory. What percent of the total number of pigeons returned to the laboratory? A. B. C. D. E. 80.5 82 82.5 85 86.5

6. A type of extra-large SUV averages 12.2 miles per gallon (mpg) on the highway, but only 7.6 mpg in the city. What is the maximum distance, in miles, that this SUV could be driven on 25 gallons of gasoline? A. B. C. D. E. 190 284.6 300 305 312

10. In the circular region shown above, sections
3 5 A and B represent – and —, respectively, 8 11

7. The ratio of two quantities is 5 to 6. If each of the quantities is increased by 15, what is the ratio of these two new quantities? A. B. C. D. E. 5:6 25:27 15:16 20:21 It cannot be determined from the information given

of the area of the circular region. Section C represents what fractional part of the area of the circular region? A. 15 –– 88 2 B. –– 11 5 C. –– 22 45 D. –– 88 E. 73 –– 88 11. At the wholesale store you can buy an 8-pack of hot dogs for \$1.55, a 20-pack for \$3.05, and a 250-pack for \$22.95. What is the greatest number of hot dogs you can buy at this store with \$200? A. B. C. D. E. 1,108 2,100 2,108 2,124 2,256

8.

6 2 + 82 − 19 = A. 3 2 B. 8 C. 9 D. 10 E. 119

The following data sufficiency problems consist of a question and two statements, labeled (1) and (2), in which certain data are given. You have to decide whether the data given in the statements are sufficient for answering the question. Using the data given in the statements plus your knowledge of mathematics and everyday facts (such as the

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number of days in July or the meaning of counterclockwise), you must indicate whether A. B. C. D. E. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. EACH statement ALONE is sufficient. Statements (1) and (2) TOGETHER are NOT sufficient.

17. One day a car rental agency rented 2/3 of its cars, including 3/5 of its cars with CD players. If 3/4 of its cars have CD players, what percent of the cars that were not rented had CD players? A. B. C. D. E. 10% 35% 45% 66.7% 90%

18. If x is 20 percent greater than 88, then x = 12. What was the percent decrease in the price of MegaTek (MGTK) stock during the market decline of March 1, 2001, to March 1, 2002? (1) The price of MGTK was \$56.20 on March 1, 2001. (2) The price of the stock on January 1, 2002, was only one-quarter of its price as of March 1, 2001. 13. Greg’s long-distance telephone plan charges him \$0.50 for the first 4 minutes of a call, and \$0.07 per minute for each subsequent minute. Greg made a call to Carrie for x minutes, where x is an integer. How many minutes long was Greg’s call? (1) The last 7 minutes of Greg’s call cost \$0.22 less than the first 7 minutes of the call. (2) The call did not cost more than \$1.05. 14. If x and y are both positive numbers, is x greater than 75% of y ? (1) 5x > 4y + 1 (2) x = 6 15. Is xyz = 1? (1) x(y z) = 1 (2) 5z = 0 16. What is the average (arithmetic mean) of x and y ? (1) The average of x + 3 and y + 5 is 14. (2) The average of x, y, and 16 is 12. Solve the problem and indicate the best of the answer choices given. A. B. C. D. E. 68 70.4 86 105.6 108

19. A farmer with 1,350 acres of land had planted his fields with corn, sugar cane, and tobacco in the ratio of 5:3:1, respectively, but he wanted to make more money, so he shifted the ratio to 2:4:3, respectively. How many more acres of land were planted with tobacco under the new system? A. B. C. D. E. 90 150 270 300 450

20. 144 + 225 + 324 = A. B. C. D. E. 18 33 36 42 45

21. What is the perimeter of a square with
2 area 9P ? 16 A. 3P 4 2 B. 3P 4 C. 3P

D. 3P 2 E. 4P 3

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22. If a three-digit number is selected at random from the integers 100 to 999, inclusive, what is the probability that the first digit and the last digit of the integer will both be exactly two less than the middle digit? A. B. C. D. E. 1:900 7:900 9:1,000 1:100 7:100

A. B. C. D. E.

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. EACH statement ALONE is sufficient. Statements (1) and (2) TOGETHER are NOT sufficient.

26. In what year was Edward born? (1) In 1988, Edward turned 17 years old. (2) Edward’s sister Lisa, who is 14 months older than Edward, was born in 1970. 27. Is rs = rx − 2? (1) r is an odd number (2) x = s + 2 28. A CEO is building an extra-wide garage in which to park his limousines. The garage is x feet wide, and at least 2 feet of space is required between each two cars and between the cars and the walls. Will all 9 limousines fit in the garage? (1) The average width of the limousines is the square root of x. (2) x = 100. 29. If q + r + s = 45, what is the value of qr? (1) q = r = s (2) q − r − s = −15

23. Which of the following inequalities is equivalent to −4 < x < 8? A. x − 1 < 7 B. x + 2 < 6 C. x + 3 < 5 D. x − 2 < 6 E. None of the above 24. 80 − 6( 36 ÷ 9) = 1 4 A. B. C. D. E. 416 224 188 104 56

25. Three different lumberjacks can chop W amount of wood in 30 minutes, 45 minutes, and 50 minutes according to their different levels of skill with the axe. How much wood, in terms of W, could the two fastest lumberjacks chop in 2 hours? A. 6 2 W 3 B. 6 W 2 C. 4 W 3 D. 3 W E. 2 2 W 3
The following data sufficiency problems consist of a question and two statements, labeled (1) and (2), in which certain data are given. You have to decide whether the data given in the statements are sufficient for answering the question. Using the data given in the statements plus your knowledge of mathematics and everyday facts (such as the number of days in July or the meaning of counterclockwise), you must indicate whether

30. Is the triangle depicted above isosceles? (Figure not necessarily drawn to scale.) (1) 180° − (a + c) = 60° (2) a = 2b − c

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Solve the problem and indicate the best of the answer choices given.

31. Last year Jackie saved 5% of her annual salary. This year, she made 10% more money than last year, and she saved 8% of her salary. The amount saved this year was what percent of the amount she saved last year? A. B. C. D. E. 56% 76% 158% 176% 188% P 0 144 171 186 Q 144 0 162 X R 171 162 0 Y S 186 X Y 0

35. To be considered for “movie of the year,” a film must appear in at least 1 4 of the top/ 10-movies lists submitted by the Cinematic Academy’s 765 members. What is the smallest number of top-10 lists a film can appear on and still be considered for “movie of the year”? A. B. C. D. E. 191 192 193 212 213

P Q R S

36. In a sample of associates at a law firm, 30 percent are second-year associates, and 60 percent are not first-year associates. What percentage of the associates at the law firm have been there for more than two years? A. B. C. D. E. 10 20 30 40 50

32. The table above shows the one-way driving distance, in miles, between four cities: P, Q, R, and S. For example, the distance between P and Q is 144 miles. If the round trip between S and Q is 16 miles further than the round trip between S and R, and the round trip between S and R is 24 miles less than the round trip between S and P, what is the value of X? A. B. C. D. E. 174 182 186 348 364

37. Which of the following fractions has the greatest value? A.

( )( )
25

48 32

B. C.

( 24 )( 33 ) ( )( 32 )
23 6

12

33. If 35 percent of 400 is 20 percent of x, then x = A. B. C. D. E. 200 350 700 900 1,400

D.

( )( ) ( )( )
23 81 35

144 24 34

E.

34. 23 − 1 23 + 1 26 + 1 212 + 1 = A. B. C. D. E.

(

)(

)(

)(

)

( 224 − 1 ) ( 224 + 1 ) ( 248 − 1 ) ( 296 + 1 ) 26 ( 212 − 1 )
PRACTICE TEST 3 \$281

41 QUESTIONS

Verbal
TIME—75 MINUTES

The questions in this group are based on the content of a passage. After reading the passage, choose the best answer to each question. Answer all questions following the passage on the basis of what is stated or implied in the passage.

Forget hostile aliens. According to a forthcoming book by noted astrophysicist Egbert Larson, the intrepid humans who first attempt interstellar space travel will face far more daunting challenges before they ever meet the Little Green Men. Larson begins with the problem of relativistic time dilation. If you travel all the way to Alpha Centauri, you’d like to come back and tell your friends about it, right? It’s not too likely to happen, though. If Mr. Einstein was right about relativity— and we’re not going to say he wasn’t—then time slows down when you approach the speed of light. A person traveling at any velocity near the speed of light will age only days for every week, month, or even year that passes on earth. Relativity does not present a problem for interstellar space travel, per se, but it does mean that interstellar civilizations or even just interstellar communications will require a mind-boggling amount of calendar juggling. Did we mention that you’d have to travel at near the speed of light? That’s because the distance between stars is so vast that even if you could travel at the speed of light—which, Larson reminds us, you can’t—it would take more than four years to reach our closest star neighbors, Alpha Proxima and Alpha Centauri, and decades or centuries to reach the other stars in our “immediate neighborhood.” And if you tried to accelerate directly to the speed of light like they do in the movies, you’d be instantly splattered on the back

of your theoretical spacecraft. Achieving anything close to light speed will require sustained acceleration at a level that human bodies can withstand— say, a crushing two gravities—for over a year. Better hope somebody brings some chips. Speaking of chips, food is going to be a problem. Since it is economically, if not physically, impossible to accelerate 200 years’ worth of food to nearly the speed of light, and since you’re not likely to find any grocery stores along the way, someone will have to figure out how to make food in space. Keeping a crew alive on the way turns out to be the trickiest part of all. Once you’ve got the nearly impossible physics of space travel worked out, you still have to figure out the chemistry and biology of keeping your air and water clean and keeping your crew fed and safe from radiation and infection, and—did we mention the 200 years?—you’ll probably need several generations of crew members to complete the trip. Ever been on a bus for more than 24 hours? It’s not a pretty picture. We applaud Larson for his insightful writing and his scrupulous attention to scientific detail. For those of you seeking a cold, hard look at the reality of interstellar space travel, this is a stellar read. But be warned: Larson doesn’t let you down gently. For those of you sincerely hoping to beam up with Scotty—and you know who you are—you might want to give this one a pass.

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1. Which of the following would make the most

appropriate title for this passage? A. Going Boldly Where No One Has Gone Before: The Promise and Peril of Interstellar Space Travel B. The Day the Earth Stood Still: Why Interstellar Space Travel Is Essential to Human Survival C. The Wrath of Larson: Egbert Larson’s Quest to Build an Interstellar Spacecraft D. Busted Flat in Beta Regulus: The Crushing Challenges of Interstellar Space Travel E. Say It Isn’t So, Mr. Einstein: Egbert Larson’s Challenge to the Theory of Relativity 2. Based on the tone and content of the passage, it is most likely which of the following? A. A book review in a journal intended for astrophysics professionals B. A movie review in an entertainment industry publication C. A book review in a science magazine aimed at a general audience D. A book review in a newspaper E. A transcript of a talk given at a science fiction convention dedicated to “The poetry of space” 3. The passage implies that all except which of the following could be threats to human health during extended interstellar voyages? A. B. C. D. E. Meteor impact Radiation poisoning Accelerating too fast Starvation Old age

5. According to the information given in the passage, if two 20-year-old twins lived on earth, and one of them left on a journey for Alpha Centauri at very close to the speed of light, then managed to survive the journey and return to earth having aged 40 years during the journey, what could she expect to find upon her return to earth? A. B. C. D. E. Her great-grandmother Her twin at the age of 20 Her twin at the age of 40 Her twin at the age of 60 Her twin’s great-grandchildren

6. Which of the following inventions, if it could be perfected and manufactured at a viable cost, would address the most challenges to human interstellar space travel, as presented in the passage? A. A ram-scoop drive that can accelerate a spacecraft of any size to four-fifths of the speed of light within 24 hours B. A cold-sleep capsule that essentially halts the passage of time for human inhabitants while protecting them from all physical harm C. A sustainable biosphere that reliably generates healthy food and automatically cleans air and water D. A neutrino-based communications system that permits instantaneous communication across any distance without any relativistic time dilation E. An impervious force field that protects the ship and its inhabitants from radiation, meteor strikes, or hostile alien attacks

4. According to the passage, which of the following will present the most difficult challenge for humans attempting interstellar space travel? A. Achieving velocities near the speed of light B. Withstanding the acceleration necessary for traversing interstellar distances C. Maintaining clean air and water on a journey that could last centuries D. Accommodating the effects of relativistic time dilation E. Enabling the humans on board to survive during the journey

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7. The author of the passage most likely mentions “Little Green Men” in the first paragraph for what purpose? A. To poke fun at the ignorance of most science fiction readers B. To introduce a daunting challenge that will have to be addressed before human interstellar space travel can become possible C. To draw a comparison between the attempts of humans to voyage in space and the more successful attempts of other civilizations D. To draw an amusing distinction between a supposed danger of space travel, as presented in the popular media, and the actual challenges posed by interstellar space travel, as perceived by scientists E. To suggest that the concept of human interstellar space travel is as much of a myth as the “Little Green Men” that appear in science fiction movies and television programs
For the following questions, select the best of the answer choices given.

9. A brand of cough syrup comes with a measuring cup attached so that customers can measure the proper dosage. A consultant has pointed out that this cup is unnecessary, since most customers have measuring cups at home. Since the cups increase the cost of packaging the cough syrup and reduce the total number of units that can be shipped in a standard package, the consultant advises that the company can increase its net revenue on this product (total revenue minus total costs) by selling the cough syrup without the measuring cups. Which of the following, if true, provides the strongest evidence that the company should not follow the consultant’s advice? A. Studies have shown that customers who use cough syrup without a measuring cup frequently take either too little or too much of the medicine, rendering the dosage either ineffective or, in cases of overdose, dangerous. B. The company has included a measuring cup with each bottle of cough syrup for the last 18 years. C. Studies have shown that 85 percent of consumers possess at home either a measuring cup, a set of measuring spoons, or both. D. Many customers neglect to follow the recommended dosage of cough syrup even when the measuring cup is packaged along with the bottle of cough syrup. E. Shipping the cough syrup bottles without the measuring cups will provide a marginal improvement in the number of cough syrup bottles that can be shipped in a standard package.
The following two questions are based on the following passage:

8. A wholesale fruit distributor, in an effort to increase its profit margins, has proposed cutting the tops off of the pineapples it ships in order to increase the number of pineapples it can ship in a standard-size truck. Which of the following, if true, gives the strongest evidence that the fruit distributor’s plan will increase its profit margins? A. Pineapples with the tops cut off have been shown to rot three times faster than uncut fruit. B. Customers buy whole pineapples in part because of their exotic, spiky appearance. C. Cutting the tops off of pineapples may inadvertently remove some of the fruit within. D. The fruit distributor ships primarily to a fruit canning company that has no use for pineapple tops. E. Pineapple juice has been shown to be an even more potent source of vitamin C than orange or cranberry juice.

A study by a group of dentists has concluded that regular use of a certain brand of mouthwash is as effective as flossing in preventing gum disease. The mouthwash company has released a television ad suggesting that people who do not like flossing can now rely solely on mouthwash and brushing to maintain good dental health. A leading manufacturer of dental floss brought a lawsuit against the mouthwash company demanding that the advertisement be discontinued on the grounds that it is misleading.

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12. An electrical appliance company has submitted a new model of washing machine for stress and durability testing. After the conventional round of tests, 26 of the 90 machines tested no longer functioned. Observing these results, the company determined that the washing machine model was acceptable for the consumer market. Which of the following, if true, most strongly supports the company’s decision regarding the washing machine? A. When the number one–rated washing machine was submitted for stress and durability testing, 96 out of 100 machines were still functioning at the end of the test. B. Because of the extreme stress of the testing process, any model that has more than two-thirds of its machines functioning at the end of the test process is considered sufficiently durable for the consumer market. C. Most consumers will tolerate a washing machine that functions only 64 times out of 90 attempts. D. Although the model tested is less durable than other models on the market, its projected price is considerably lower than that of the most durable models. E. The electrical failure that brought down most of the 26 washing machines that ceased functioning could probably be avoided if the machine were redesigned.
The following questions present a sentence, part of which or all of which is underlined. Beneath the sentence, you will find five ways of phrasing the underlined part. The first of these repeats the original; the other four are different. If you think the original is best, choose the first answer; otherwise choose one of the others. These questions test correctness and effectiveness of expression. In choosing your answer, follow the requirements of standard written English; that is, pay attention to grammar, choice of words, and sentence construction. Choose the answer that produces the most effective sentence; this answer should be clear and exact, without awkwardness, ambiguity, redundancy, or grammatical error.

PRACTICE TEST 3

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13. Having accounted for only 13 percent of the student body at Northlake High, students who attended Megalopolis Middle School dominate the Northlake High student government. A. B. C. D. E. Having accounted for With Despite having been Although accounting for As

than people who do not use smokeless tobacco. A. be more prone to heart disease, hypertension, and mouth cancers B. are proner to heart disease, hypertension, and mouth cancers C. are more prone to heart disease, hypertension, and mouth cancers D. experience heart disease, hypertension, and mouth cancers at heightened rates E. suffer heart disease, hypertension, and mouth cancers at a higher risk 17. Chef Sylvia Bostock’s eclectic offerings at her new restaurant, Sylvia’s, range from an Asianinspired tuna tartelette in a soy-ginger demiglace with a succulent cowboy rib-eye served atop a small mountain of fried onions. A. B. C. D. E. with to in addition to and and to

14. Because the key witness died just prior to the start of the trial, Detectives Mack and Smith were not able in determining the extent of administrative corruption. A. Detectives Mack and Smith were not able in determining the extent of B. therefore the detectives, Mack and Smith, were unable to determine the extent of C. Mack and Smith, the detectives, were not able of determining the extent to D. Detectives Mack and Smith were not able to determine the extent of E. the extent was unable to be determined by Detectives Mack and Smith of 15. Health Department statistics demonstrate that children reading high on glucose with family histories of diabetes are twice as likely as the general population to develop diabetes. A. reading high on glucose with family histories of diabetes B. with high glucose readings whose families have a history of diabetes C. with high glucose readings and who have a diabetic history in the family D. having high glucose readings and also having histories of diabetes in their family E. with a history of diabetes running in the family and with high glucose readings 16. Medical experts have amassed evidence concluding that users of smokeless tobacco be more prone to heart disease, hypertension, and mouth cancers

18. The governing board of the new league has modified its rules so that preexisting teams can stay together even though not all their members meet the new minimum age requirement. A. not all their members meet the new minimum age requirement B. the new minimum age requirement has not been met by all their members C. not all their members have met the new minimum age, as required D. all their members have not met the new minimum age requirement E. all their members do not meet the new minimum age requirement

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For the following questions, select the best of the answer choices given.

19. Since 1960, the fast-growing town of Hotstone, Arizona, has drawn water from the Gray River, which feeds Lake Mudfish. If the town’s water use continues to grow at its present rate, in about 20 years the water level of Lake Mudfish will inevitably decrease to the point that it can no longer support its biologically fragile population of fish. The prediction above is based on which of the following assumptions? A. As the town’s water requirements grow, it will not be able to meet those requirements by drawing on water sources other than the Gray River. B. Since 1960, the lake’s population of fish has become more biologically fragile. C. The amount of water that the lake loses to evaporation each year will increase over the next two decades. D. There are multiple sources of water besides the Gray River that feed into Lake Mudfish. E. The town of Hotstone will be able to reverse its trend of increasing water use if it implements an aggressive water conservation program. 20. Public protests can cause even the most powerful companies to change their policies. For example, an activist group recently staged a demonstration in front of the HydraBore corporate headquarters to protest the company’s use of the chemical Ectomazathol. Within three months of the demonstration, HydraBore replaced Ectomazathol in its production plants with another chemical. Which of the following, if true, casts the most doubt on the connection between the public protest and the decision of the company to change chemicals? A. Preliminary studies show that the new chemical may be more carcinogenic than Ectomazathol. B. The recently introduced chemical that is replacing Ectomazathol is less expensive

and more effective in its industrial application than Ectomazathol. C. HydraBore devoted no publicity efforts to announce its switch from Ectomazathol to the new chemical. D. As protests against HydraBore have become more frequent, the company has subsequently increased its public relations budget. E. The activist group that staged the demonstration has been linked to illegal acts of theft and sabotage within other corporate headquarters. 21. A recent spate of art thefts at a major museum has led to a drastic increase in the insurance premiums that the museum must pay to insure its collection. Many art fans are concerned that the museum, which traditionally has charged no entrance fee, will be forced to charge a high entrance fee in order to pay for the increased insurance premiums. Which of the following, if true, would most alleviate the concern of the art fans that the museum will be forced to charge high entrance fees? A. Law enforcement officials recently apprehended the Belgian Bobcat, a notorious art thief who has been linked to at least 20 art heists. B. Citing a dispute with the insurance company over the terms of its coverage, the museum has chosen to cancel its insurance policy. C. The majority of visitors to the museum are schoolchildren, who could not reasonably be expected to pay a high entrance fee. D. The museum pays for the majority of its total expenses from its large endowment, which is earmarked specifically for purchasing new art. E. The museum recently installed a state-ofthe-art burglar alarm system that will make future thefts almost impossible.

PRACTICE TEST 3

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22. Which of the following, if true, best completes the passage below? The traditional view of Homer is that of a blind bard who wrote down the epic poems known as the Iliad and the Odyssey in the eighth century B.C.E. We know now, however, that this picture cannot be true. The language used in the epic poems contains elements of the Greek language dating from the twelfth to the eighth centuries B.C.E., but the Greek writing system was not developed until the late seventh century, when it was used to record clerical notes. A more accurate statement regarding Homer, therefore, is that, if he existed, he most likely ______________. A. wrote the poems down in the fifth century B.C.E., using a preexisting oral tradition of Greek epic poetry. B. was involved in the recording of clerical notes in Greek in the seventh century. C. composed the poems orally in the eighth century and then dictated them to a scribe in the late seventh century. D. composed the poems orally in the twelfth century, using a predecessor of the Greek language. E. composed the poems orally in the eighth century, using elements of preexisting Greek epic poetry.
The questions in this group are based on the content of a passage. After reading the passage, choose the best answer to each question. Answer all questions following the passage on the basis of what is stated or implied in the passage.

that they can better protect and preserve these cultural treasures than can the developing nations and impoverished ethnic groups that frequently seek their return. They further argue that more people can see the treasures if they are proudly displayed in a major museum, as opposed to some poorly funded national museum in a backwater country; evidently, the quantity of viewers is more important than the relevance of the art and artifacts to the viewer. The arguments of the museum curators fall apart in an instance such as the Elgin Marbles. These majestic marble sculptures, which once graced the Parthenon on the Acropolis in Athens, were stolen by Lord Elgin in the nineteenth century and given to the British Museum, which holds them to this day. The people of Athens have built a beautiful, modern museum on the Acropolis to display the Elgin Marbles and other treasures from the Greek cultural heritage, so there can be no valid argument that the Greeks are unable to house the sculptures properly. Furthermore, more people visit the Acropolis every day than visit the British Museum. 23. Of the following, the most appropriate title for the passage above would be: A. The Elgin Marbles: Timeless Symbols of the Glory That Was Greece B. The Role of Great Museums in the Preservation of Cultural Artifacts C. Repatriation of Cultural Treasures: The British Museum’s Dirty Little Secret D. The Value of Cultural Treasures in Defining National Identity E. A Curious Curator: Lord Elgin and the Rise of the British Museum 24. The third paragraph plays what role in the passage? A. It summarizes all the points expressed in the first two paragraphs. B. It raises new arguments that expand on those previously expressed. C. It suggests a possible area for useful research in the future. D. It rejects the arguments expressed in the first paragraph. E. It provides concrete evidence against arguments expressed in the second paragraph.

One of the biggest questions facing the art world today is the dilemma over the repatriation of cultural treasures. Although the subject has not been widely noted by the general public, in recent decades museums and art dealers have repeatedly faced off against the representatives of nations and ethnic groups whose cultural legacies have been robbed by the rapacious collecting of these so-called art experts. Advocates of repatriation have argued that cultural treasures should be returned to their nations of origin, both because of basic fairness and because the artwork and cultural artifacts in question are best understood within their local context. Several prominent museums, most notably the British Museum in London and the Louvre in Paris, have defended themselves on the grounds

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25. The situation involving the repatriation of the Elgin Marbles to Athens is most similar to which of the following? A. A Native American tribe in Oregon requests that a museum in Chicago return some ceremonial masks that could help in fundraising efforts to build a proposed museum in Portland. B. The nation of Peru in South America threatens the nation of Ecuador with military action if Ecuador does not hand over various gold artifacts of the Inca Empire, which originated in Peru. C. The National Archeology Museum of Cairo in Egypt requests that the Louvre return eight mummies from the time of Ramses the Great for the Cairo Museum’s new exhibit hall dedicated to artifacts from Ramses’ court. D. The nation of Greece requests the nation of Turkey to provide Greek archeologists with free access to ancient Greek sites on the Ionian coast of Turkey, and to transfer any cultural artifacts found there to the National Archeology Museum in Athens. E. A museum in Baton Rouge, Louisiana, requests that the Texas History Museum in Austin, Texas, send the original “Lone Star” flag to Baton Rouge for a new exhibit entitled, “Texas: Our Neighbor to the East.” 26. What is the purpose of the final sentence of the passage? A. To express pride in the cultural treasures of Athens B. To refute the argument that more people can see the Elgin Marbles at the British Museum than at the Acropolis C. To comment on the relative number of tourists at two of Europe’s most famous tourist attractions D. To express concern that the large number of tourists on the Acropolis will damage the Elgin Marbles, should they be returned E. To provide an appropriate end to a rousing debate 27. The author’s attitude toward museum curators who oppose the repatriation of cultural treasures is best summarized as what?

A. B. C. D. E.

Righteous indignation Bemused sarcasm Seething anger Condescending approval Grudging admiration

28. Which of the following, if true, would best support the position taken by the advocates of repatriation, as expressed in the first paragraph? A. Of seven gold Inca statues sent from the Field Museum in Chicago to the National Archeology Museum in Lima, Peru, four were stolen within six months of being put on display. B. Mummies taken from the dry heat of Egypt and relocated to the damp climate of London have shown disturbing signs of decay. C. Operating a first-rate art and archeology museum is financially unfeasible for most developing nations, which face a difficult enough challenge feeding their people. D. A type of sculpture from central Africa appears dull and nondescript in a museum setting, but when placed in the region of its origin can clearly be seen to replicate the colors and shapes of local rock formations. E. British colonists in India in the nineteenth century felt that it was their right to claim the nation’s artistic treasures as their own in exchange for importing the benefits of a modern industrial society.
The following questions present a sentence, part of which or all of which is underlined. Beneath the sentence, you will find five ways of phrasing the underlined part. The first of these repeats the original; the other four are different. If you think the original is best, choose the first answer; otherwise choose one of the others. These questions test correctness and effectiveness of expression. In choosing your answer, follow the requirements of standard written English; that is, pay attention to grammar, choice of words, and sentence construction. Choose the answer that produces the most effective sentence; this answer should be clear and exact, without awkwardness, ambiguity, redundancy, or grammatical error.

PRACTICE TEST 3

\$289

29. According to government health statistics, Americans born before 1925 develop obesity by the age of 65 only 8 percent of the time, but 35 percent of those born since 1950 did so by age 35. A. Americans born before 1925 develop obesity by the age of 65 only 8 percent of the time, but 35 percent of those born since 1950 did so by age 35. B. Only 8 percent of Americans born before 1925 developed obesity by the age of 65; if they are born since 1950, 35 percent develop obesity by the age 35. C. Only 8 percent of Americans born before 1925 developed obesity by the age of 65; of those born since 1950, 35 percent developed obesity by the age of 35. D. Obesity develops by the age of 65 in only 8 percent of Americans born before 1925, and by 35 by the 35 percent born since 1950. E. Of Americans born before 1925, only 8 percent of them have developed obesity by the age of 65, but 35 percent of those born since 1950 do by the age of 35. 30. In his groundbreaking work on special relativity, Albert Einstein displayed an intellectual boldness in the face of a reluctant scientific establishment that was not unlike that of Galileo Galilei, who refused to accept the intellectual limits placed on him by the censors of the Church. A. B. C. D. E. not unlike that of Galileo Galilei, who refused like Galileo Galilei and his refusal not unlike Galileo Galilei, who refused like that of Galileo Galilei for refusing as that of Galileo Galilei, who refused

opted to settle the lawsuit rather than facing the protracted legal expenses of a court battle. A. have opted to settle the lawsuit rather than facing B. have opted settling the lawsuit instead of facing C. have opted to settle the lawsuit rather than face D. had opted for settlement of the lawsuit instead of facing E. had opted to settle the lawsuit rather than face 33. The ManStop, Boston’s hot new men’s clothing store, offers a selection that is on range from conservative pin-striped suits for that day at the office to stylish cashmere pullovers for that night on the town. A. B. C. D. E. is on range from ranging from ranges to ranges from having ranged from

For the following questions, select the best of the answer choices given.

34. An agricultural cooperative wants to sell more of its less popular vegetables, zucchini in particular. A consultant has suggested that the cooperative’s farmers should attempt to market a purple form of zucchini instead of the conventional green form, because people generally dislike green-colored vegetables. Which of the following, if true, casts the most doubt on the accuracy of the consultant’s assertion? A. Broccoli and green peas, which are both green vegetables, are among the most popular vegetables in the country. B. Grapes and eggplants, which both have purple skin, are popular among consumers of all ages. C. Summer squash, a yellow-colored cousin of the zucchini, is one of the most popular summer vegetables. D. Green tomatoes are far less popular than red tomatoes. E. A chewing gum company reports that its purple-colored grape gum is less popular than its green-colored sour apple flavor.

31. The rising of the rate of tardiness among MegaTech employees has generated concern among management that the employees are not sufficiently focused on increasing shareholder value. A. B. C. D. E. The rising of the rate Rising rates The rising rate Because of the rising rate Because the rising rate

32. Increasingly over the last few years, corporations involved in patent litigation have

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THE PRACTICE TESTS

35. Homely Hotels has a customer loyalty program in which for every four nights a customer spends at a Homely Hotel, he or she receives a coupon good for one free night at any Homely Hotel. Recently people have begun selling these coupons on the Internet for less than the cost of a night at a Homely Hotel. This marketing of coupons has resulted in decreased revenue for the Homely Hotel chain. To discourage this undesirable trade in free-stay coupons, it would be best for Homely Hotels to restrict: A. The number of coupons a customer can receive in one year. B. Use of the coupons to the specific hotel in which they were issued. C. The valid dates of the coupons to only the month immediately following the date of issue. D. Use of the coupons to the recipient or people with the same last name. E. Use of the coupons to Homely Hotel franchises that charge an equal or lesser nightly rate than the franchise that issued the coupon. 36. An American manufacturer of space heaters reported a 1994 fourth-quarter net income (total income minus total costs) of \$41 million, compared with \$28.3 million in the fourth quarter of 1993. This increase was realized despite a drop in U.S. domestic retail sales of space-heating units toward the end of the fourth quarter of 1994 as a result of unusually high temperatures. Which of the following, if true, would contribute most to an explanation of the increase in the manufacturer’s net income? A. In the fourth quarter of 1994, the manufacturer paid its assembly-line workers no salaries in November or December because of a two-month-long strike, but the company had a sufficient stock of space-heating units on hand to supply its distributors. B. In 1993, because of unusually cold weather in the Northeast, the federal government authorized the diversion of emergency funding for purchasing space-heating units to be used in the hardest-hit areas.

C. Foreign manufacturers of space heaters reported improved fourth-quarter sales in the American market compared with their sales in 1993. D. During the fourth quarter of 1994, the manufacturer announced that it would introduce an extra-high-capacity space heater in the following quarter. E. In the third quarter of 1994, a leading consumer magazine advocated space heaters as a cost-effective way to heat spaces of less than 100 square feet.
The following questions present a sentence, part of which or all of which is underlined. Beneath the sentence, you will find five ways of phrasing the underlined part. The first of these repeats the original; the other four are different. If you think the original is best, choose the first answer; otherwise choose one of the others. These questions test correctness and effectiveness of expression. In choosing your answer, follow the requirements of standard written English; that is, pay attention to grammar, choice of words, and sentence construction. Choose the answer that produces the most effective sentence; this answer should be clear and exact, without awkwardness, ambiguity, redundancy, or grammatical error.

37. Archeological excavations of Roman ruins on the Greek island of Crete show that securing control over the maritime trade routes of the Eastern Mediterranean was a primary goal of the Romans, as it was of the Greeks in preceding centuries. A. B. C. D. E. as it was of the Greeks like that of the Greeks as that of the Greeks just as the Greeks did as did the Greeks

38. The family’s mood, which had been enthusiastic at the beginning of the trip, sank as the temperature has risen, dramatically, but not enough for calling off the whole trip. A. has risen, dramatically, but not enough for calling B. has risen, but not dramatically enough to call C. rose, but not so dramatically as to call D. rose, but not dramatically enough to call E. rose, but not dramatically enough for calling

PRACTICE TEST 3

\$291

39. Although no proof yet exists of the electromagnetic disturbances observed being the results of nuclear weapons testing, diplomats are treating the situation with utmost delicacy. A. of the electromagnetic disturbances observed being the results of nuclear weapons testing B. regarding the observed electromagnetic disturbances having been the results of nuclear weapons testing C. that the electromagnetic disturbances observed were the results of nuclear weapons testing D. that nuclear weapons testing resulted in the electromagnetic disturbances having been observed E. that the electromagnetic disturbance observed were resulting from nuclear weapons testing 40. Hip dysplasia is more common among German shepherds than dogs of other breeds. A. B. C. D. E. than than is so of compared to in comparison with than among

A. The only lucid arguments printed in the newspaper concerning the new bond proposal was put forth by the high school principal in a series of letters to the newspaper’s editor. B. The principal of the high school wrote a series of letters to the newspaper’s editor that put forth the only lucid argument concerning the new bond proposal that was printed in the newspaper. C. In a series of letters to the newspaper’s editor, the principal of the high school put forth the only lucid argument concerning the new bond proposal to be printed in the newspaper. D. The high school’s principal’s series of letters to the newspaper’s editor lucidly put forth the only arguments concerning the new bond proposal to be printed in the newspaper. E. Putting forth the only lucid arguments concerning the new bond proposal to be printed in the newspaper, the series of letters to the newspaper’s editor were written by the high school’s principal.

41. The only lucid arguments printed in the newspaper concerning the new bond proposal was put forth by the high school principal who wrote a series of letters to the newspaper’s editor.

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THE PRACTICE TESTS

Practice Test 4
ANALYTICAL WRITING 1

d

Analysis of an Issue
TIME—30 MINUTES

Since unhealthy people increase health-care costs for all of society, society should impose greater penalties on those people who voluntarily indulge in unhealthy activities, such as smoking, excessive drinking, or overeating. Discuss the extent to which you agree or disagree with the opinion stated above. Support your views with reasons and/or examples from your own experiences, observations, or reading.

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ANALYTICAL WRITING 2

Analysis of an Argument
TIME—30 MINUTES

directions: In this section, you will be asked to write a critique of the argument presented below. You may, for example, consider what questionable assumptions underlie the thinking, what alternative explanations or counterexamples might weaken the conclusion, or what sort of evidence could help strengthen or refute the argument. Read the argument and the instructions that follow it, and then make any notes that will help you plan your response. Write your response on a separate sheet of paper. If possible, type your essay on a word processor. Observe the 30-minute time limit.

The following statement appeared in a consumer magazine: A fear of crime has led many homeowners to purchase monitored burglar alarm systems, but these people are wasting their money. The primary benefit of any burglar alarm system is one of deterrence, and this effect can be achieved just as well by having a sign in front of the house suggesting that the house is equipped with an alarm, whether or not the alarm system is monitored or even exists. Moreover, if a sign fails to deter burglars from entering a house, there is very little chance that the guards who monitor the alarm system will arrive at the home in time to catch the burglars, since the burglars will surely leave as soon as the alarm sounds. Therefore, while it makes sense to have a sign suggesting that a house has a monitored alarm, and it may make sense to have an audible alarm, there is no reason to pay the high monthly fee for a monitored system. Discuss how well reasoned you find this argument. In your discussion, be sure to analyze the line of reasoning and the use of evidence in the argument. For example, you may need to consider what questionable assumptions underlie the thinking and what alternative examples or counterexamples might weaken the conclusion. You can also discuss what sort of evidence would strengthen or refute the argument, what changes in the argument would make it more logically sound, and what, if anything, would help you better evaluate its conclusion.

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THE PRACTICE TESTS

37 QUESTIONS

Quantitative
TIME—75 MINUTES

The following data sufficiency problems consist of a question and two statements, labeled (1) and (2), in which certain data are given. You have to decide whether the data given in the statements are sufficient for answering the question. Using the data given in the statements plus your knowledge of mathematics and everyday facts (such as the number of days in July or the meaning of counterclockwise), you must indicate whether

note: In data sufficiency problems that ask for the value of a quantity, the data given in the statements are sufficient only when it is possible to determine exactly one numerical value for the quantity.

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. D. EACH statement ALONE is sufficient. E. Statements (1) and (2) TOGETHER are NOT sufficient. numbers: All numbers used are real numbers. figures: A figure accompanying a data sufficiency problem will conform to the information given in the question, but will not necessarily conform to the additional information given in statements (1) and (2). Lines shown as straight can be assumed to be straight, and lines that appear jagged can also be assumed to be straight. You may assume that the position of points, angles, regions, etc., exist in the order shown and that angle measures are greater than zero. All figures lie in a plane unless otherwise indicated.

1. In the figure above, is AB > BC ? (Note: Figure not necessarily drawn to scale.) (1) AB > CD (2) (AD − AB) > (AD − BC) 2. A box contains 90 jelly beans, of which some are orange, some are purple, and some are black. How many black jelly beans are in the box? (1) There are 27 orange jelly beans. (2) There are twice as many purple jelly beans as orange jelly beans. 3. Is 3x greater than 100? (1) 9x = 36 (2) 1 > 0.01 3x 4. How many more dogs than cats are in the veterinarian’s office? (1) There is a total of 30 dogs and cats in the office. (2) The number of cats is the square root of the number of dogs.

PRACTICE TEST 4

\$295

5. If p is a positive integer, and p an integer? (1) p is an even number. (2) p is a multiple of 3.

0, is

p2 + p 2p

Solve the problem and indicate the best of the answer choices given.

9. A travel company wants to charter a plane to the Bahamas. Chartering the plane costs \$8,000. So far, 18 people have signed up for the trip. If the company charges \$300 per ticket, how many more passengers must sign up for the trip before the company can make any profit on the charter? A. B. C. D. E. 7 9 13 27 45

numbers: All numbers used are real numbers. figures: A figure accompanying a problem-solving question is intended to provide information useful in solving the problem. Figures are drawn as accurately as possible EXCEPT when it is stated in a specific problem that its figure is not drawn to scale. Straight lines may sometimes appear jagged. All figures lie in a plane unless otherwise indicated. 6. A certain prosthodontist specializes in implanting gold and silver teeth in his patients’ mouths. He charges \$650 for a gold tooth and \$325 for a silver tooth. If his total fees for implanting gold and silver teeth last week were \$15,925 in total, and he implanted five more gold teeth than silver teeth, how many teeth in total did he implant over the week? A. B. C. D. E. 31 32 33 34 35

10. If x 2 + 9x − 3 = 3x 2 + 2x( 4 − x ) , then x2 = A. B. C. D. E. 2 3 4 9 16

11. The pilot of a small aircraft with a 40-gallon fuel tank wants to fly to Cleveland, which is 480 miles away. The pilot recognizes that the current engine, which can fly only 8 miles per gallon, will not get him there. By how many miles per gallon must the aircraft’s fuel efficiency be improved to make the flight to Cleveland possible? A. B. C. D. E. 2 4 12 40 160

7. What is the ratio of 3/7 to the product 3(7/3)? A. B. C. D. E. 3:7 1:3 3:21 1:7 3:49

8. If the average (arithmetic mean) of a and b is 110, and the average of b and c is 160, what is the value of a – c ? A. B. C. D. E. −220 −100 100 135 It cannot be determined from the information given

12. A circle graph shows how the MegaTech corporation allocates its Research and Development budget: 14% microphotonics; 24% home electronics; 15% food additives; 29% genetically modified microorganisms; 8% industrial lubricants; and the remainder for basic astrophysics. If the arc of each sector of the graph is proportional to the percentage of the budget it represents, how many degrees of the circle are used to represent basic astrophysics research? A. B. C. D. E. 8 10 18 36 52

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THE PRACTICE TESTS

The following data sufficiency problems consist of a question and two statements, labeled (1) and (2), in which certain data are given. You have to decide whether the data given in the statements are sufficient for answering the question. Using the data given in the statements plus your knowledge of mathematics and everyday facts (such as the number of days in July or the meaning of counterclockwise), you must indicate whether A. B. C. D. E. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. EACH statement ALONE is sufficient. Statements (1) and (2) TOGETHER are NOT sufficient.

Solve the problem and indicate the best of the answer choices given.

17. An engineer designed a ball so that when it was dropped, it rose with each bounce exactly one-half as high as it had fallen. The engineer dropped the ball from a 16-meter platform and caught it after it had traveled 46.5 meters. How many times did the ball bounce? A. B. C. D. E. 5 6 7 8 9

The following two questions refer to the following diagram:

13. If x + y = 36, what is the value of xy ? (1) y − x = 14 (2) y = 2x + 3 14. A hotdog vendor sold \$45 worth of hotdogs at lunchtime Tuesday. Each hotdog cost \$1.50. What percentage of his day’s stock of hotdogs did the vendor sell at lunchtime? (1) The vendor started the day with 120 hotdogs. (2) The vendor sold twice as many hotdogs at dinnertime as he sold at lunchtime. 15. For real numbers a, b, and c, is ab = bc + 3? (1) ab = 3b (2) b + 3 = c 16. What is the number of male employees at the factory? (1) If the factory were to hire 150 more employees and 2/3 of them were female, the ratio of male to female employees would be 8:3. (2) The factory has at least twice as many male employees as female employees, and it employs at least 150 females.

A newspaper polled 1,000 likely voters about which of the following issues, if any, played an important role in their decision-making process for an upcoming election: education, crime, and/or taxes. Of the voters surveyed, a total of 495 named education, 490 named crime, and 440 named taxes. In the figure above, the overlapping areas between two circles represent the people who named only those two items; the overlapping area between the three circles represents those people who named all three issues. 18. What percentage of those polled named only education or only crime but no other issue? A. B. C. D. E. 25.5% 31.5% 39% 55% 98.5%

PRACTICE TEST 4

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19. How many of the 1,000 people polled responded “none of the above” to the questions? A. B. C. D. E. 140 110 80 20 0

23. The flat triangular lot depicted above is available for development. If x + x = 2 150 meters, what is the area of the lot in square meters? A. B. C. D. E. 125 150 3 1, 500 1, 250 3 2, 500 3

20. The equation R − 3 = S + 8 relates the 28 35 values of two linked currencies, where R is the value in dollars of one currency and S is the value in dollars of the other currency. Which of the following equations can be used to convert dollar values from the R currency to the S currency? 5R − 47 A. S = 4 4R + 47 B. S = 5 5R + 17 C. S = 4 4R − 17 D. S = 5 5R − 12 E. S = 4 21. If x is a positive number and 1/2 the square root of x is the cube root of x, then x = A. B. C. D. E. 64 32 16 4 1

24. For any numbers w and z, w z = w 3z(8 − w 2). If both z and w z are positive numbers, which of the following could be a value of w?

.

.

A. B. C. D. E.

9 3 0 −2 −9

1+1 25. 4 5 = 1 8 A. 2 5 B. 9 20 C. 9 8 D. 9 5 E. 18 5 26. Last year’s receipts from the sale of greeting cards during the week before Mother’s Day totaled \$189 million, which represented 9 percent of total greeting card sales for the year. Total greeting card sales for the year totaled how many million dollars? A. B. C. D. E. 17,010 2,100 1,890 1,701 210

22. If Josh, Doug, and Brad have a total of \$72 between them, and Josh has three times as much money as Brad but only three-fourths as much as Doug, how much money does Doug have? A. B. C. D. E. \$8 \$9 \$27 \$32 \$36

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27. What is the value of 5x2 − 1.9x − 3.7 for x = −0.3? A. B. C. D. E. −4.72 −3.82 −3.58 −2.68 0.57

The following data sufficiency problems consist of a question and two statements, labeled (1) and (2), in which certain data are given. You have to decide whether the data given in the statements are sufficient for answering the question. Using the data given in the statements plus your knowledge of mathematics and everyday facts (such as the number of days in July or the meaning of counterclockwise), you must indicate whether A. B. C. D. E. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. EACH statement ALONE is sufficient. Statements (1) and (2) TOGETHER are NOT sufficient.

31. The figure above shows the shape of a brick patio. If arc AB is a semicircle and ABCD is a square, what is the perimeter of the patio? (1) The radius of the semicircle described by arc AB is 4. (2) The perimeter of the square ABCD is 32. 32. A call to Rosie’s Psychic Hotline costs \$5.99 for the first 2 minutes and \$1.99 for each additional minute. Stuart called the hotline for x minutes, where x is an integer. How many minutes long was the call? (1) The total charge for the call was \$11.96. (2) The charge for the last 3 minutes of the call was \$0.01 less than half the total cost of the call. 33. If Z is represented by the decimal 0.W 7, what is the digit W ? (1) Z > 2 – 3 9 (2) Z > –– 10
Solve the problem and indicate the best of the answer choices given.

28. Two cyclists are racing up a mountain at different constant rates. Cyclist A is now 50 meters ahead of cyclist B. How many minutes from now will cyclist A be 150 meters ahead of cyclist B? (1) 5 minutes ago, cyclist A was 200 meters behind cyclist B. (2) Cyclist A is moving 25% faster than cyclist B. 29. Is integer x divisible by 48? (1) x is divisible by 16. (2) x is divisible by 12. 30. Is 3 < x < 5 ? (1) x < 20 (2) x > 5

34. If a cube has a volume of 125, what is the surface area of one side? A. B. C. D. E. 5 25 50 150 625

PRACTICE TEST 4

\$299

35. An investor bought 200 shares of stock in ABCD company in 1990. By 1992, the 2 investment was worth only – of its original 3 value. By 1995, the 200 shares were worth 1 only – of their value in 1990. By what percent 2 did the value of the investment drop from 1992 to 1995?
2 A. 16 –% 3

37. Which of the following cannot be the median of five positive integers a, b, c, d, and e? A. a B. d + e C. b + c + d D. b + c + d 3 E. a + b + c + d + e 5

B. 25%
1 C. 33 –% 3

D. 50%
2 E. 66 –% 3

36. In the rectangular quadrant system shown above, which quadrant, if any, contains no point (x, y) that satisfies the equation x2 − 2y = 3? A. B. C. D. E. none I II III IV

300#

THE PRACTICE TESTS

41 QUESTIONS

Verbal
TIME—75 MINUTES

For the following questions, select the best of the answer choices given.

1. Companies that advertise on television complain that digital television recording (DTR) services make it possible for consumers to watch television programs without viewing the commercials that these advertisers have paid the television networks to broadcast. The DTR service providers respond that their services may actually help the advertisers, because without their service, many consumers would not have been able to watch the programs—or the commercials in them—in the first place. Which of the following, if true, offers the most support to the advertisers’ claims that the DTR services are currently hurting their businesses? A. Even the best commercials are usually less entertaining than the programs that consumers choose to watch for themselves. B. DTR services charge such high rates that only a small percentage of consumers subscribe to them. C. The average per-second cost of advertising on television has risen every year for the past two decades. D. More than 90 percent of subscribers to DTR services opt to use a setting that automatically edits out commercials. E. DTR services alter the television viewing experience by allowing customers to view the program of their choice at the time of their choosing.

2. When airlines were deregulated in the 1970s, the average price of a ticket was \$135. Three decades later, the average price is \$275, there are twice as many in-air collisions, fliers in small markets are at the mercy of predatory carriers, and air rage is at an all-time high. It is time to re-regulate the air travel industry. All of the following statements, if true, weaken the above argument except for which statement? A. Because of inflation, a \$275 ticket today is actually 10 to 20 percent less expensive than a \$135 ticket was in 1975. B. Deregulation has increased the choices available to fliers in terms of both time of flight and carrier. C. Airlines are currently flying more than five times as many passenger miles per year as they did in 1975. D. Compared with passengers in large urban areas, passengers in small markets pay, on average, twice as much per mile flown on domestic flights because their airports are generally served by fewer airlines. E. Psychologists have been able to determine no connection between the deregulation of the airline industry and the onset of increased levels of air rage.

PRACTICE TEST 4

\$301

3. Skilled blacksmiths who could forge useful items out of iron used to play a central role in American life. The onset of industrialization and the mass production of iron products, however, have made the blacksmith’s traditional role mostly obsolete. Still, there will always be a job available for a good blacksmith. Which of the following, if true, provides the most support for the conclusion that a job will always be available for a good blacksmith? A. Many people are willing to pay considerably more for tools hand-crafted by a blacksmith than for tools created by a machine. B. Blacksmiths cannot produce iron products with the speed or consistency of machines. C. Blacksmiths traditionally apprenticed to a master blacksmith for seven or more years before entering business independently. D. The cowboy never would have conquered the West without the horseshoes crafted by blacksmiths. E. As skilled craftsmen, blacksmiths traditionally served as community leaders throughout North America and Europe. 4. When unscrupulous people shoplift, a vicious cycle results. Retailers must raise their prices in order to make up for the lost sales, and the higher prices encourage more people to shoplift. This vicious cycle hurts honest consumers worst of all, because they have to pay higher prices. The vicious cycle described above could not happen unless which of the following is true? A. Shoplifters usually steal only items that they need but cannot afford. B. Retailers do not take shoplifting losses into account when they initially set their prices. C. The best way for retailers to address shoplifting is by punishing shoplifters to the fullest extent of the law. D. Some people would shoplift no matter how low retailers set their prices. E. It costs retailers more to pay security guards to prevent shoplifting than just to absorb the cost of occasional losses due to theft.

5. When Brad offered his old wooden desk at a garage sale, no one bought it, even though he offered it for only \$10. When he offered it at the local auction house, however, someone bought it for \$850. Which of the following, if true, best explains why Brad was able to sell the desk for a high price at the auction while he could not sell it for a much lower price at the garage sale? A. Brad advertised that the proceeds of the garage sale would benefit a local charity, while he made no such claims for the proceeds from the auction. B. One of the legs of the desk was shorter than the other three, producing an unbalanced writing surface. C. The auction house specializes in selling antique furniture, which is generally valued more highly than the discarded furniture sold at garage sales. D. Brad insisted that anyone who bought the desk had to use it as an actual workspace. E. Prospective buyers at auctions are often more interested in the auction process than in the items up for bid.
The following questions present a sentence, part of which or all of which is underlined. Beneath the sentence, you will find five ways of phrasing the underlined part. The first of these repeats the original; the other four are different. If you think the original is best, choose the first answer; otherwise choose one of the others. These questions test correctness and effectiveness of expression. In choosing your answer, follow the requirements of standard written English; that is, pay attention to grammar, choice of words, and sentence construction. Choose the answer that produces the most effective sentence; this answer should be clear and exact, without awkwardness, ambiguity, redundancy, or grammatical error.

6. Four Dynacorp Optimall Omniprocessors were shipped in the fourth quarter, and it brought to 13 the number of these ultra-highcapacity processors shipped during the year. A. B. C. D. E. and it brought by bringing and brings having brought bringing

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7. After his 1962 season, in which he set a record for on-base percentage, Mitch McAlister left his old team and signed with the Springfield Argonauts, with an annual salary of \$550,000 and was the highest salary in professional baseball at that time. A. Argonauts, with an annual salary of \$550,000 and was the B. Argonauts, earning \$550,000 per year and it was the C. Argonauts for a yearly wage of \$550,000, being the D. Argonauts, with annual pay of \$550,000 per year, which was the E. Argonauts for an annual salary of \$550,000, the 8. Nile perch, voracious predators that will eat anything smaller than themselves, are natives of northern Africa but were introduced to Tanzania’s Lake Victoria in a foolhardy attempt during the 1960s of boosting the local sport-fishing industry; since their introduction, these sturdy fish have decimated most other aquatic species in the lake. A. are natives of northern Africa but were introduced to Tanzania’s Lake Victoria in a foolhardy attempt during the 1960s of boosting B. are native in northern Africa but were introduced to Tanzania’s Lake Victoria during the 1960s as foolhardy attempts to boost C. are native to northern Africa but were introduced to Tanzania’s Lake Victoria during the 1960s in a foolhardy attempt to boost D. had been native to northern Africa but during the 1960s were introduced to Tanzania’s Lake Victoria in a foolhardy attempt to boost E. are native to northern Africa but were introduced to Tanzania’s Lake Victoria as a foolhardy attempt of boosting

9. No giant squid has ever survived in captivity because these giant animals of the deeps require extremely high water pressure for the purpose of maintaining its internal osmotic balance. A. deeps require extremely high water pressure for the purpose of maintaining its B. deep requires extremely high water pressure to maintain its C. deep require extremely high water pressure in order to maintain their D. deeps requires extremely high water pressure so that it can maintain its E. deep require for maintenance extremely high water pressure for their 10. The state medical review board is considering a new regulation that physicians practicing in state facilities with past malpractice suits having been filed against them are required to disclose any such suits to prospective patients. A. that physicians practicing in state facilities with past malpractice suits having been filed against them are required to disclose any such suits to prospective patients B. that requires physicians practicing in state facilities disclose any past malpractice suits filed against them to prospective patients C. to require physicians with past malpractice suits filed against them and who practice in state facilities to disclose these to prospective patients D. for physicians that practice in state facilities requiring them to have disclosed to prospective patients past malpractice suits filed against them E. requiring physicians who practice in state facilities to disclose to prospective patients any past malpractice suits filed against them

PRACTICE TEST 4

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For the following questions, select the best of the answer choices given. 11. Our criminal justice system is inherently flawed because it relies on amateur juries of decent citizens, who lack the perspective to understand the criminal mind. To have an effective criminal justice system would require professional juries, who would be able to deal with these criminals in a way that gets results. The argument above depends on which of the following assumptions? A. Professional jurors will be more reliable than amateur jurors because they will not attempt to avoid jury duty. B. Professional jurors will not be burdened by the biases against race, gender, and religion that amateur jurors bring into the courtroom. C. Dealing with criminals in a way that gets results requires an understanding of the criminal mind. D. No amount of professional training can impart the perspective of the criminal mind necessary to run an effective criminal justice system. E. Jurors possessing the perspective to understand the criminal mind are unfit to serve on a jury, because they are likely to be criminals. 12. Advertisement: The most flavorful olives in the world are kalamata olives. The more kalamata olives used to make a bottle of olive oil, the more flavorful the oil, and no company buys more kalamata olives than Zorba’s Olive Oil. Therefore, when you buy Zorba’s Olive Oil, you’re buying the most flavorful olive oil available today. The reasoning presented in the advertisement is flawed because it overlooks the possibility that: A. Not all of Zorba’s competitors use kalamata olives in their oil. B. Zorba’s sells more olive oil than any other company. C. The most flavorful olive oil is not necessarily the best olive oil.

D. Because of bulk discounts, Zorba’s pays less per kilogram of kalamata olives than does its competitors. E. The number of kalamata olives harvested every year is far less than the number of Spanish olives harvested every year. 13. The cypress trees of the Louisiana wetlands are threatened by the exploding population of nutria, a type of South American rodent introduced into the area in the 1930s in hopes of starting a nutria fur industry. Unfortunately, no one wanted the fur, and now the rodents number in the millions. A park ranger has suggested introducing the South American jaguar, the nutria’s natural predator, into the Louisiana wetlands as a way to control the nutria population. Which of the following, if true, casts the most doubt on the ranger’s plan to introduce jaguars as an effective way to control the nutria population? A. Past attempts to control the nutria population through traps and poison have resulted in limited and temporary population reductions. B. A program in Florida found that the best way to conserve the root systems of wetland trees such as cypresses is to surround the trees’ roots with tough plastic barriers. C. The jaguar is a large and deadly predator that, if introduced, could kill livestock, pets, or even humans that it encounters in the Louisiana wetlands. D. During the past year an unusually cold winter killed an estimated 35 percent of the nutria population in the Louisiana wetlands. E. The South American jaguar is a predator of the ferret, which is currently the chief predator of the nutria in the Louisiana wetlands.
The questions in this group are based on the content of a passage. After reading the passage, choose the best answer to each question. Answer all questions following the passage on the basis of what is stated or implied in the passage.

Pretty much everybody agrees that clean air is a good thing, right? Evidently not so. Since the 1960s, when people started talking about clean air

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in the first place, the American energy industry, which includes coal companies, oil companies, and utility companies, has dragged its heels on every initiative to improve the quality of the air we breathe. Even after the Clean Air Act of 1970 and its amendments in 1977 and 1990 made it clear that controlling air pollution is a national priority, these companies have found tricks and loopholes to avoid compliance. Perhaps the most egregious loophole is the one that allows older power plants to disregard limits on sulfur dioxide emissions until they undergo a major renovation, at which point they have to comply. Sulfur dioxide from coal-burning power plants is the primary cause of acid rain in North America. The Clean Air Act states that when coalburning power plants upgrade their equipment, they must then comply with sulfur dioxide limitations by either installing scrubbing equipment that cleans the emissions or using fuel with lower sulfur content. The law tied the timing of compliance to major renovations in order to give power plants a grace period in which to comply. Many power plants, however, have exploited a loophole in this law by instituting a series of “minor” renovations that, in effect, upgrade their equipment without requiring them to comply with the Clean Air Act. Some plants have cheated the system by undergoing “minor” renovations for decades. The power companies claim that they have to resort to these underhanded measures because the cost of compliance with the Clean Air Act is too high. And if everyone else is cheating the system, why should they have to install costly sulfur dioxide scrubbers? This cost argument falls apart upon scrutiny. Since 1977, more than 400 power plants across the country have managed to comply with the restrictions and are still making money. The sulfur dioxide scrubbing equipment has turned out to be far less expensive than the power industry naysayers claimed it would be. Many power plants have even complied with the emissions limits and reduced their operating costs by switching from high-sulfur Appalachian coal to the low-sulfur coal produced in western states such as Wyoming and Idaho. Western coal is not only cleaner than eastern coal, but also, because it is generally closer to the surface, as much as 30 percent less expensive to extract. Clearly, the costs of compliance with the Clean Air Act can be justified, but if these companies were honest, such justifications would not have to be made. If they were honest, they would acknowledge

the costs of not complying: the health costs of increased rates of asthma and lung cancer in highemissions areas; the environmental costs of acidscarred forests and lakes; the aesthetic costs of a haze of sulfur dioxide cutting visibility across the eastern United States to only half of what it was in pre-industrial times. When you look at the true costs you have to ask, is any cost too high for clean air? 14. Which of the following best expresses the purpose of this passage? A. To explain how a loophole in the Clean Air Act allows power plants to avoid compliance with emissions restrictions B. To raise awareness of the problems caused by sulfur dioxide emissions from coalburning power plants C. To argue against a specific implementation of the Clean Air Act that relates to greenhouse gas emissions D. To argue that companies should not exploit a loophole in the Clean Air Act concerning an atmospheric pollutant E. To advocate the passage of a new Clean Air Act that places limits on sulfur dioxide emissions 15. The author’s tone can best be described as which of the following? A. B. C. D. E. Angry and subjective Calm and objective Analytic and ambivalent Grim and self-satisfied Tentative and biased

16. The author most likely begins and concludes the passage with questions for what reason? A. To suggest possible areas for current and future research B. To pose a question that is answered in the body of the passage, and then to formulate a question that arises naturally out of the discussion C. To gain the readers’ attention and encourage their agreement with the arguments in the passage D. To suggest through rhetorical questions that the problems described in the passage do not actually have answers E. To test the readers’ knowledge of the material discussed in the passage

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17. According to information given in the passage, which of the following statements presents the most accurate comparison of an average ton of coal from Wyoming with an average ton of coal from the Appalachian range in West Virginia? A. The former is cheaper and has higher sulfur content than the latter. B. The latter is found closer to the surface and contains more sulfur than the former. C. The former can help coal-burning power plants meet limits on sulfur dioxide emissions and costs more than the latter. D. The latter generates more energy per pound of coal than the former. E. The former is found closer to the surface than the latter and helps coal-burning power plants meet limits on sulfur dioxide emissions. 18. According to the information given in the passage, sulfur dioxide emissions are linked to all except which of the following phenomena? A. Reduced visibility in the eastern United States B. Damage to the ozone hole C. Increased rates of asthma D. Acid rain E. Damaged forests 19. In the fourth paragraph, the passage mentions the “400 power plants” for what purpose? A. To provide concrete evidence that many power plants have complied with the Clean Air Act provisions without undergoing ruinous financial hardship B. To demonstrate the size and influence of the energy industry in the United States C. To demonstrate that only a fraction of the power plants in the country have complied with the Clean Air Act, while hundreds of others have avoided compliance through tricks and loopholes D. To demonstrate that companies can both comply with the Clean Air Act and achieve reductions in their operating costs by employing new, more efficient technologies E. To suggest that those companies that have not complied are in the minority

20. Which of the following statements, if true, would provide the strongest argument for a utility company spokesman wishing to refute the arguments expressed in the passage? A. Over the last decade, the energy industry has funded an environmental initiative that has planted more than 200,000 new trees. B. The dangers of acid rain to human health have been wildly exaggerated by environmental extremists who seek to scare the general public. C. The specifications of the Clean Air Act, although well intentioned, in practice require power plants to adopt less efficient technologies that increase emissions of atmospheric pollutants other than sulfur dioxide that have been linked to equally serious problems. D. A substantial upgrade to a coal-burning power plant that includes the installation of sulfur dioxide scrubbing equipment can cost hundreds of millions of dollars, although companies can often recoup most of these costs over the following years as a result of efficiency benefits from the upgrade. E. The scientific data upon which the Clean Air Act was based have not been corroborated by the scientists at the Center for Atmospheric Truth, a research group funded by a consortium of energy companies.
The following questions present a sentence, part of which or all of which is underlined. Beneath the sentence, you will find five ways of phrasing the underlined part. The first of these repeats the original; the other four are different. If you think the original is best, choose the first answer; otherwise choose one of the others. These questions test correctness and effectiveness of expression. In choosing your answer, follow the requirements of standard written English; that is, pay attention to grammar, choice of words, and sentence construction. Choose the answer that produces the most effective sentence; this answer should be clear and exact, without awkwardness, ambiguity, redundancy, or grammatical error.

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21. Although he played several musical instruments while being a child, Maestro Macintosh did not begin playing the piano until he was 23 years old. A. B. C. D. E. while being a child as a child as in childhood at the time of his childhood at the time when he was a child

25. Nutritionists say that you cannot eat enough fruits and vegetables, arguing that it provides nutrition essential to health. A. B. C. D. E. that it provides nutrition that they provides nutrition they provide the nutrients it provides the nutrients that they provide the nutrients

22. Unless the conservator can find a way to protect the photographs in the archives from light and air, these precious historical documents have deteriorated and will continue to do so both in color and in fine detail. A. have deteriorated and will continue to do so B. will continue to deteriorate C. have been and will continue to deteriorate D. will continue to deteriorate, as they already have E. will be deteriorating yet more 23. Under SEC guidelines, a company in this situation is required either to submit revised financial statements or that they withdraw their plans for a public stock offering. A. B. C. D. E. that they withdraw their plans to withdraw its plans that it withdraw planning to have been withdrawn from their plans it should withdraw its plans

For the following questions, select the best of the answer choices given.

26. In theory, the Habbendorf rotary engine could be a great racing engine, but in practice, it is not. The reason is that the available fuels do not have sufficient octane to obtain maximum performance from the engine. The answer to which of the following questions would be most relevant to evaluating the adequacy of the explanation given above for why the Habbendorf rotary engine is not a great racing engine? A. If the Habbendorf rotary engine were to operate at maximum performance levels, how would its performance compare to that of an engine recognized as a great racing engine? B. At what level of octane in its fuel does the Habbendorf rotary engine achieve maximum performance? C. What levels of speed, acceleration, and efficiency must an engine display in order to be considered a “great racing engine”? D. Could a Habbendorf rotary engine be modified so that it is able to achieve maximum performance with the fuels currently available? E. If a car equipped with a Habbendorf rotary engine were to race against a comparable car equipped with a great racing engine, by how much would the performance of the great racing engine surpass that of the Habbendorf rotary engine?

24. Unless I am greatly mistaken, any apparent connection between my dog and the destroying of your petunias is purely coincidental. A. connection between my dog and the destroying of B. connection between my dog and the destruction of C. connection of my dog with the destruction of D. connection between my dog and the destroying to E. connection from my dog with the destruction to

PRACTICE TEST 4

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27. Government deregulation of the long-distance telephone business has resulted in increased competition among telephone carriers, thus resulting in lower prices for consumers. This process, however, will ultimately result in lower-quality service for consumers, because as the telephone carriers drop their prices to compete with one another for customers, they will be forced to cut corners on nonessential items like customer service. Which of the following, if true, casts the most doubt on the argument that government deregulation of the telephone business will result in lower-quality customer service? A. Technological advances have decreased the cost of providing long-distance telephone service to less than one-half of its cost prior to deregulation. B. In a customer survey regarding the electric utility business, another industry that recently went through deregulation, surveyors found that customer dissatisfaction with service was 30 percent higher than prior to deregulation. C. Customers have listed poor customer service as their number one reason for switching from one long-distance telephone service provider to another. D. Some companies have decreased the cost of customer service by installing automated telephone response systems that eliminate the need for expensive live employees. E. The greatest competition for long-distance telephone service providers will come not from traditional telephone companies, but from cellular telephone service providers.
The next two questions refer to the following passage:

B.

C.

D.

E.

body mass, than the dosage any human would take under normal circumstances. Because of the different body chemistry of humans and rats, some compounds can be dangerous for rats but safe for humans, and vice versa. Tests of this same painkiller on dogs showed that 3 out of 50 dogs developed lesions on their livers during the course of the experiment. The researchers found that during the experiment, the rats showed a significantly lower sensitivity to pain than rats do under normal circumstances. In an experiment of this length with this number of rats, it is not unusual for up to 50 rats to die during the experiment for reasons unrelated to the experiment itself.

29. Which of the following, if true, would cast the most doubt on the pharmaceutical company’s conclusion? A. Fifteen of the 39 dead rats were later found to have died of a rare form of liver cancer that is generally seen in only 1 out of 600,000 lab rats. B. The director of the experiment, although a respected scientist, is not a medical doctor, and therefore will not be able to continue as director of the experiment once it switches from animal to human trials. C. Although the painkiller in question has been shown to block certain forms of pain, its duration of efficacy is less than that of other painkillers currently on the market. D. Human trials of another drug produced by this pharmaceutical company were called off after 30 out of 1,000 rats died of heart failure during the animal testing phase of the experiment. E. The pharmaceutical company is eager to introduce new drugs to the market because its best-selling product, a drug that reduces blood pressure, will soon lose its patent protection.
The questions in this group are based on the content of a passage. After reading the passage, choose the best answer to each question. Answer all questions following the passage on the basis of what is stated or implied in the passage.

A pharmaceutical company tested a new painkiller on 1,000 lab rats that were fed large doses of the painkiller for a two-month period. By the end of the experiment, 39 of the rats had died. The company concluded that the painkiller was sufficiently safe to test on humans. 28. Which of the following, if true, provides the most support for the pharmaceutical company’s conclusion? A. The amount of painkiller fed to the rats was substantially greater, in relation to
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James Joyce revolutionized the novel, the short story, and modern literature as we know it. He was born in Dublin, the first of 10 children in a Catholic family. His father was a civil servant whose poor financial judgment left the family impoverished for much of Joyce’s youth. Young James attended Dublin’s fine Jesuit schools, which gave him a firm grounding in theology and classical languages— subjects that appeared repeatedly in his later work. The story of his early life and his intellectual rebellion against Catholicism and Irish nationalism are told in the largely autobiographical novel A Portrait of the Artist as a Young Man. In 1902, at the age of 20, Joyce left Dublin to spend the rest of his life in Paris, Trieste, Rome, and Zurich, with only occasional visits back home. Despite this self-imposed exile, Dublin was the setting for most of his writings. Dubliners (1914), Joyce’s most accessible work, is a collection of short stories describing the paralyzing social mores of middle-class Catholic life. “The Dead,” the final story in the collection, is frequently listed as one of the finest short stories ever written. Joyce’s next book, Ulysses, took seven years to write; once he finished writing it, he almost couldn’t find anyone to publish it. Upon the novel’s publication, both Ireland and the United States immediately banned it as obscene. Despite these obstacles, Ulysses has come to be generally recognized as the greatest twentieth-century novel written in English. The novel was revolutionary in many ways. The structure was unique: Joyce recreated one full day in the life of his protagonist, Leopold Bloom, and modeled the actions of the story on those of Ulysses in the Odyssey. In recounting Bloom’s day, Joyce mentions everything that happens to Bloom—including thoughts, bodily functions, and sexual acts—providing a level of physical actuality that had never before been achieved in literature. To provide a psychological insight comparable to the physical detail, Joyce employed a then-revolutionary technique called stream of consciousness, in which the protagonist’s thoughts are laid bare to the reader. From 1922 until 1939, Joyce worked on a vast, experimental novel that eventually became known as Finnegan’s Wake. The novel, which recounts “the history of the world” through a family’s dreams, employs its own “night language” of puns, foreign words, and literary allusions. It has no clear chronology or plot, and it begins and ends on incomplete sentences that flow into each other. Many of

Joyce’s supporters thought he was wasting his time on the project, although the playwright Samuel Beckett, who later won the Nobel Prize for Literature, helped Joyce compile the final text when his eyesight was failing. Today, Finnegan’s Wake is viewed as Joyce’s most obscure and possibly most brilliant work. 30. Which of the following would make the most appropriate title for this passage? A. The Long Way Home: Ulysses and Finnegan’s Wake B. James Joyce, Ulysses, and the Battle against Censorship C. The Works of James Joyce, Ireland’s Literary Genius D. The Hidden Value of James Joyce’s Great Novels E. A Portrait of James Joyce as a Young Man 31. Based on the information in the passage, which of the following would be the most accurate statement about Dubliners and Finnegan’s Wake? A. Dubliners contains one of the greatest short stories in the English language, and Finnegan’s Wake is the greatest story in the English language. B. Many of the chief characters in Finnegan’s Wake were earlier introduced in Dubliners. C. The linguistic experimentation of Dubliners paved the way for the “night language” of Finnegan’s Wake. D. Dubliners is a longer book than Finnegan’s Wake. E. Dubliners is a more accessible book than Finnegan’s Wake. 32. Joyce’s works helped introduce all except which of the following literary elements into modern English literature? A. Narration through second-person address B. Novel structure based on real-time chronology C. Linguistic experimentation D. Literary realism concerning physical reality E. Stream of consciousness

PRACTICE TEST 4

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33. According to the passage, in what year was Joyce born? A. B. C. D. E. 1880 1882 1885 1902 1914

The following questions present a sentence, part of which or all of which is underlined. Beneath the sentence you will find five ways of phrasing the underlined part. The first of these repeats the original; the other four are different. If you think the original is best, choose the first answer; otherwise choose one of the others. These questions test correctness and effectiveness of expression. In choosing your answer, follow the requirements of standard written English; that is, pay attention to grammar, choice of words, and sentence construction. Choose the answer that produces the most effective sentence; this answer should be clear and exact, without awkwardness, ambiguity, redundancy, or grammatical error.

34. The author most likely mentions James Joyce’s childhood, family, and education to serve what purpose? A. To suggest that he had to write in order to make a living B. To suggest that he became a writer because of his father’s influence C. To provide the background and cultural context for his literary work D. To provide evidence that his literary genius was present when he was a child E. To explain his opposition to Catholicism and socialism in his later life 35. Who is the most likely intended audience for this passage? A. Insurance professionals at a company seminar B. University professors of English literature at a symposium on twentieth-century Irish playwrights C. High school students in Ireland studying their nation’s traditional folklore D. College students studying twentiethcentury English literature E. Elementary school students studying the Odyssey 36. Which of the following can be inferred about Joyce’s attitude toward Catholicism as practiced in Ireland at the end of the nineteenth century? A. He felt that it repressed intellectual freedom and individual expression. B. He viewed it as the central component of the Irish national psyche. C. He feared that it was impeding the Irish nationalist movement. D. He felt that it forced him to leave Dublin for Paris, Trieste, Rome, and Zurich. E. He believed that Dublin’s Jesuit schools provided the finest education in all of Ireland.

37. Many doctors direct their patients to namebrand drugs, but smart consumers know that generic drugs cost half as much as buying name-brand drugs. A. generic drugs cost half as much as buying name-brand drugs B. buying generic drugs costs half as much as name-brand drugs C. generic drugs cost half as much as namebrand drugs D. buying generic drugs cost half as much as buying name-brand drugs E. to buy generic drugs costs half as much as buying name-brand drugs 38. Usually found in pools of stagnant water or mud, crawfish are esthetically unappealing arthropods, except if they are boiled, at which point it yields a tasty treat. A. crawfish are esthetically unappealing arthropods, except if they are boiled, at which point B. crawfish are esthetically unappealing arthropods, but after a proper boiling C. the crawfish is an esthetically unappealing arthropod, in contrast to after being properly boiled D. the crawfish is an arthropod that does not appeal esthetically, but subsequent to having been boiled properly E. the crawfish is an esthetically unappealing arthropod, although after a proper boiling

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39. While the new health insurance regulations may be onerous for large corporations, it can potentially be disastrous for small business owners, who in many cases will have to lay off employees in order to pay for the extended coverage. A. it can potentially be disastrous for small business owners, who B. they are potential disasters for small business owners, since C. potentially they will be disastrous for small business owners, whom D. for small business owners it is a potential disaster, because E. they are potentially disastrous for small business owners, who 40. After leaving the Pentagon, MacTaggart could have profited from his connections with defense contractors, but he refused to do so. A. After leaving the Pentagon, MacTaggart could have profited from his connections with defense contractors, but he refused to do so. B. MacTaggart could have profited from his connections with defense contractors after leaving the Pentagon, but he refused to do it.

C. MacTaggart could have profited after leaving the Pentagon from his connections with defense contractors, but he refused to do so. D. Having left the Pentagon, MacTaggart could have used his connections with defense contractors to profit, but he refused to do it. E. Refusing to profit from his connections with defense contractors, MacTaggart could have done so after leaving the Pentagon. 41. Product marketing jobs at MegaCorp are difficult to fill because they require specialized skills, demand great responsibility, but also barely any vacation time. A. B. C. D. E. demand great responsibility, but also great responsibility, and also great responsibility, and with carry great responsibility, and carry great responsibility, and offer

PRACTICE TEST 4

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Practice Test 5
ANALYTICAL WRITING 1

f

Analysis of an Issue
TIME—30 MINUTES

Real-world experience is more useful in business than anything that can be learned in school. Discuss the extent to which you agree or disagree with the opinion stated above. Support your views with reasons and/or examples from your own experiences, observations, or reading.

313

ANALYTICAL WRITING 2

Analysis of an Argument
TIME—30 MINUTES

directions: In this section, you will be asked to write a critique of the argument presented below. You may, for example, consider what questionable assumptions underlie the thinking, what alternative explanations or counterexamples might weaken the conclusion, or what sort of evidence could help strengthen or refute the argument. Read the argument and the instructions that follow it, and then make any notes that will help you plan your response. Write your response on a separate sheet of paper. If possible, type your essay on a word processor. Observe the 30-minute time limit.

The MegaTek Corporation’s vice president of marketing made the following statement to the company’s board of directors: MegaTek has been losing market share to UltraCorp for three years straight. Customer surveys suggest that consumers perceive UltraCorp products to be of higher quality than those produced by MegaTek. MegaTek spends more annually on research and development than UltraCorp does, and it pays its employees a higher average salary, so we do not believe that our products are actually inferior; rather, the perception is due to the fact that UltraCorp charges higher prices and spends more money on advertising. In order to regain the lost market share from UltraCorp, MegaTek should raise its prices and devote more money to advertising. Discuss how well reasoned you find this argument. In your discussion, be sure to analyze the line of reasoning and the use of evidence in the argument. For example, you may need to consider what questionable assumptions underlie the thinking and what alternative examples or counterexamples might weaken the conclusion. You can also discuss what sort of evidence would strengthen or refute the argument, what changes in the argument would make it more logically sound, and what, if anything, would help you better evaluate its conclusion.

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37 QUESTIONS

Quantitative
TIME—75 MINUTES

Solve the problem and indicate the best of the answer choices given.
NUMBERS: FIGURES:

All numbers used are real numbers.

A figure accompanying a problem-solving question is intended to provide information useful in

solving the problem. Figures are drawn as accurately as possible EXCEPT when it is stated in a specific problem that its figure is not drawn to scale. Straight lines may sometimes appear jagged. All figures lie in a plane unless otherwise indicated.

1. Sam is training for the marathon. He drove 12 miles from his home to the Grey Hills Park and then ran 6 miles to Red Rock, retraced his path back for 2 miles, and then ran 3 miles to Rock Creek. If he is then n miles from home, what is the range of possible values for n? A. B. C. D. E. 1 ≤n ≤23 3 ≤n ≤21 5 ≤n ≤19 6 ≤n ≤18 9 ≤n ≤15

3. There are 450 birds at a small zoo. The number of birds is 5 times the number of all the other animals combined. How many more birds are there than nonbird animals at the zoo? A. B. C. D. E. 400 360 270 180 90

2. Amber works 20 days a month at d dollars per day for m months out of the year. Which of the following represents her monthly pay? m A. 20d B. 20d C. 10md 6 20d D. m E. 20md

4. If x, y, and z are positive integers, and 4x = 5y = 6z, then the least possible value of x + y + z is A. B. C. D. E. 15 28 37 42 60

5. Three hundred multiples of three are picked at random, and three hundred multiples of four are picked at random. Approximately what percentage of the six hundred selected numbers are even? A. B. C. D. E. 100% 75% 66% 50% 33%

PRACTICE TEST 5

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Score 92 91 ? 83 71

Number of students 4 6 3 7 5

numbers: All numbers used are real numbers. figures: A figure accompanying a data sufficiency problem will conform to the information given in the question, but will not necessarily conform to the additional information given in statements (1) and (2). Lines shown as straight can be assumed to be straight and lines that appear jagged can also be assumed to be straight. You may assume that the position of points, angles, regions, etc., exist in the order shown and that angle measures are greater than zero. All figures lie in a plane unless otherwise indicated. note: In data sufficiency problems that ask for the value of a quantity, the data given in the statements are sufficient only when it is possible to determine exactly one numerical value for the quantity. 8. What is the value of y ? (1) y 2 + 8y + 16 = 0 (2) y < 0 9. The integer x is how much greater than 4? 1 (1) 10x = 0.000001 (2) 10 x = 1,000,000

6. The incomplete table above shows a distribution of scores for a class of 25 students. If the average (arithmetic mean) score for the class is 83, what score is missing from the table? A. B. C. D. E. 75 77 81 84 86

2 6 4 7. (5 )( 2 )( 3 ) = 2 72 5 A. 2 25 B. 3 C. 25 D. 50 E. 150

The following data sufficiency problems consist of a question and two statements, labeled (1) and (2), in which certain data are given. You have to decide whether the data given in the statements are sufficient for answering the question. Using the data given in the statements plus your knowledge of mathematics and everyday facts (such as the number of days in July or the meaning of counterclockwise), you must indicate whether A. B. C. D. E. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. EACH statement ALONE is sufficient. Statements (1) and (2) TOGETHER are NOT sufficient.

10. In triangle ABC above, if ∠ BAD and ∠ ADB have measures of 2n°, and if ∠ ACB has a measure of n°, what is the length of side AB ? (Figure not necessarily drawn to scale.) (1) n = 25° (2) CD = 4

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11. A dairy farmer has two milk pails, M and P . Milk pail M is 1/3 full. How much milk is in P relative to M? (1) If M is poured into P P will be full. , (2) Milk pail P is smaller than M. 12. Is y between 1 and 2, exclusive? (1) y 2 is less than y (2) y 2 + y is between 1 and 2, exclusive
Solve the problem and indicate the best of the answer choices given.

16. If the area of a circle is 81π, then the diameter of the circle is A. B. C. D. E. 9 18 36 9π 18 π

17. A standard Veggiematik machine can chop 36 carrots in 4 minutes. How many carrots can 6 standard Veggiematik machines chop in 6 minutes? A. B. C. D. E. 36 54 108 216 324 =

13. What is the perimeter of the figure above? (Note, figure not necessarily drawn to scale) A. B. C. D. E. 155 185 220 235 250

18.

( 0.0063 )( 0.117 ) ( 0.03 )( 0.007 )( 0.0003 )
A. B. C. D. E. 117,000 11,700 3,900 1,170 390

14. In a certain growth fund, 3/5 of the investment capital is invested in stocks, and of that portion, 1/3 is invested in preferred stocks. If the mutual fund has \$846,000 invested in preferred stocks, what is the total amount of money invested in the fund? A. B. C. D. E. \$1,974,000 \$2,538,000 \$3,264,000 \$3,826,000 \$4,230,000

19. In a sample of patients at an animal hospital, 30 percent are cats and 60 percent are not dogs. What fraction of those patients who are not cats are dogs? A. 1 – 7 1 B. – 3 C. 2 – 5 3 D. – 5 E. 4 – 7 20. Two dogsled teams raced across a 300-mile course in Wyoming. Team A finished the course in 3 fewer hours than did team B. If team A’s average speed was 5 miles per hour greater than that of team B, what was team B’s average speed, in miles per hour? A. B. C. D. E. 12 15 18 20 25

15. (32+1)(812+1)(92+1)(32−1)= A. B. C. D. E. 814+1 99−1 316−1 332−1 396+1

PRACTICE TEST 5

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The following data sufficiency problems consist of a question and two statements, labeled (1) and (2), in which certain data are given. You have to decide whether the data given in the statements are sufficient for answering the question. Using the data given in the statements plus your knowledge of mathematics and everyday facts (such as the number of days in July or the meaning of counterclockwise), you must indicate whether A. B. C. D. E. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. EACH statement ALONE is sufficient. Statements (1) and (2) TOGETHER are NOT sufficient.

24. In the figure above, what is the length of WZ ? (Note, figure not necessarily drawn to scale) (1) xy = 64 (2) x2 = y2 25. Over the course of a year, a certain house appreciated in value by 10 percent while the house next door decreased in value by 10 percent as a result of foundation damage. At the end of the year, the reduced price of the second house was what percentage of the increased price of the first house? (1) The amount by which the first house increased in value was half as much as the amount by which the second house decreased in value. (2) At the end of the year, the second house was worth \$70,000 more than the first house.
Solve the problem and indicate the best of the answer choices given.

21. In a club for left-handed people that also admits the ambidextrous, are more than 1/3 of the members ambidextrous? (1) Exactly 50 percent of the male members of the club are ambidextrous. (2) The number of females in the club is exactly 1 fewer than half the number of male members. 22. If a 0, is b greater than zero?

(1) a + b = 10 (2) ab = 24 23. A truck driver wants to load as many identical cylindrical canisters of olive oil as can fit into the 3-meter × 4-meter × 9-meter storage space of his truck. How many canisters can he load into the truck? (1) Each canister has a volume of 62,500π cubic centimeters. (2) The height of each canister is four times the radius.

26. Of 40 applicants for a job, 32 had at least 5 years of prior work experience, 24 had advanced degrees, and 16 had at least 5 years of prior work experience and advanced degrees. How many of the applicants had neither 5 years of prior work experience nor advanced degrees? A. B. C. D. E. 0 2 4 8 16 3a 2 + 15 = b 0, and a − , then b = a a (5−a)(3+a) (3−a)(5+a) 2a2 − 15 −3a2 + a − 15 15 − 2a2

27. If a A. B. C. D. E.

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2∆7 × ∅14 80, 698 28. If ∆ and ∅ represent single digits in the correctly worked computation above, what is the value of ∆ times ∅? A. B. C. D. E. 6 10 12 15 18

32. If x, y, and z are positive integers and x2 = y2 + z2, which of the following must be true? I. x > z II. x = y + z III. y2 + z2 is a positive integer A. B. C. D. E. I only II only III only I and II only I and III only

29. A retailer sells 5 shirts. The first 2 he sells for \$64 and \$39. If the retailer wishes to sell the 5 shirts for an overall average price of over \$50, what must be the minimum average price of the remaining 3 shirts? A. B. C. D. E. \$49.00 \$49.67 \$50.00 \$51.33 \$55.50

The following data sufficiency problems consist of a question and two statements, labeled (1) and (2), in which certain data are given. You have to decide whether the data given in the statements are sufficient for answering the question. Using the data given in the statements plus your knowledge of mathematics and everyday facts (such as the number of days in July or the meaning of counterclockwise), you must indicate whether A. B. C. D. E. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. EACH statement ALONE is sufficient. Statements (1) and (2) TOGETHER are NOT sufficient.

30. The MegaTek Corporation is displaying its distribution of employees by department in a circle graph. The size of each sector of the graph representing a department is proportional to the percentage of total employees in that department. If the section of the circle graph representing the manufacturing department takes up 72° of the circle, what percentage of MegaTek employees are in manufacturing? A. B. C. D. E. 20% 25% 30% 35% 72%

33. If M is a set of five numbers p, q, r, s, and t, is the range of numbers in M greater than 5? (1) The average (arithmetic mean) of p, q, r, s, and t is 5. (2) p − r > 5.

31. If x * y =

( 2x – y ) for all integers ( 2y – x ) x and y, then (−5) * 2 = A. −12 B. −4 –– 3 −8 C. –– 9 4 D. – 3 E. 12

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34. Of the 3,600 registered voters in Smith County who took part in the county referendum on altering the property tax exemption, 2,400 were Democrats and 1,200 were Republicans. What was the total number of female voters who voted in favor of the exemption? (1) The number of female Democrats who voted in favor of the exemption was three times the number of female Republicans who voted in favor of the exemption. (2) The 150 male Republicans who voted in favor of altering the exemption represented 2/5 of all Republicans who voted in favor of altering the exemption. 35. Is the value of x 3y − x 2y 2 + x y 3 equal to 0? (1) x = 0 (2) y = 0

36. Is the positive integer y a prime number? (1) 80 < y < 95 (2) y = 3x + 1, where x is a positive integer 37. What is the area of square floor X? (1) The perimeter of the floor is a whole-number multiple of 10. (2) The diagonal of the floor measures 5 2 .

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41 QUESTIONS

Verbal
TIME—75 MINUTES

The questions in this group are based on the content of a passage. After reading the passage, choose the best answer to each question. Answer all questions following the passage on the basis of what is stated or implied in the passage.

Congressman Hastings has proposed that Congress should abolish the Electoral College system for electing the president and replace it with a system of direct popular election. The Electoral College system is flawed, he argues, because it runs directly counter to the democratic principle that every citizen’s vote should count equally. Because of the winner-take-all system in which the candidate who receives the most popular votes in a state receives all of that state’s electoral votes, the citizens who voted for the losing candidate are effectively disenfranchised from the national election, even if their candidate lost the state by only a handful of votes. Moreover, because each state’s number of electors is the same as its number of members of Congress, the citizens of small states get a disproportionately larger vote than citizens of more populous states. In the 1988 election, for example, the combined voting-age population of the six least populous states— Alaska, Delaware, North Dakota, South Dakota, Vermont, and Wyoming—was 3,119,000. These six states held 21 electoral votes among them. Florida, with a voting-age population of 9,614,000, also had 21 electoral votes. Because of inequities of this nature, there have been four presidential elections in which the candidate who won the Electoral College actually lost the popular vote: 1824, 1876, 1888, and 2000. Congressman Markham has argued that Hastings’s proposed changes are unnecessary and even dangerous. First of all, he argues, the Electoral

College system, whatever its flaws, has resulted in a stable democratic government for more than 200 years, which shows that it is doing something right. Second, the winner-take-all system helps create decisive majorities in the Electoral College, thereby reducing the problem of disputed elections that we might see in the event of direct popular elections. Third, the current system of allocating electors helps protect the interests of small states, which would be largely neglected in favor of large states if the Electoral College were based entirely on population. Protecting these states’ rights is essential to upholding the principle of federalism (in which the states and the federal government maintain distinct powers). When the Electoral College system was first formalized by the Twelfth Amendment in 1804, a direct popular vote would have been impossible to implement, and the Electoral College was probably the best way to approximate the will of the people. Advances in technology and communication, however, now mean that a direct popular vote would be as simple, if not simpler, to administer than the current Electoral College system. Alternative ways to reform the system would be to do away with the winner-take-all system of state electors, to base the numbers of electors strictly on state populations, or to have a direct popular election but to weight the votes from different states differently in order to preserve the influence of small states.

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1. The passage is primarily concerned with which of the following? A. Evaluating the merits of the Electoral College system as a means of protecting federalism B. Examining the impact of the Twelfth Amendment on the history of the American presidency C. Disputing the validity of the American democratic process D. Presenting arguments regarding the best way to elect the president of the United States E. Comparing arguments regarding the nature of democratic processes 2. Which of the following best describes the structure of the passage? A. It presents a critique of an institution, then provides a defense of that institution, and then offers possible compromises between the two positions. B. It presents an argument, lists problems with that argument, and then ultimately refutes the argument. C. It discusses both sides of a controversial topic and then chooses the side with the stronger arguments. D. It analyzes flaws in a traditional institution and then provides a series of steps to remedy the flaws. E. It presents two competing viewpoints and then shows the logical errors in both positions. 3. From the information provided in the paragraph, what can be inferred about the election of 1892? A. Its result was disputed on the grounds that smaller states had a disproportionate influence on the outcome. B. The winner of the election received more popular votes than his opponent. C. The winner-take-all system of state electoral votes led to a decisive majority for the winner in the Electoral College. D. Reforming the Electoral College system was an issue of contention in this election. E. This election led to the formalization of the Electoral College by the Twelfth Amendment.

4. Hastings’s response to Markham’s argument that the history of the American government “shows that it [the Electoral College] is doing something right” would most likely be which of the following? A. Under the current system, each voter in Alaska has proportionately three times as much voting power as each candidate in Florida. B. We do not know whether or not the American government would have been equally stable had the president been elected by a direct popular election since the beginning. C. If the candidate who lost the popular election won the presidency four times in 200 years, there is something wrong with the system. D. Maintaining a strong federal system is less important than upholding the principle that each vote should count equally. E. A process that maintained the Electoral College but removed the winner-take-all system would substantially reduce the disenfranchisement that occurs under the current system. 5. According to the passage’s presentation of Markham’s sentiments regarding federalism, which of the following systems for electing the president would be most objectionable to him? A. An Electoral College system identical to the one currently in use B. An Electoral College in which each state’s number of electors was based strictly on population, but the winner-take-all system was maintained C. An Electoral College in which each state’s number of electors was based strictly on that state’s number of members of Congress, but in which the winner-take-all system was replaced by a divided electoral vote proportional to the state’s popular vote D. A direct popular election in which the votes from citizens of smaller states were given more weight than citizens from larger states E. A direct popular election

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6. Which of the following examples from international politics, if true, would give Markham the most support in his argument against Hastings? A. A nation in Africa that modeled its government on the American governmental system after achieving independence from a European colonial power recently entered into a civil war that has effectively ended any true democratic processes. B. The ancient city-state of Athens had a form of direct popular election in the fifth century B.C.E., but this government fell as a result of the Peloponnesian War that Athens fought against Sparta. C. A South American nation that deposed its long-standing military dictatorship and instituted in its place a democratic government with a president elected through a direct popular election has experienced both economic growth and improved relations with the international community. D. A nation in Central Europe that recently changed its government from a longstanding parliamentary monarchy to a government led by a popularly elected premier was recently thrown into chaos when the popularly elected premier declared a dictatorship. E. The system of proportional power sharing by the members of the European Union has resulted in a number of thorny disputes between member states that will probably grow more severe as new nations from Eastern Europe enter the EU. 7. According to the information given in the passage, which of the following statements about Florida and South Dakota is most accurate? A. Florida is a larger state in area than South Dakota. B. South Dakota has a larger population than Florida. C. The ratio of members of Congress to electors in the Electoral College is lower for the state of Florida than it is for South Dakota.

D. South Dakota has more members of Congress per voting-age citizen than Florida does. E. A higher percentage of the voting-age population in South Dakota exercises its constitutional right to vote than is observed among the voting-age population of Florida.
The following questions present a sentence, part of which or all of which is underlined. Beneath the sentence, you will find five ways of phrasing the underlined part. The first of these repeats the original; the other four are different. If you think the original is best, choose the first answer; otherwise choose one of the others. These questions test correctness and effectiveness of expression. In choosing your answer, follow the requirements of standard written English; that is, pay attention to grammar, choice of words, and sentence construction. Choose the answer that produces the most effective sentence; this answer should be clear and exact, without awkwardness, ambiguity, redundancy, or grammatical error.

8. Although it has not been confirmed such proteins in whole milk are inducing in children under 12 months milk allergies, most pediatricians advise waiting until the child is one year old before introducing whole milk into his or her diet. A. such proteins in whole milk are inducing in children under 12 months milk allergies B. that under 12 months the proteins in whole milk can induce milk allergies in children C. of proteins in whole milk inducing milk allergies in children under 12 months D. the proteins in whole milk can induce milk allergies in children under 12 months E. that the proteins in whole milk can induce milk allergies in children under 12 months

PRACTICE TEST 5

\$323

9. The tango club, which appeared moribund five years ago, has picked up a new step; its numbers are now three times more than when the club president decided to bring in a live band. A. step; its numbers are now three times more than B. step; its numbers are now three times greater than C. step, their numbers now threefold that which they had been D. step; now with numbers three times greater than E. step, now with three times the number they had 10. During the bronze sculpture boom of the late 1950s, more than 20 tons of bronze were shipped to the SoHo district of Manhattan so as they might sculpt countless bronze statues, busts, abstract shapes, and whimsical figurines. A. B. C. D. E. so as they might sculpt in order that they might be sculpted into so that there could be sculpted for the sculpting of such that they could be sculpted into

who discovered the basic structure of DNA in 1953, which was the double helix. E. The basic structure of DNA, the double helix, was discovered by James Watson, later head of the Human Genome Project, along with another of two young scientists, the Englishman Francis Crick, in 1953. 12. Atmospheric scientists in recent years have observed increasing concentrations of chlorofluorocarbons in the tertiary layer of the stratosphere, findings consistent with the documented growth in chlorofluorocarbon emissions from industrial activity. A. findings consistent with the documented growth in chlorofluorocarbon emissions from industrial activity B. which are consistent with the documented growth in chlorofluorocarbon emissions from industrial activity C. a finding consistent with growth in chlorofluorocarbon emissions from industrial activity, as documented D. finding documented growth consistent with chlorofluorocarbon emissions from industrial activity E. which findings are consistent with industrial activity’s documented growth in chlorofluorocarbon emissions 13. The medical board, concerned by the drop in insurance payments and the failure of the accounting department to obtain the anticipated funds, resolved to pursue legal action against the insurance company. A. concerned by the drop in insurance payments and the failure of the accounting department to obtain B. concerning the drop in payments by insurance and the failure of the accounting department to obtain C. because of its concern for the dropping insurance payments and the accounting department’s failure at obtaining D. in its concern that the drop in insurance payments and the failure of the accounting department to obtain E. being concerned about the drop in insurance payments and the accounting department failing to obtain

11. James Watson, who later headed the Human Genome Project, along with Englishman Francis Crick discovered the double helix in 1953, the basic structure of DNA, when the two were young scientists. A. James Watson, who later headed the Human Genome Project, along with Englishman Francis Crick discovered the double helix in 1953, the basic structure of DNA, when the two were young scientists. B. The double helix, the basic structure of DNA, was discovered in 1953 by two young scientists, the Englishman Francis Crick and James Watson, who later headed the Human Genome Project. C. The basic structure of DNA, the double helix, was discovered in 1953 by the Englishman Francis Crick and James Watson, later head of the Human Genome Project, two young scientists. D. The Englishman Francis Crick and James Watson, later heading the Human Genome Project, were the young scientists

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14. The number of violent crimes committed in the greater metropolitan area of Sao Paolo, Brazil, more than doubled from 1975 to 1990 by the influx of drugs. A. B. C. D. E. more than doubled increased by more than twice increased more than two times was increased more than double was more than doubled

the damaged tires with new Toughgrip tires? A. Toughgrip tires are the only tires the driver can afford. B. The driver feels obligated to buy tires from his brother, who sells only Toughgrip tires. C. One of the tires was slashed by a rival driver, while the other two blew out in traffic because of material defects. D. The Toughgrip Company offered to replace all of the tires free of charge because the tires were covered under a 60,000-mile warranty. E. The taxi company for which the driver works has endorsed Toughgrip as the official tire of their company’s cars.
The following two questions are based on the following passage:

For the following questions, select the best of the answer choices given.

15. One of the biggest threats to a company’s productivity is absenteeism. Studies have shown that companies with in-house child-care programs see fewer absences among their employees who are parents than companies without such programs. Therefore, many companies could boost their productivity by starting in-house child-care programs. Which of the following, if true, most weakens the above argument? A. Companies that reimburse outside child-care programs actually see less absenteeism among working parents than companies with in-house programs. B. In-house child-care programs create distractions for nonparents that can harm their productivity. C. Absenteeism is not a serious problem for companies that impose harsh penalties on employees who miss work. D. Studies have shown that employees with children are more likely than those without children to remain in the same job for more than five years. E. Potential employees generally view companies with in-house child-care programs as more desirable places to work than companies without such programs. 16. A taxi driver purchased four tires of the Toughgrip brand for his cab. Within six months of his purchasing these tires, three of them suffered irreparable blowouts. Despite the poor track record of these tires, the driver replaced all three of the damaged tires with new Toughgrip tires. Which of the following, if true, does NOT support the driver’s decision to replace

An automaker is facing financial difficulties. The vice president of marketing has determined that the root of the company’s problems is low brand loyalty. The vice president proposes, therefore, that the company begin an aggressive advertising campaign focused on children aged from three to eight years. By securing strong brand recognition with this demographic, he argues, the company will have an advantage when these customers reach an age when they can buy cars. 17. Which of the following, if true, provides the strongest support for the vice president’s proposal? A. Federal law prohibits the advertising of alcohol or tobacco on any medium for which the primary audience is under 21 years of age. B. Children aged three to eight, even if they had the money to purchase a car, will not legally be able to drive one for several years. C. The cost of advertising on children’s programs is comparable to the cost of advertising on adult special-interest programs. D. Focus groups have consistently observed that the automaker’s brand is associated with “tradition” and “older” drivers. E. Studies have shown that lifelong customers of certain products, such as particular brands of toothpaste or peanut butter, frequently credit their brand loyalty to exposure to the product at an early age.
PRACTICE TEST 5 \$325

18. Which of the following, if true, raises the most serious doubts about the vice president’s proposal? A. Studies have shown that children are an important factor in the car-buying decision for 75 percent of parents with children under 18 years of age. B. The financial difficulties facing the company will result in the company’s declaring bankruptcy within five years if the difficulties are not addressed effectively. C. The company’s most recent advertising campaign, focused on the theme of “Rev up your life,” has received positive ratings from the demographic aged 18 to 29. D. Children are accustomed to viewing ads for car toys while watching their favorite television programs, so ads for actual cars will appeal to them. E. The vice president who made the proposal has only one year of experience in the automotive industry, but has spent more than 20 years in the financial services and children’s entertainment industries.
The questions in this group are based on the content of a passage. After reading the passage, choose the best answer to each question. Answer all questions following the passage on the basis of what is stated or implied in the passage.

Dear Sirs, Given all the coverage that the emergence of hybrid cars has received in your pages in recent months, your readers may be interested to learn that gasoline-electric hybrids are not a new phenomenon at all, but rather the latest incarnation of an idea that has been kicking around for over a century. Indeed, the hybrid car has been around almost as long as the automobile itself. At the turn of the twentieth century, as the automotive age dawned, three power-generating technologies competed for dominance: steam, gasoline, and electricity. In the year 1900, steam was well known as the power source of the industrial revolution, and electricity was widely regarded as the power source of the future, so it was not at all obvious that internal combustion engines burning a fractional distillate of crude petroleum would have any particular edge in this race for the powertrains of America. Indeed, when engineer H.

Piper filed the first patent application for a gasolineelectric hybrid motor in 1905, his intention was to use the gas to give a little kick to his perfectly serviceable electric engine. His goal: an engine that could accelerate from 0 to 25 miles per hour in 10 seconds. Piper achieved his goal. Electric and hybridelectric engines powered more than 35,000 vehicles sold in 1912. These cars were perfectly adequate for the time, but over the following decade they mostly disappeared from the market, through no fault of their own. The cause of their decline was the spectacular improvements in the cost and performance of gasoline-powered cars. An onslaught of fast and cheap internal combustion cars from Ford, General Motors, and Buick essentially buried the electric and electric-hybrid motors by the 1920s. Continuing performance improvements in internal combustion engines and inexpensive gas pretty much kept hybrids buried until the oil crises of 1973 and 1979 gave Americans a reason to start thinking about fuel efficiency. Engineers had the motivation to think about fuel-efficient hybrids, but they still lacked the means to make hybrids economically competitive with gas-powered cars, because the performance of gas-electric engines lagged far behind that of gas-powered engines in acceleration, top speed, and cruising range. Dramatic improvements in electronics and computer technology during the 1990s, however, finally made the hybrid a reality. Advances in battery performance and, most importantly, computerguided electric power transfer created a car that could drive like a regular car, but do so on half the tank of gas. As another century dawns, perhaps we are entering into a new automotive age. 19. Based on the tone and content of the passage, the author of the passage is most likely which of the following? A. An automotive engineer writing to his company management B. An enthusiast of automotive history writing to the editors of a car magazine C. A college engineering student writing to a car manufacturer D. A history professor writing to a television producer of historical documentaries E. An environmental activist writing to the editors of a newspaper

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20. The purpose of the article could best be summarized as which of the following? A. To correct a mistaken impression about the performance of gasoline-electric hybrid cars B. To educate readers about the economic and technological potential of hybrid cars C. To refute a factually inaccurate statement made previously in the publication regarding the history of hybrid cars D. To acquaint readers with the history of gasoline-electric hybrid cars E. To educate readers about technological innovations at the dawn of the automotive age 21. According to the passage, electric and hybrid cars failed to capture the American automotive market in the early twentieth century because of what factor? A. The improvement in cost and performance of gasoline-powered cars B. The superior fuel efficiency of hybrid cars C. The substandard performance of steampowered cars D. Consumer fear of being electrocuted by gasoline-electric hybrids E. Government subsidies for gasoline- and coal-powered cars 22. According to the information given in the passage, which of the following best characterizes the different motivations behind the earliest experiments with gasoline-electric hybrids and the experiments going on in modern times? A. The earliest experiments with hybrids sought to improve the fuel efficiency of electric engines, while modern experiments seek to improve the performance of gas-burning engines. B. The earliest experiments with hybrids sought to improve the fuel efficiency of gas-burning engines, while modern experiments seek to improve the performance of electric engines. C. Modern experiments with hybrids seek to improve the fuel efficiency of gas-burning engines, while the earliest experiments sought to improve the performance of electric engines.

D. Modern experiments with hybrids seek to improve the cruising range of gaspowered cars, while earlier experiments sought to improve the handling and safety of electric cars. E. The earliest experiments with hybrids sought to combine the power of steam with the efficiency of electricity, while modern experiments seek to combine the efficiency of electricity with the power of gas. 23. The passage lists which of the following as a reason for the resurgence of interest in the gasoline-electric hybrid engine? A. The onslaught of fast and inexpensive internal combustion cars from Ford, General Motors, and Buick B. Advances in battery performance and electricity transfer C. The Iranian hostage crisis of 1979 D. Dramatic improvements in computer technology E. The oil crisis of 1973 24. Which of the following examples of business and technology bears the most similarity to the history of the hybrid car, as presented in the passage? A. American aerospace companies in the 1960s created working prototypes of supersonic passenger aircraft that could complete intercontinental flights in half the time of conventional aircraft, but these projects were canceled because of concerns that the high-altitude craft posed too great a threat to the integrity of the ozone layer. B. Although oil companies first attempted deep-sea drilling in the Gulf of Mexico in the 1930s, these deep-sea projects could not compete with land-based drilling projects until advances in drilling technology and the rising price of oil made deep-sea drilling economically viable in the late twentieth century. C. Automakers in the 1980s, after concluding that the average driver could not be relied on to use seat belts consistently, chose to adopt airbags as a standard safety feature.

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D. Lighter-than-air craft, such as Zeppelins, made up a substantial part of total air traffic in the early twentieth century, but they rapidly fell out of favor after airplanes proved to be a faster and safer form of transportation. E. Although railroads carried more than 90 percent of all land-based commercial cargo in the United States in 1910, by 1980 railroads had been surpassed by trucks in total cargo carried, because of the greater speed and flexibility offered by the heavy truck as compared with the railroad. 25. Based on the information given in the passage, which of the following can be inferred about an electric-gasoline hybrid car in 1950? A. It would have been difficult to find a power supply for such a car. B. Its acceleration would have been roughly comparable to that of a gasoline-burning car that cost less than half as much as the hybrid car. C. It would have been viewed as “the car of the future.” D. Its performance would have been limited by contemporary battery technology. E. Had it been produced, it would have sold more than 35,000 units per year.
For the following questions, select the best of the answer choices given.

program was piloted has been dropping steadily for over a decade. C. Teenagers at the public schools where the “Stop Drugs Now” program was piloted reported higher average levels of drug use than did teenagers at private schools in the same counties where the program was not piloted. D. There is evidence that teenagers who start smoking at an early age are more likely to experiment with illegal drugs than teenagers who do not smoke. E. The percentage of teenagers who reported using drugs at the schools where the “Stop Drugs Now” program was piloted dropped more in the last year than in any other year over the last decade. 27. A car manufacturer periodically discounts certain car models to its dealers to coincide with intensive advertising campaigns focused on those cars. After analyzing the results of this program, the manufacturer found that sales of the discounted cars were strong, but it also concluded that it could reap greater profits if it did not hold promotions in this way. Which of the following statements, if true, best accounts for the manufacturer’s conclusion about profitability? A. Some consumers worry that discounted cars are more likely to be defective. B. The car manufacturer had not been effective in controlling the production costs of the cars, and these rising costs ate into the manufacturer’s profits. C. Although dealers requested large numbers of the cars at discounted prices, they generally sold the cars at the normal retail price, thereby keeping more of the profit for themselves. D. Many consumers buy large-ticket items, such as cars, only when they are on sale. E. The manufacturer’s intensive advertising campaign did not sufficiently emphasize the cars’ high levels of performance on road tests.

26. Drug use among teens concerns many people in California. Advocates of the “Stop Drugs Now” program, which was piloted in public schools in five California counties last year, argue that the program should be used throughout the state to decrease drug use among teenagers. Which of the following statements, if true, would most strengthen the argument of the advocates of “Stop Drugs Now” that the program should be expanded statewide? A. School programs are far less important than parental messages in influencing a teenager’s decision to use drugs. B. Drug use among teens in the five counties where the “Stop Drugs Now”

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28. Advertisement: We at Vesuvius Vacuums always give our customers what they deserve, and they deserve the very best. That’s why we use only SuperTec air filters. Which of the following, if true, would most undermine the argument expressed in the advertisement? A. In a test of three leading air filters, the SuperTec air filter performed at the same level as one of the filters and at a higher level than the other. B. The SuperTec air filter is the only kind of air filter that will fit in the model of vacuum sold by Vesuvius Vacuums. C. In a national study by a prominent consumer group, Vesuvius Vacuums gained a “superior” rating for product quality. D. The customers of Vesuvius Vacuums have expressed no preferences concerning the type of air filter used in the product. E. The specific air filter used in a given vacuum makes only a small difference in the long-term performance of that vacuum. 29. Oil is a nonrenewable resource, whereas sunshine is limitless. So why not run cars on solar power? Because a car powered by solar collecting panels would be fine on a sunny day, but as soon as the sun went behind a cloud, the car would no longer function. Which of the following is presupposed in the argument against running a car on solar power? A. Solar power is cleaner than fossil fuels, and it involves less geopolitical risk. B. In most of the northern hemisphere, it can be expected that more than 150 days a year will be cloudy. C. No system exists for storing solar energy for a car’s use when the car is not in direct sunlight. D. No one has yet introduced a commercially viable process for mass-producing solar cells that convert more than 10 percent of incoming sunlight into usable energy. E. Consumers accustomed to the rapid acceleration of gasoline-powered cars will not accept the weak acceleration of solar-powered cars.

The following questions present a sentence, part of which or all of which is underlined. Beneath the sentence, you will find five ways of phrasing the underlined part. The first of these repeats the original; the other four are different. If you think the original is best, choose the first answer; otherwise choose one of the others. These questions test correctness and effectiveness of expression. In choosing your answer, follow the requirements of standard written English; that is, pay attention to grammar, choice of words, and sentence construction. Choose the answer that produces the most effective sentence; this answer should be clear and exact, without awkwardness, ambiguity, redundancy, or grammatical error.

30. Chauncy, like most bulldogs, has a fondness for meat and gravy. A. B. C. D. E. like most bulldogs, has as most bulldogs, have like many bulldogs, have like most bulldogs, having as with many bulldogs, has

31. Last season, oranges from South Florida were as bountiful as, if not more bountiful than, oranges from the normally more bountiful northern region. A. as bountiful as, if not more bountiful than, oranges B. equally bountiful, if not more so, to oranges C. as bountiful, if not bountifuller, than oranges D. so bountiful, and maybe more bountiful, than oranges E. as bountiful, if not more bountiful, as oranges 32. Every lawyer knows that it is difficult to prove culpability in technically complicated lawsuits if there is a lack of some expert to testify about the complicated technical aspects. A. if there is a lack of some expert to testify B. unless there will be an expert who might testify C. should there be no testimony from an expert D. without an expert’s testimony E. lacking some expert to testify

PRACTICE TEST 5

\$329

33. To be a great salesman requires strong personal skills, the ability to think fast, and demands a can-do attitude. A. requires strong personal skills, the ability to think fast, and demands B. requires strong personal skills, the ability to think fast, and C. requires strong personal skills, demands the ability to think fast, and D. requiring strong personal skill, an ability to think fast, and demands E. demands strong personal skills, an ability to think fast, but with 34. The tremendous insight of Einstein was that the passage of time does not appear the same while standing still as it does to a person traveling at a substantial portion of the speed of light. A. while standing still as it does to a person traveling B. to a person standing still as to a person traveling C. to a person who is standing still as a person who is traveling D. while standing still as to traveling E. to a person standing still as to a person who travels 35. Professor Markham’s theory fails to explain the extent to which savings from personal income has shifted to short-term bonds, money-market funds, and other near-term investments by the instability in the futures market. A. to which savings from personal income has shifted B. of savings from personal income that has been shifted C. of savings from personal income shifting D. to which savings from personal income have shifted E. to which savings from personal income has been shifted

36. Approximately \$120 billion in venture capital is estimated as having poured into technology stocks during the late 1990s, creating a valuation bubble that burst in 2000. A. Approximately \$120 billion in venture capital is estimated as having poured into technology stocks during the late 1990s, creating B. During the late 1990s approximately \$120 billion in venture capital is estimated to have poured into technology stocks and created C. During the late 1990s it is estimated that there was approximately \$120 billion in venture capital that was poured into technology stocks, creating D. It is estimated that during the late 1990s, approximately \$120 billion in venture capital poured into technology stocks, creating E. It is estimated that there was approximately \$120 billion in venture capital that poured into technology stocks during the late 1990s and created 37. Jim Smyth may be a charismatic speaker, but it seems to be counterproductive to have a high school dropout as mayor in a town where illiteracy functionally affects 37 percent of the electorate. A. where illiteracy functionally affects 37 percent of the electorate B. in which functionally the electorate is 37 percent illiterate C. where 37 percent of the electorate are functionally illiterate D. which has 37 percent of the electorate functionally illiterate E. where, of the electorate, 37 percent of them functionally are illiterate

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THE PRACTICE TESTS

For the following questions, select the best of the answer choices given.

Which of the following, if true, provides the strongest argument that the councilman’s plan will not increase the city’s revenue? A. A system that promotes parking fines will anger citizens, and they will consequently vote the councilman out of office if the plan goes through. B. The city owns only 14 parking spots in the downtown area. C. The costs of assessing and collecting the parking fines will surpass the revenues likely to be collected from the new plan. D. Ray’s parking garage, the only competition for the city-owned parking places downtown, charges \$18 per day for its parking places. E. It has been observed that on an average day, approximately three different cars park in each of the city-owned parking spots downtown. 40. Over the last five years, Eagle Trust Bank has seen the number of its retail customer accounts drop by over 40 percent. Over this same period, the price of Eagle Trust stock has increased by more than 80 percent. This phenomenon has perplexed certain investors, who believe that a bank’s stock should drop if its number of customer accounts drops. Which of the following, if true over the last five years, best accounts for the observed movement in the price of Eagle Trust stock? A. Two years ago Eagle Trust was investigated by the Securities and Exchange Commission for accounting irregularities, but last year the company was cleared of all charges. B. Eagle Trust recently implemented a highly publicized program for no-fee home mortgages. C. Eagle Trust is in the process of switching its customer base from retail customers to commercial customers, which now account for over 75 percent of the bank’s revenues. D. There have been many aggressive new entrants into the retail customer banking business over the last five years. E. Eagle Trust is known for offering one of the best employee benefits packages in the industry.

38. The decline in the price of biotech stocks has hurt many institutions that had invested heavily in biotech companies. Last year the state university added 200,000 shares of a biotech stock to its holdings. The stock in question has declined in value by more than 90 percent over the last 12 months. The college, however, did not purchase the stock, but received it as a gift. Therefore, the price decline will not harm the university’s finances. Which of the following, if true, casts the most doubt on the conclusion that the price decline of biotech stocks will not harm the university’s finances? A. The biotech sector is volatile; some stocks that lose 90 percent of their value in one year may regain all of their value and more in the following year. B. The university needs to pay capital gains taxes only on a stock sale that results in a gain; stocks sold at a loss will incur no tax penalty. C. Although the biotech sector is down, the overall health-care sector, in which the university has invested heavily, is up for the year. D. The biotech company in question has a promising new drug in development that could revolutionize the treatment of type II diabetes. E. The university began construction of a new laboratory last year that the provost had expected to pay for with the proceeds from the sale of the biotech stock in question. 39. A city councilman has proposed a controversial new plan to increase city revenues from the parking places downtown. He has proposed that instead of charging \$1.20 per hour for parking in these spots, the city should make all parking spots five-minute loading zones, and then assess \$15 parking fines on anyone who parks in the spots for more than five minutes.

PRACTICE TEST 5

\$331

41. Recent scientific studies have proven that ulcers are caused, at least in part, by the heliobacter bacterium. Dr. Redding has hypothesized that a natural way to prevent and cure ulcers is to eat large amounts of raw broccoli, which contains potent organic compounds that are beneficial to gastric health. All of the following statements support Dr. Redding’s hypothesis, EXCEPT: A. It has been shown that people who consume raw broccoli on a regular basis have a 65 percent lower chance of developing ulcers than do the general population. B. One of the organic compounds found in broccoli has been shown to have an antibiotic effect on the heliobacter bacterium.

C. Dr. Redding conducted a study in which groups of patients suffering from ulcers either ate large quantities of broccoli or ate a diet that included no vegetables; several of the patients who ate the large quantities of broccoli showed marked improvement in their conditions. D. Broccoli is one of the most potent dietary sources of antioxidants, the organic compounds shown to combat the free radicals that are thought to cause cancer. E. Test animals with chemically induced ulcers showed some signs of improvement when raw broccoli was incorporated into their diets.

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Practice Test 6
ANALYTICAL WRITING 1

d

Analysis of an Issue
TIME—30 MINUTES

It is better to have more free time than to have more material things. Discuss the extent to which you agree or disagree with the opinion stated above. Support your views with reasons and/or examples from your own experiences, observations, or reading.

333

ANALYTICAL WRITING 2

Analysis of an Argument
TIME—30 MINUTES

directions: In this section, you will be asked to write a critique of the argument presented below.You may, for example, consider what questionable assumptions underlie the thinking, what alternative explanations or counterexamples might weaken the conclusion, or what sort of evidence could help strengthen or refute the argument. Read the argument and the instructions that follow it, and then make any notes that will help you plan your response. Write your response on a separate sheet of paper. If possible, type your essay on a word processor. Observe the 30-minute time limit.

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37 QUESTIONS

Quantitative
TIME—75 MINUTES

The following data sufficiency problems consist of a question and two statements, labeled (1) and (2), in which certain data are given. You have to decide whether the data given in the statements are sufficient for answering the question. Using the data given in the statements plus your knowledge of mathematics and everyday facts (such as the number of days in July or the meaning of counterclockwise), you must indicate whether

note: In data sufficiency problems that ask for the value of a quantity, the data given in the statements are sufficient only when it is possible to determine exactly one numerical value for the quantity. 1. A hiker in a national forest stopped at a ranger station to add water to her canteen. How many ounces of water were in the canteen when she arrived at the ranger station? (1) The hiker added 24 ounces to the canteen at the ranger station. (2) After the hiker added water to the canteen, the canteen was 75 percent full. 2. If b > a, then a is what percent of b? (1) a = 4 (2) b = 4a 3. If all apples at a certain grocery store are equally priced, and all pears at the grocery store are equally priced, what is the price of a pear? (1) Eight pears cost eighty cents more than eight apples. (2) Ten apples cost twenty cents more than eight pears.

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. D. EACH statement ALONE is sufficient. E. Statements (1) and (2) TOGETHER are NOT sufficient. numbers: All numbers used are real numbers. figures: A figure accompanying a data sufficiency problem will conform to the information given in the question, but will not necessarily conform to the additional information given in statements (1) and (2). Lines shown as straight can be assumed to be straight, and lines that appear jagged can also be assumed to be straight. You may assume that the position of points, angles, regions, etc., exist in the order shown and that angle measures are greater than zero. All figures lie in a plane unless otherwise indicated.

PRACTICE TEST 6

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4. If each of the segments marked on the board above is of equal length, and if x and y represent the indicated lines on the board, then what is the distance between x and y? (There are twelve inches in a foot). (1) The board is five feet long. (2) x is 18 inches from the nearest end of the board. 5. Any decimal that has a finite number of nonzero digits is a terminating decimal. For example, 16, 12.43, and 0.26 are all terminating decimals. If a and b are positive integers and the ratio a/b is expressed as a decimal, is a/b a terminating decimal? (1) b = 5 (2) 70 < a < 80
Solve the problem and indicate the best of the answer choices given.

7. A hiker walked for 3 days. She walked 18 miles on the first day, walking 3 miles per hour. On the second day she walked for one less hour, but she walked one mile per hour faster than on the first day. On the third day she walked the same number of hours as on the first day, but at the same speed as on the second day. How many miles in total did she walk? A. B. C. D. E. 24 44 58 60 62

8. 16 + 64 =

A. 4 B. 4 5 C. 5 2 D. 8 5 E. 16 2
9.

numbers: All numbers used are real numbers. figures: A figure accompanying a problem-solving question is intended to provide information useful in solving the problem. Figures are drawn as accurately as possible EXCEPT when it is stated in a specific problem that its figure is not drawn to scale. Straight lines may sometimes appear jagged. All figures lie in a plane unless otherwise indicated.

(0.5) 9 = (0.5) A. B. C. D. E. 0.0125 0.025 0.1 0.25 0.625

11

6. A company, Chauncy Co., has an annual travel budget of \$55,000. The accounting department estimates that transportation expenses will increase 5 percent in the coming year, and nontransportation travel expenses will increase by 15 percent in the coming year. Last year, Chauncy Co. spent \$19,500 on transportation-related expenses, and \$35,000 on nontransportation travel expenses. If the annual travel budget does not increase this year, and if the accounting department’s estimates are correct, how far over the annual travel budget will expenses be this year? A. B. C. D. E.
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10. The promoters of the Springfield music festival estimated a 50 percent increase in ticket sales from last year, but because of bad weather, ticket sales actually decreased by 25 percent from last year’s level. What percent of the projected ticket sales were the actual ticket sales? A. B. C. D. E. 45 50 55 65 75

11. If the average (arithmetic mean) of x and y is 40, and z − x = 60, what is the average of y and z? A. B. C. D. E. 20 50 65 70 140

Expenses will not go over the budget. \$500 \$4,225 \$5,725 \$60,725

THE PRACTICE TESTS

12. When Greenville State University decided to move its fine arts collection to a new library, it had to package the collection in 20-inch by 20-inch by 15-inch boxes. If the university pays \$0.50 for every box, and if the university needs 3.06 million cubic inches to package the collection, what is the minimum amount the university must spend on boxes? A. B. C. D. E. \$255 \$275 \$510 \$1,250 \$2,550

16. Over the weekend, a shoe store sold 1/3 of the shoes in its stock. The average price of the shoes sold was \$60 per pair. What was the total revenue from shoe sales over the weekend for this shoe store? (1) When the store closed on Sunday night, 600 pairs of shoes were still in stock. (2) The store began the weekend with 900 pairs of shoes. 17. A jar contains 30 coins, of which 20 are nickels and 10 are dimes. If 7 coins are removed, how many nickels are left? (1) More nickels are removed than dimes. (2) The remaining coins in the jar are worth \$1.55.
Solve the problem and indicate the best of the answer choices given.

The following data sufficiency problems consist of a question and two statements, labeled (1) and (2), in which certain data are given. You have to decide whether the data given in the statements are sufficient for answering the question. Using the data given in the statements plus your knowledge of mathematics and everyday facts (such as the number of days in July or the meaning of counterclockwise), you must indicate whether A. B. C. D. E. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. EACH statement ALONE is sufficient. Statements (1) and (2) TOGETHER are NOT sufficient.

q r qt 18. If s t = for all numbers q, r, s, and t, −rs −8 −6 then 4 3 = A. B. C. D. E. −3 −1 1 4/3 4

13. If n is a positive integer and m = 6.25 × 10n, what is the value of n? (1) 500 < m < 5,000 (2) m < 6,250 14. If p + q = 400 and p < q, is p + q < r + s? (1) p + r + s = 600 (2) q + r > 400 15. If n is an integer, and n a positive integer? (1) n2 = 25 (2) 5n = 25
2 0, is 100 + n n

19. A certain tire company can produce tires at a cost of \$22,500 per batch plus \$9 per tire. The company can sell tires to the wholesaler at a cost of \$20 per tire. If a batch of 15,000 tires is produced and sold, what is the company’s profit per tire? A. B. C. D. E. \$9.00 \$9.50 \$11.00 \$13.50 \$20.00

20. Of the following, which is most nearly equal to but not greater than 15 ? A. B. C. D. E. 3.7 3.8 3.9 4.0 4.1

PRACTICE TEST 6

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21. A moving company charges a flat rate of \$550 for loading its trucks and an additional \$20 per 1/5 mile for moves within the city. How much would a move of 2.8 miles within the city cost? A. B. C. D. E. \$690 \$790 \$830 \$880 \$1,010

The following data sufficiency problems consist of a question and two statements, labeled (1) and (2), in which certain data are given. You have to decide whether the data given in the statements are sufficient for answering the question. Using the data given in the statements plus your knowledge of mathematics and everyday facts (such as the number of days in July or the meaning of counterclockwise), you must indicate whether A. B. C. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. EACH statement ALONE is sufficient. Statements (1) and (2) TOGETHER are NOT sufficient.

22. Donna is a mountain biking enthusiast. One Saturday, she spent the morning biking up an uphill trail at an average speed of 20 kilometers per hour, and then returned by the same route in the afternoon at an average speed of 25 kilometers per hour. If the downhill trip in the afternoon took 3/4 of an hour less than the uphill trek in the morning, how many kilometers did Donna ride each way? A. B. C. D. E. 50 55 65 70 75

D. E.

23. If x, y, and w are nonzero numbers and x − y = w, which of the following is equal to 1? A. B. C. D. x −w y x +w −y x−y w−y y +w −x 25. Is the triangle depicted above equilateral? (Figure not necessarily drawn to scale.) (1) x + y + z = 180° (2) y = z 26. If w + x + y = 42, what is the value of xyz? (1) x and y are consecutive odd integers (2) w = 2x 27. What is the value of integer x? 24. If 12 percent of x is 30 percent of 480, then x is A. B. C. D. E. 144 640 960 1,200 1,440 (1) x is a positive integer (2) 17 ≤ x ≤ 18

w−y E. x

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THE PRACTICE TESTS

28. What is the value of x − y ? (1) (x − y)2 = 25 (2) 4x = 4(y + 3) 29. A farmer sells buckets of onions for \$2, buckets of potatoes for \$4, and buckets of squash for \$5. How many buckets of squash did the farmer sell? (1) The farmer sold one bucket of onions. (2) In total, the farmer sold 7 buckets of produce for \$33.
Solve the problem and indicate the best of the answer choices given.

32. In the flat triangular surface depicted above, if x = 6 feet, what is the area of the surface in square feet? (Figure not necessarily drawn to scale.) A. B. 3 8 3 8

30. If x dollars are invested at 12 percent for one year and y dollars are invested at 8 percent for one year, the annual income from the 8 percent investment will exceed the annual income from the 12 percent investment by \$64. If \$5,000 is the total amount invested between x and y, how much is invested at 12 percent? A. B. C. D. E. \$1,680 \$1,997 \$3,003 \$3,320 \$3,500

C. 3 3 8 3 D. 4 E. 3 3 4 33. Which of the following is equal to x24 for all positive values of x? A. B. C. D. E. x12 + x12 (−x12)−2 (x6)6 (x2)(x3)(x4) (x72)1/3

7+2 =7 31. If and xy = 4, then 7y + 2x = x y A. 28 B. 14 C. 7 4

D. 4 7 E. 2 7

34. A particular rocket car can travel for sustained periods at a maximum speed of 240 miles per hour. How many minutes would it take this rocket car to travel 86 miles? A. B. C. D. E. 2.8 181/2 211/2 22 24

35. The square root of 800 is between which of the following integers? A. B. C. D. E. 21 and 25 24 and 28 27 and 31 30 and 34 33 and 37

PRACTICE TEST 6

\$339

36. If x is an integer and y = 4x + 3, which of the following cannot be a divisor of y? A. B. C. D. E. 5 6 7 9 23

37. A real estate developer has bought 1,872 acres of land on which to build a new neighborhood. He plans to zone the area for roads, common area, and housing plots on a ratio of 2:3:8, respectively. If a planned lake will take up 16 acres of the common area, how many acres of the common area will be left over for the clubhouse and golf course? A. B. C. D. E. 128 144 416 432 450

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THE PRACTICE TESTS

41 QUESTIONS

Verbal
TIME—75 MINUTES

The following questions present a sentence, part of which or all of which is underlined. Beneath the sentence, you will find five ways of phrasing the underlined part. The first of these repeats the original; the other four are different. If you think the original is best, choose the first answer; otherwise choose one of the others. These questions test correctness and effectiveness of expression. In choosing your answer, follow the requirements of standard written English; that is, pay attention to grammar, choice of words, and sentence construction. Choose the answer that produces the most effective sentence; this answer should be clear and exact, without awkwardness, ambiguity, redundancy, or grammatical error.

1. Because of our laws concerning habeas corpus, prosecutors will rarely move forward with a murder prosecution should there be no body as evidence that a murder took place. A. B. C. D. E. should there be no body as evidence without a body as evidence unless there may be a body to show without having found a body for evidence lacking the possession of a body for evidence

3. Found exclusively on the Galapagos Islands, marine iguanas are the only species of iguana to enter the water, where they seek out the algae that make up the bulk of its diet. A. marine iguanas are the only species of iguana to enter the water, where they seek out the algae B. the marine iguana, being the only species of iguana to enter the water, searches for the algae C. the marine iguana is the only species of iguana to enter the water, where it searches for the algae D. marine iguanas are the only iguana species entering the water, where it seeks out the algae E. the marine iguana is the only iguana species to enter the water, where they search for the algae

2. Thomas Jefferson viewed religious freedom, as the other founding fathers, as a fundamental component of a free society. A. Thomas Jefferson viewed religious freedom, as the other founding fathers, as a fundamental component B. Thomas Jefferson, being like the other founding fathers, viewed religious freedom as a fundamental component C. Thomas Jefferson viewed religious freedom as a fundamental component, like the other founding fathers, D. Thomas Jefferson, like the other founding fathers, understood the naturally fundamental component of religious freedom E. Thomas Jefferson, like the other founding fathers, viewed religious freedom as a fundamental component

PRACTICE TEST 6

\$341

4. Because a rockslide had blocked much of the passage, the spelunking team was not able of exploring the full extent of the cave. A. the spelunking team was not able of exploring the full extent of B. the full extent was not able to be explored by the spelunking team of C. the spelunking team was unable in exploring, to its full extent, D. therefore the spelunking team was unable to explore the full extent of E. the spelunking team was unable to explore the full extent of 5. A distinguished physician who worked from the 1930s to the 1970s, many new medical techniques, perhaps most notably in the field of epidural steroids, were pioneered by Dr. Marvin Leason. A. many new medical techniques, perhaps most notably in the field of epidural steroids, were pioneered by Dr. Marvin Leason B. Dr. Marvin Leason notably pioneered many new medical techniques, perhaps most so in the field of epidural steroids C. Dr. Marvin Leason pioneered many new medical techniques, perhaps most notably in the field of epidural steroids D. the field of epidural steroids was perhaps the most notable of the many new medical techniques pioneered by Dr. Marvin Leason E. perhaps most notable among the new medical techniques pioneered by Dr. Marvin Leason were those in the field of epidural steroids
For the following questions, select the best of the answer choices given.

should be required to post their lecture notes online? A. At the most popular classes, there are often insufficient quantities of lecture note copies to accommodate all of the students. B. Students have acknowledged that if the lecture notes are posted online, they will be less likely to go to class. C. Professors complain that the university does not provide sufficient copying funds, so that professors often have to pay for copies of lecture notes out of their own pockets. D. Over 80 percent of students have access to the Internet in their dorm rooms, and all students have 24-hour access to the Internet at the computer lab. E. The university has publicly stated that one of the educational goals of the university is to help all students gain competency with the Internet.
The following two questions are based on the following passage:

The Southfork Steel Company is in trouble. Since 1960 it has made guaranteed payments to retirees out of a pension fund paid into by current employees as a percentage of their salaries. The restructuring of the Southfork workforce, however, has meant that fewer employees are now needed to produce the same amount of work as in the days of the retired employees. Since current employees are unwilling to pay a larger percentage of their salaries into the pension system than their predecessors did, the pension fund will inevitably go bankrupt.

6. Students at a certain university have complained that some of their professors do not provide copies of their lecture notes at every class. The student body president has argued that, in order to further the educational purposes of the university, all professors should be required to post their lecture notes online. Which of the following, if true, most weakens the students’ argument that the professors

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THE PRACTICE TESTS

7. Which of the following, if true, suggests that

the passage is correct in its conclusion that the pension fund will inevitably go bankrupt? A. Employees who retire today will, on average, live five years longer than those who retired in the 1960s. B. The workers’ union has consistently vetoed any efforts on the part of management to cut the level of pension payments to retired employees. C. Although Southfork Steel now produces almost twice as much steel as it did during the 1960s, overseas competition has driven the price of steel, adjusted for inflation, to less than one-third of its price in the 1960s, and there is no indication that prices will increase at any time in the future. D. Consultants have advised Southfork management that it can improve efficiency at the plant by implementing further workforce restructuring that could decrease the total number of employees by approximately 10 percent. E. Southfork employees in management do not take part in the general pension system, but instead pay into and collect from a separate system that guarantees higher payments. 8. Which of the following, if true, casts the most doubt on the conclusion in the passage that the pension fund will inevitably go bankrupt? A. The pension fund is invested in a conservative portfolio of bonds and money market funds that perform, on average, slightly better than inflation. B. Financial analysts have determined that, with current levels of payments into and out of the plan, the pension fund will remain solvent for at least another seven years. C. If the company is bought or goes out of business, the payments to retirees from the pension funds are likely to become subject to arbitration by either the new owners or the bankruptcy trustees, in which case the “guaranteed” payments could be readjusted to lower levels, or possibly terminated.

D. The restructuring of the workforce has dramatically increased the efficiency of steel production at Southfork, resulting in substantially higher revenues per employee than in the past, and consequently much higher salaries. E. Although the modern era is referred to as a “postindustrial” age, the worldwide demand for steel has never been higher. 9. A recent study showed that more than
50 percent of people who commit violent crimes had seen at least one act of violence on television during the preceding week. Many psychologists

suggest that exposure to acts of violence, even when they are obviously fictional, can increase a person’s propensity to commit violent acts. If government regulators were to ban all violence on television, therefore, we could expect the incidence of violent crimes to decrease by over 50 percent.

The two portions in boldface in the passage above play which of the following roles? A. The first portion is an inference related to the conclusion of the argument; the second portion supports the conclusion. B. The first portion is a conclusion that is not necessarily true based on the evidence; the second portion supports that conclusion. C. The first portion is evidence that supports the argument; the second portion is a conclusion that is not necessarily true based on the evidence. D. The first portion is evidence that supports the argument; the second portion is a conclusion that must be true based on the evidence. E. The first portion is a conclusion that must be true based on the evidence; the second portion is an inference related to that conclusion.
The questions in this group are based on the content of a passage. After reading the passage, choose the best answer to each question. Answer all questions following the passage on the basis of what is stated or implied in the passage.

Of all aspects of Indian culture, the caste system is perhaps the most bewildering to outsiders.

PRACTICE TEST 6

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For visitors unaccustomed to this system of hereditary social divisions, the complex and mostly unwritten rules governing whom a person can marry, what kind of work she can do, and even what kind of food she can eat may seem puzzling and mysterious. One reason for this confusion is that the concept of caste is actually divided into two separate but related concepts in Indian culture: varna and jati. Varna, which literally means “color,” is the most basic social division. There are four varna: the Brahmans, the traditional priest class; the Kshatriya, the warrior class; the Vaishya, the skilled workers and merchants; and the Sudra, laborers whose role is to serve the three higher classes. Below the Sudra are a class known as the Untouchables, who technically fall outside of the varna system because they are supposedly “unclean” in a ritual sense. The Untouchables are the lowest class in India, but they make life possible for everyone else because they take care of the jobs that would “pollute” the higher classes, such as working with dead animals or cleaning sewage. The Indian statesman Mohandas Gandhi, in an effort to promote social equality, encouraged people to refer to Untouchables as the Harijan, which means “Children of God.” Each varna is then divided into hundreds or thousands of jati, a term that literally means “birth.” The jati are kinship groups with hereditary roles and professions, such as leatherworker or brickmaker. Observant Hindus have traditionally married within their varna and jati. The origins of the caste system are obscure. The prevailing theory among anthropologists is that the Varna system emerged shortly after the so-called Aryan Invasion of the second millennium B.C. According to this theory, a population of IndoEuropean invaders conquered northern India around 1500 B.C. The Indo-Europeans placed themselves in the three highest rungs of society (Brahman, Kshatriya, and Vaishya), corresponding to the traditional division of Indo-European societies into priests, warriors, and commoners, while placing the conquered local populations into the worker classes of the Sudra and the Untouchables. This theory does not account for the jati system, however, which has parallels in no other IndoEuropean society. Most anthropologists suggest that the jati system predates the varna system, and that it might have originated in the Harappan civilization that prevailed in northern India prior to the Aryan Invasion.

10. What is the primary purpose of the passage? A. To compare and contrast two theories on the origin of the caste system in India B. To shed some light on an aspect of Indian society that can be confusing to outsiders C. To highlight the social injustices still faced by the Untouchable caste in India today D. To discredit the theory that the “Aryan Invasion” brought an end to the Harappan civilization E. To explain to the reader the distinction between the Brahman and Kshatriya castes 11. The final paragraph plays what role in relation to the rest of the passage? A. It offers information that raises doubts about the conclusions expressed in the previous paragraph. B. It discusses an alternative view to points stated as facts in the second paragraph. C. It restates the question raised in the opening paragraph, using information offered in the second and third paragraphs. D. It offers background information for the system described in the two preceding paragraphs. E. It summarizes points raised elsewhere in the passage. 12. What can we infer about the intentions of Mohandas Gandhi from the mention of him in the passage? A. He wished to switch the respective socioeconomic positions of the highest and the lowest castes in Indian society. B. He desired the reconciliation of India with Pakistan. C. He rejected the so-called Aryan Invasion in favor of an autochthonous explanation for the roots of Indian culture. D. He supported the cultural dominance of the Brahman “priest” caste over the Kshatriya “warrior” caste. E. He wished to free a class of people from the stigma of an unfavorable name.

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13. The relationship of jati to varna is most comparable to which of the following relationships? A. The relationship of individual playing cards to a fifty-two-card deck B. The relationship of a group of related species of animals to the genus to which the species belong C. The relationship of a compact disk to the songs contained on that disk D. The relationship of a transmission to the car in which the transmission has been installed E. The relationship of an updated version of software to the original version of that software 14. What inference could reasonably be drawn from the second to last sentence of the passage? A. Unlike the situation of the jati, parallels can be found between the varna system and the social divisions found in other Indo-European societies. B. The jati system is actually a product of the Dravidian cultures of central and southern India. C. Although more anthropologists support the Aryan Invasion theory than support any other explanation for the origins of the caste system, a majority of anthropologists do not believe this theory. D. The jati system, unlike the varna system, developed after the influence of IndoEuropeans in India had already been established. E. The Sudra did not willingly accept the low-caste jati to which they were assigned, but these social roles were forced upon them anyway. 15. According to the passage, the caste system would affect all except which of the following scenarios in a caste-observant Indian person’s life? A. A Brahman is having dinner with foreign visitors and is offered either a hamburger or a bowl of rice. B. A Vaishya mother is considering which of the young women in the local town would make suitable marriage prospects for her son.

C. Two Sudra teenagers engage in a foot race, and the younger of the two wins the race. D. A 40-year-old man from the Untouchable caste has moved from the countryside to a large city and must look for work in order to support his family. E. The home of a Kshatriya family is located near a city sewer line, which bursts one day and floods the family’s garage.
The following questions present a sentence, part of which or all of which is underlined. Beneath the sentence, you will find five ways of phrasing the underlined part. The first of these repeats the original; the other four are different. If you think the original is best, choose the first answer; otherwise choose one of the others. These questions test correctness and effectiveness of expression. In choosing your answer, follow the requirements of standard written English; that is, pay attention to grammar, choice of words, and sentence construction. Choose the answer that produces the most effective sentence; this answer should be clear and exact, without awkwardness, ambiguity, redundancy, or grammatical error.

16. While my brother says the Springfield Isotopes are the best team in the league, I contend that the Capital City Tigers are as good, if not the most good, of any other team in the league. A. B. C. D. E. as good, if not the most good, of better, if not the best, to the equal to, if not better to, as good as, if not better than, as good as, if not equal to,

17. In his study on the failures of the American educational system, Professor Harris states that over two million high school seniors in this country are functionally illiterate, and at least as much as four million others cannot read at an eighth-grade level. A. at least as much as four million others cannot B. at least as many as four million and more cannot C. more than four million of other students are unable to D. there was at least four million other students unable to E. more than four million others cannot

PRACTICE TEST 6

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For the following questions, select the best of the answer choices given. 20. Being overweight increases a person’s risk

B. High-protein diets are easier than conventional diets for most dieters to follow because they allow dieters to eat filling foods like meat and eggs. C. Although many dieters initially show rapid weight loss on high-protein diets, most of them regain the weight as soon as they go off the diet. D. Society should be more understanding of overweight people, and should not pressure them to pursue extreme diets. E. The high-protein diet fad has created a niche dieting industry that grosses over \$2 billion per year. 21. An analyst at a furniture company has noted that the company loses approximately \$2 million per year on its money-back guarantee, which stipulates that the company will return the purchase price to any customer whose furniture breaks within the first year, regardless of the way in which the furniture was broken. The analyst argues that the company could increase its net revenues (total revenues minus total costs) if it abolished the money-back guarantee. Which of the following, if true, provides the best reason for the company not to follow the analyst’s advice? A. A study has shown that only 25 percent of the broken furniture claims that the company has honored in the last five years were due to manufacturing defects. B. The \$2 million that the company expends on the money-back guarantee represents only 4 percent of the company’s total costs. C. A popular consumer magazine gave the furniture company its highest rating for overall quality of product. D. The company’s largest competitor has a more restrictive money-back guarantee that covers only furniture broken due to manufacturing defects within six months of purchase. E. Customers cite the money-back guarantee as the primary reason they buy furniture from this company.

of heart disease, stroke, and high blood pressure. Studies have shown that highprotein diets help people lose weight who have not been able to lose weight in any other way. Therefore, high-protein diets can be an important part of a healthy lifestyle. Which of the following, if true, most undermines the conclusion expressed above about high-protein diets? A. High-protein diets have been linked to heightened rates of high cholesterol, stomach cancer, and kidney failure.

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22. An American manufacturer of racing bikes reported a 1996 second-quarter gross income of \$18 million, compared with \$11.5 million in the second quarter of 1995. This increase was realized despite a drop in U.S. sales of racing bikes in 1996 compared with 1995, which was partly attributable to the unusually high sales in 1995 as a result of the unprecedented success of an American cyclist in a high-profile international race. Which of the following, if true, would contribute most to an explanation of the increase in the manufacturer’s gross income in 1996? A. Foreign manufacturers of racing bikes announced increased sales of their products in Europe in 1996 compared with 1995. B. In the first quarter of 1996, the American cyclist who won the high-profile international race in 1995 announced that he was switching to the racing bike made by the manufacturer in question. C. In the first quarter of 1995, the manufacturer in question first began selling its top-of-the-line “Titanium Extreme” model. D. In the second quarter of 1996, the manufacturer announced that it would begin production of skateboarding equipment in the following quarter. E. Intense competition in the racing bike market forced a competitor of the manufacturer to go out of business in the fourth quarter of 1996. 23. To persuade consumers to buy more of its cameras, the PictureSharp Camera company has launched an advertising campaign in coordination with its dealers to promote the slogan, “A Picture Is Worth a Million Words.” The dealers participating in the program are experiencing very robust sales, but PictureSharp analysts are concerned that the campaign is not successfully meeting its goals. Which of the following, if true, most justifies the concerns of the PictureSharp analysts that the campaign is not successful? A. The new PictureSharp slogan is a thinly veiled imitation of the better-known saying, “a picture is worth a thousand words.”

B. PictureSharp is one of the leading manufacturers of digital cameras, which although generally more expensive than conventional film cameras, are considerably more versatile. C. Many consumers who saw the commercials in this advertising campaign were concerned that they lacked the artistic skill to create a picture that would actually be worth “a million words.” D. Although almost all PictureSharp camera dealers participated in the advertising campaign by displaying promotional materials in their stores, some of them did not display or distribute all of the marketing materials that PictureSharp sent them. E. All PictureSharp dealers also sell other brands of cameras, some of which are comparable to PictureSharp cameras in features and quality but significantly lower in price, allowing the dealers to charge a higher markup than for PictureSharp cameras.
The questions in this group are based on the content of a passage. After reading the passage, choose the best answer to each question. Answer all questions following the passage on the basis of what is stated or implied in the passage.

If you ask a person on the street to name the top predator in the sea, most people would probably say the great white shark. But they would be wrong. A great white shark is a relentless eating machine, superbly designed for its role at the top of the food chain, but the fact is, when a great white shark meets a killer whale, the killer whale has lunch. Not bad for an animal that is neither a whale nor a killer. The killer whale, known to scientists as orcinus orca, is one of the largest, fastest, and most intelligent predators in the world’s oceans. The orca is not technically a whale, but rather the largest member of the dolphin family. The name “orca” has become the preferred name for the animal, because the name “killer whale” perpetuates the myth that orcas are dangerous to humans; in fact, there has never been a recorded incident of an orca attacking a human in the wild. This is not to say, however, that orcas are not dangerous to other marine species. Orcas in the wild have been observed consuming an astonishing variety of marine species, including salmon, tuna, sharks, giant squid, penguins, sea lions, dolphins, and even other whales, which the

PRACTICE TEST 6

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orcas hold under water until they drown. It is thought that the English name “killer whale” came from a mistranslation of the Spanish name asesina de ballenas, or “whale killer.” Despite decades of study, many aspects of the creatures’ life cycle and habits remain mysteries. Biologists only recently determined that there are, broadly speaking, three separate types of killer whale: residents, transients, and offshores. The residents live in large pods of up to 40 animals and primarily eat fish; these are the most social of the killer whale types, with each pod having distinctive songs and complex social interactions. Transients are much quieter animals who roam large distances in groups of two to six while hunting marine mammals such as sea lions and dolphins. It is the transients who earned the orca the reputation of being whale killers. The third type of orca is the offshore variety, which rarely ventures toward coasts. These poorly understood animals travel in large groups, are somewhat smaller than their coastal cousins, and are thought to eat fish, sharks, and squid, but probably not other mammals. 24. The statement in the first paragraph that the killer whale is “neither a whale nor a killer” has which of the following meanings? A. The preferred name for the orcinus orca is the orca, a name that does not have the negative connotations of “killer whale.” B. The killer whale is a type of dolphin that is not known to have ever attacked a human in the wild. C. The orca is actually a more powerful predator than even the great white shark. D. The killer whale is a type of dolphin that kills other whales by holding them under water until they suffocate. E. Some believe that the name “killer whale” is an inaccurate translation of a term used by Spanish sailors that means “whale killer.” 25. According to the information presented in the passage, what can be inferred about an orca that is observed killing and eating a juvenile minke whale? A. The orca is part of a large pod of orcas that rarely approaches coastal areas.

B. The orca is eating the minke whale only because the orca’s normal food, fish such as salmon and tuna, cannot be found in the area. C. The orca engaged in distinctive songs and complex social interactions with the minke whale prior to killing it. D. The orca is most likely of the variety of killer whales known as transients. E. If the orca had not eaten the minke whale, the minke whale would most likely have been eaten by a great white shark. 26. Which of the following questions is most likely to represent one of the “mysteries” mentioned at the beginning of the third paragraph? A. Do all orcas maintain the same diet, or do some specialize in certain types of prey? B. Is the orca more closely related to whales or to dolphins? C. Do different orca pods exhibit any form of organization in their whale songs? D. Do orcas view swimming humans as a desirable source of food? E. What is the average lifespan of an orca of the offshore variety?
The following questions present a sentence, part of which or all of which is underlined. Beneath the sentence, you will find five ways of phrasing the underlined part. The first of these repeats the original; the other four are different. If you think the original is best, choose the first answer; otherwise choose one of the others. These questions test correctness and effectiveness of expression. In choosing your answer, follow the requirements of standard written English; that is, pay attention to grammar, choice of words, and sentence construction. Choose the answer that produces the most effective sentence; this answer should be clear and exact, without awkwardness, ambiguity, redundancy, or grammatical error.

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THE PRACTICE TESTS

27. Some soldiers that were killed and seriously injured in the fighting last year were not trained according to regulations. A. Some soldiers that were killed and seriously injured in the fighting last year were not B. In the fighting last year some of the soldiers that were killed or seriously injured were not C. Last year some of the soldiers that were killed and seriously injured in last year’s fighting had not been D. Some soldiers that were killed or seriously injured in the fighting last year had not been E. Some soldiers that were killed or seriously injured in last year’s fighting have not been 28. While most early robot designers equipped their robots with “legs,” more recent robot designers have opted for movable treads, which make continual contact with the ground over a wide area in contrast with specific spots on the ground. A. B. C. D. E. in contrast with rather than at as opposed to at instead of as against

30. Intense lobbying by the financial services industry has resulted in regulations that favor creditors as opposed to consumers, which is seen when creditors may garnish the wages of consumers in default on loans even after these consumers have declared bankruptcy. A. as opposed to consumers, which is seen when creditors may garnish B. regarding consumers; creditors, for instance, may now have garnished C. over consumers; creditors may now, for example, garnish D. in terms of consumers, like when creditors are able to garnish E. over consumers, such as when creditors now may garnish 31. The combat code of medieval knights resembled that of Japanese samurai and therefore, had they faced firearms in combat, would most likely have reacted in a similar manner to the Japanese samurai of the Meiji Revolution. A. The combat code of medieval knights resembled that of Japanese samurai B. Medieval knights upheld a combat code that resembled the combat codes of Japanese samurai C. Medieval knights upheld a combat code resembling that of Japanese samurai D. Medieval knights’ upholding of a combat code resembling that of Japanese samurai, E. The medieval knight’s combat code resembled that of Japanese samurai

29. Stalactites and stalagmites, accretions of minerals formed over time by dripping water, are common features in the region’s corners. A. formed over time by dripping water, are common B. that are formed by water dripping over time, are common C. formed through time by the dripping of water, are common D. having formed over time through dripping water, is a E. , which are formed over time by the dripping of water, are commonly

PRACTICE TEST 6

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For the following questions, select the best of the answer choices given.

32. Recent epidemiological studies have shown that the residents of Greenborough County have substantially higher rates of pancreatic and stomach cancer than do the residents of the state as a whole. Researchers have concluded that the high rates of these cancers are due to the presence in the county of a large petrochemical facility that manufactures chemicals known to be carcinogenic. Which of the following, if true, most weakens the researchers’ conclusion? A. The county’s residents have the highest rate in the state of smoking, a habit that has been conclusively linked with higher rates of several types of cancer. B. The residents of the county get their water from springs that could not have been contaminated by the petrochemical plant implicated by the researchers. C. The petrochemical plant has been found to be in violation of EPA emissions standards five times in the last two years. D. Residents of Greenborough County, like people throughout the state, are fond of spicy and fatty foods that have been linked to a number of health problems. E. There are no known medical treatments that can permanently halt the development of certain forms of pancreatic cancer. 33. Automotive accidents are one of the leading causes of death in children. Child safety advocates argue that harsh penalties should be imposed on drivers who fail to place children under 30 pounds in rear-facing children’s seats in the rear of the car whenever a car is in motion. Such penalties, they argue, will help save children’s lives. All of the following statements support the argument of the child safety advocates EXCEPT: A. The rear seats of a car are safer for all passengers, both adults and children, in the event of an accident. B. Studies have shown that children in rearfacing seats have been shown to sustain less serious injuries in accidents than children in front-facing seats.

C. Studies have shown that children under 30 pounds can sustain serious injuries in even minor accidents if they are not properly restrained. D. Studies have shown that children between 60 and 90 pounds are safest in a car when using both a seat belt and a properly sized booster seat. E. Some drivers will not abide by regulations unless they are forced to do so by the threat of harsh penalties.
The following two questions refer to the following passage:

A prestigious private high school has made available to local families a tuition prepayment plan to ease the burden of paying the school’s hefty tuition when a student matriculates. The plan allows parents of children under three years old to reserve a spot for their child at the school by making a payment of one-fourth of the current annual tuition for the high school. The parents then make an identical payment every year for the next 15 years, and the student’s full four-year tuition is considered paid in full, regardless of how much the regular tuition payments have risen in the intervening years. 34. Under which of the following circumstances would taking part in the prepayment plan NOT be advisable for parents? A. If the tuition at the school has risen an average of 4 percent per year for the last twenty years B. If the child in question is particularly talented at math, but the high school is more known for its advanced humanities programs than its math program C. If the parents of the child in question are uncertain that they will reside in the state for more than 10 years D. If the school has an arrangement with the local university whereby students can take courses at the university if they have surpassed the level of courses offered at the high school E. If the school offers athletic scholarships to a small number of talented athletes

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35. Under which of the following circumstances would it be advisable for parents to take part in the prepayment plan? A. If the school assures parents that participation in the prepayment plan will be taken into consideration when the school admissions council makes decisions about which first-year students to admit to the school B. If the parents are certain that their child will attend this high school, and if the rate of tuition increase would surpass the rate of return that the parents could earn if they invested the same 16 payments in interest-bearing investments of their own choosing C. If the children of other parents who have taken part in the prepayment plan have been successful at the high school and gone on to enroll at Ivy League universities D. If the parents feel that this high school will provide the best educational, athletic, and social experience that their child could receive E. If the school can guarantee that its level of prestige at the time of the student’s matriculation will be as great as or greater than its current level
The questions in this group are based on the content of a passage. After reading the passage, choose the best answer to each question. Answer all questions following the passage on the basis of what is stated or implied in the passage.

Since the 1970s, a multitude of scientists from the fields of climatology, oceanography, and biology have been warning the governments of the world that unless human societies reduce their emissions of “greenhouse gases”—gases such as carbon dioxide and methane that increase the capacity of the atmosphere to retain heat—worldwide global warming caused by these gases will result in catastrophic consequences for people and the environment. In December 1997, a group of delegates from over 100 nations gathered together in Kyoto, Japan, in order to work out the details of the Kyoto Protocol to the United Nations Framework Convention on Climate Change, the most comprehensive international effort to date to combat the rise of greenhouse gas emissions.

The chief goal of the Kyoto Protocol is for industrialized nations to reduce their emissions of greenhouse gases by 5.2 percent compared to 1990 levels. The gases targeted by the protocol are carbon dioxide, methane, nitrous oxide, sulfur hexafluoride, HFCs, and PFCs. The protocol contains some provisions for developing nations, but as the percapita emissions of greenhouse gases from these nations are much lower than those of industrialized nations, the majority of the reductions called for by the protocol come from the European Union (8 percent reduction from 1990 levels), the United States (7 percent reduction), and Japan (6 percent reduction). Proponents of the Kyoto Protocol maintain that although it is not sufficient by itself to halt global warming, it represents an important first step toward a sustainable global economy. These proponents argue that most of the reductions in greenhouse gases can be achieved through improvements in efficiency and the use of cleaner fuels. While they concede that the provisions of the protocol may slow economic growth in affected nations, they maintain that the potential economic costs are far outweighed by the benefits of avoiding the ravages of global warming, which they say could include rising sea levels, erratic weather patterns, and long-term reductions in biodiversity. Critics of the Kyoto Protocol argue that it is unnecessary, unfair, and too costly to implement. It is unnecessary, they maintain, because the scientific community is still divided on the questions of whether global warming is happening and, if it is, whether human activity is the cause. They say it is unfair because the provisions primarily limit the emissions growth of industrialized nations while giving free rein to developing nations such as India and China, which actually emit more greenhouse gases than most industrialized nations, and that this situation will give these developing nations an economic edge in the global marketplace. Furthermore, they argue, the costs of switching fuels and limiting energy use will severely damage the economy, and the negative effects of this economic depression will outweigh any theoretical gains to be had by delaying global warming.

PRACTICE TEST 6

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36. Which of the following best describes the structure of the passage? A. It raises a problem, discusses plans to address the problem, and then evaluates the merits of those plans. B. It highlights a potential threat to the environment, discusses an international effort to alleviate this threat, and suggests possible areas for future research. C. It introduces a proposal, describes it in greater detail, and gives arguments for and against it. D. It presents an argument, evaluates both sides of the argument, and then comes down on the side with the stronger logical reasoning. E. It introduces an idea, discusses the controversy that the idea has generated, and finally dismisses the idea.
37. According to the passage, what is the likely

38. By observing the author’s tone, it can be inferred that which of the following most accurately represents the author’s opinions? A. The author is in favor of immediate implementation of the Kyoto Protocol by all nations. B. The author believes that the costs of the Kyoto Protocol should fall equally on industrialized and developing nations. C. The author doubts that the Kyoto Protocol is an effective measure to address the problem of global warming. D. The author is not convinced that the problems raised by global warming justify the severe restrictions imposed by the Kyoto Protocol on national economies. E. The author believes the Kyoto Protocol is more comprehensive than prior efforts to address the problem of global warming at an international level. 39. According to the information given in the passage, which of the following would be most likely to help a nation meet the reduction targets of the Kyoto Protocol? A. A power plant switches its fuel source from bituminous to anthracite coal, thereby reducing the amount of sulfur dioxide that the plant releases into the air. B. An aluminum processing plant alters the mix of the chemicals used in its smelting process so that the amount of nitrous disulfide emitted by the plant is increased and the amount of sulfur hexafluoride is decreased. C. A petrochemical plant that produces plastics adjusts its manufacturing process so that the ratio of HFCs to PFCs emitted by the plant is altered from 1:12 to 1:8. D. A metropolitan area switches its power source from a plant that burns coal to one that burns natural gas, which emits significantly less carbon dioxide per kilowatt of power generated than coal, although leaks in the natural gas pipeline have increased the amount of methane emitted in the area. E. To reduce smog, a state mandates that all state employees on state business must drive electric vehicles instead of gasolinepowered vehicles; the energy used by these electric cars comes from coal- and oil-burning power plants that emit carbon dioxide.

response of a supporter of the Kyoto Protocol to the argument that implementation of the protocol will cause undue economic hardship for industrialized nations? A. It is only fair for industrialized nations to pay the majority of the expenses for enforcing the protocol, since industrialized nations have the majority of the money in the world. B. While the Kyoto Protocol may cause some economic hardship to certain industries in industrialized nations, the protocol represents an important first step toward the development of a sustainable global economy. C. Technological improvements, such as the hybrid fuel-cell car, will allow fuelefficient machines to offer the same performance as older inefficient machines. D. The economic costs of enforcing the Kyoto Protocol will be outweighed by the benefits. E. The unnecessary costs of enforcing the Kyoto Protocol will outweigh any theoretical benefits to be had by reducing greenhouse gases.

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40. Which of the following, if true, would best reconcile the claim that developing nations like India and China “actually emit more greenhouse gases than most industrialized nations” with the previously stated claim that “the per-capita emissions of greenhouse gases from these nations are so much lower than those of industrialized nations”? A. Both China and India have larger populations than any three industrialized nations combined. B. Once China and India develop economically to a level comparable to that of an industrialized nation in Europe or North America, it is expected that these previously developing countries will have to limit their carbon emissions as well. C. The concept of “greenhouse gases” is controversial because it has not been proven definitively that the “greenhouse effect” exists. D. Some of the most advanced forms of industry, such as the computer industry and biotechnology, emit far less greenhouse gases per unit of economic output than less advanced industries, such as agriculture or heavy manufacturing. E. Economic development in developing countries such as India and China is hampered by lack of investment capital, lack of economic infrastructure, and the presence of persistent social problems that hinder government efforts to spur development.

41. Which of the following, if true, would most weaken the argument of the critics of the Kyoto Protocol that implementing the protocol would be too costly? A. While it is true that the scientific community is not unanimously in agreement that global warming is occurring, more than 95 percent of climatologists at universities and government-funded laboratories in Europe and North America agree that global warming is a real phenomenon. B. Hybrid fuel-cell cars are less expensive to operate than conventional cars because of their much greater fuel efficiency, but it is unlikely that these operational savings will ever be able to cost-justify the much greater initial investment required to purchase one of these hybrid cars. C. Nuclear power, although completely free of carbon emissions and comparable in operating cost to an oil-burning power plant, brings the added back-end cost of disposing of the spent nuclear waste, which is both radioactive and highly toxic. D. Although it is unfair in a sense to impose different emissions restrictions on different countries, it is only fair to impose the most restrictive limitations on countries whose advanced economic development will allow them to conform to the regulations without losing the benefits of an industrialized economy. E. One nation that switched the fuel of 35 percent of its power plants from coal to natural gas in order to reduce carbon dioxide emissions found that natural gas, although initially more expensive than coal, dropped in price to a level comparable to that of coal because natural gas companies increased production in order to meet the market demand.

PRACTICE TEST 6

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PRACTICE TEST 1

1 QUANTITATIVE 1 VERBAL

1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37.

D B C C C B E D B D A B B D B C A C B C A E E A B C D A B B E B C C D A D

1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 41.

A C B A B E C A D B B D B A C D A D D E C B C A B C D E B C B E B D A A D C C A B

PRACTICE TEST 1

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PRACTICE TEST 2

2 QUANTITATIVE 2 VERBAL

1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37.

E D A D B B E C E A C A D A C E A B D D E B D E C B B C B E C B D E B B C

1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 41.

D B D B A A D B C A D E C B B B A E C C A C C C B D E A D A D C A A D E C B E C D

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PRACTICE TEST 3

3 QUANTITATIVE 3 VERBAL

1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37.

C D D C B D E C B A B E C A B D E D D E C B D B A A B C A E D B C A B C A

1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 41.

D C A E E B D D A C D B D D B C B A A B B E C E C B A D C A C C D A D A A D C E C

\$357

PRACTICE TEST 4

4 QUANTITATIVE 4 VERBAL

1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37.

B C D C A A E B B D B D D A C E A C B A A E D E E B D A C E D D B B B A C

1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 41.

D D A B C E E C C E C B E D A C E B A C B B B B E A C E A C E A B C D A C E E A E

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THE PRACTICE TESTS

PRACTICE TEST 5

5 QUANTITATIVE 5 VERBAL

1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37.

C B B C B A C A D B E D E E C B E B E D C C C C A A E D A A B E B C D C B

1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 41.

D A B C E D D E B D B A A E B C E B B D A C E B D E C B C A A D B B E D C E C C D

\$359

PRACTICE TEST 6

6 QUANTITATIVE 6 VERBAL

1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37.

E B C D A D E B D B D A A A B D B B B B C E A D E C E B B A A E E C C B C

1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 41.

B E C E C B C D C B D E B A C D E A A A E B E B D E D B A C C A D C B C D E B A E

360#

THE PRACTICE TESTS

PRACTICE TEST 1

QUANTITATIVE

1. Greg sells gaskets. On three sales, Greg has received commissions of \$385, \$70, and \$190, and he has one additional sale pending. If Greg is to receive an average (arithmetic mean) commission of exactly \$220 on the four sales, then the fourth commission must be: A. B. C. D. E. \$135 \$155 \$220 \$235 \$645

4. Over a three-week period, the price of an ounce of gold increased by 25% in the first week, decreased by 20% in the following week, and increased by 5% in the third week. If the price of gold was G dollars per ounce at the beginning of the three weeks, what was the price, in terms of G, at the end of the three weeks? A. B. C. D. E. 0.95G G 1.05G 1.1G 1.15G

ANSWER: D For the average of four commissions to be \$220, the total must be 220 ¥ 4 = 880. 880 minus the sum of the three listed commissions (385 + 70 + 190 = 645) equals \$235.

ANSWER: C At the end of the first week, the price was 1.25 ¥ G = 1.25G. At the end of the second week, it was 0.8 ¥ 1.25G = G. At the end of the third week, the price was 1.05 ¥ G = 1.05G.

2. In an effort to plan out expenses, the Roberts family is representing its annual budget as a circle graph. Each sector of the graph is proportional to the amount of the budget it represents. If “clothes and shoes” takes up 54° of the chart, how much of the Roberts’s \$20,000 annual budget is dedicated to clothes and shoes? A. B. C. D. E. \$1,500 \$3,000 \$4,500 \$5,000 \$5,400

5. If a cube has a total surface area of 96, what is its volume? A. B. C. D. E. 16 36 64 81 96

ANSWER: B 54∞ is 15 percent of the 360∞ in a circle; 15 percent of \$20,000 is \$3,000.

ANSWER: C A cube has six sides, so if the total surface area is 96, then the surface area of a square side is 96/6 = 16. The area of a square is the square of the length of its sides, so the length of a side is the square root of 16 = 4. The volume of a cube is the cube of the length of its sides, so 4 ¥ 4 ¥ 4 = 64.

3. What is the value of 3x 2 − 1.8x + 0.3 for x = 0.6? A. B. C. D. E. −0.3 0 0.3 1.08 2.46

ANSWER: C The equation 3(0.6 ¥ 0.6) 1.8(0.6) + 0.3 = 1.08 - 1.08 + 0.3 = 0.3

PRACTICE TEST 1

\$361

6. The table below shows the enrollment in various classes at a certain college. Class Biology Physics Calculus Number of Students 50 35 40

(2) In a 32-ounce bottle of the salad dressing, there is half as much oil as there is vinegar.
ANSWER: D (1) alone is sufficient, because if there are 12.4 ounces of vinegar, then there are 18.6 – 12.4 = 6.2 ounces of oil; 6.2/12.4 = 1:2. (2) alone is sufficient because it tells you directly that the ratio of oil to vinegar is 1:2.

Although no student is enrolled in all three classes, 15 are enrolled in both Biology and Physics, 10 are enrolled in both Biology and Calculus, and 12 are enrolled in both Physics and Calculus. How many different students are in the three classes? A. B. C. D. E. 51 88 90 125 162

9. At a certain pancake festival with 600 attendees in which every attendee ate at least 1 pancake, how many people had only 1 pancake? (1) At the festival there were 1,200 pancakes served, and no person had more than 3 pancakes. (2) Seventy-two percent of the attendees at the festival had 2 or more pancakes.
ANSWER: B (1) alone is not sufficient, because there could have been 300 people who had 1 pancake and 300 people who had 3 pancakes, or 600 people who had 2 pancakes. (2) alone is sufficient, because you can directly infer from the statement that 100 - 72 = 28 percent of attendees, or 168, had only 1 pancake.

ANSWER: B To find the total number of students, you must separate them into nonoverlapping groups so that no one is counted twice. The students taking only Biology are the 50 students minus the 15 also taking Physics and the 10 also taking Calculus, so there are 25 students taking just Biology. Using this same method, the number of students taking just Physics is 35 - 15 - 12 = 8, and the number taking just Calculus is 40 - 10 12 = 18. The total number, then, is 25 + 8 + 18 + 10 + 15 + 12 = 88.

10. A rectangle is equal in area to a square with sides of length 12. Is the diagonal of the rectangle greater in length than 20? (1) The rectangle has a length of 16. (2) The rectangle has a width of 9.
ANSWER: D Both (1) and (2) independently allow you to infer both the length and the width of the rectangle, because if the rectangle is equal in area to a square with sides of length 12, then its area = 12 ¥ 12 = 144, and so the width is 144/16 = 9 and the length is 144/9 = 16. By the Pythagorean theorem, we can determine that the diagonal is equal to the square root of 92 + 162 = 337. You do not have to determine the actual square root of 337 to determine that it is less than 20, because 20 ¥ 20 = 400.

7. In a nationwide poll, P people were asked 2 questions. If 2/5 answered “yes” to question 1, and of those 1/3 also answered “yes” to question 2, which of the following represents the number of people polled who did not answer “yes” to both questions? A. B. C. D. E. 2/15 P 3/5 P 3/4 P 5/6 P 13/15 P

ANSWER: E The people who answered “yes” to both questions are 1/3 of 2/5 P, so 2/15 P. Therefore, the people who did not answer “yes” to both questions are P - 2/15 P = 13/15 P.

8. A certain salad dressing made only of oil and vinegar is premixed and sold in the grocery store. What is the ratio of oil to vinegar in the mix? (1) An 18.6-ounce bottle of the salad dressing contains 12.4 ounces of vinegar.

11. A type of candy comes in two flavors, sweet and sour, and in two colors, yellow and green. The color and flavor of the individual pieces of candy are not related. If in a certain 5 1 box of this candy – of the yellow pieces and – 4 7 of the green pieces are sour, what is the ratio of the number of yellow pieces to the number of green pieces in the box? (1) In the box, the number of sweet yellow pieces is equal to the number of sour green pieces.

(2) In the box, the number of green pieces is two less than the number of yellow pieces.
ANSWER: A (1) alone is sufficient because it sets up a ratio between the colors and flavors; if 1/4 of the yellow pieces are sour, then 3/4 of the yellow pieces are sweet, and if 5/7 of the green pieces are sour, then 2/7 of the green pieces are sweet; if the number of sweet yellow pieces is equal to the number of sour green pieces, then 3 /4 of the number of yellow pieces is equal to 5/7 of the number of green pieces; if y represents the number of yellows and g represents the number of greens, then the ratio can be represented as 3y/4 = 5g/7, which can be restated as 21y = 20g, or y/g = 20/21. Statement (2) alone is not sufficient because it does not give sufficient information to determine the total number of either the greens or the yellows.

ANSWER: B The equation describes a line that crosses the x axis at -2/3 and crosses the y axis at -2/5, so it never passes through quadrant I. You can plug in points from each axis to verify.

14. If a copier makes 3 copies every 4 seconds, then continues at this rate, how many minutes will it take to make 9,000 copies? A. B. C. D. E. 60 100 120 200 3,000

ANSWER: D At 3 copies every 4 seconds, the copier will finish the batch in (9,000/3) ¥ 4 seconds, or 12,000 seconds. There are 60 seconds in a minute, so 12,000/60 = 200 minutes.

12. In isosceles triangle ABC, what is the value of ∠C ? (1) The measure of ∠B is 47° (2) The measure of ∠A is 96°
ANSWER: B (1) alone is insufficient, because –C could be the matching angle of the isosceles triangle with –B at 47∞, or it could match with –A at 66.5∞, or it could be the nonmatching angle at 96∞. (2) alone is sufficient, because if –A is 96∞, then it cannot be one of the matching angles of the isosceles triangle because two 96∞ angles cannot fit in a triangle, so –C must be one of two 47∞ angles.

15. To be considered grade AA, an egg must weigh between 75 and 90 grams, including the shell. Shells of grade AA eggs weigh between 3 and 5 grams. What is the smallest possible mass, in grams, of a 12-egg omelet, assuming that only grade AA eggs are used, the shells are all discarded, and no mass is lost in the cooking process? A. B. C. D. E. 800 840 864 900 1,080

ANSWER: B The smallest omelet will result from 75-gram eggs with shells of 5 grams each, resulting in 70 grams per egg added to the omelet. 70 grams/egg ¥ 12 eggs = 840 grams.

16.

( 0.2 )5
A. B. C. D. E.

(0.2)8

=

13. In the rectangular quadrant system shown above, which quadrant, if any, contains no point (x, y) that satisfies the equation 3x + 5y = −2? A. B. C. D. E. none I II III IV

0.0008 0.001 0.008 0.04 0.08

( 0.2 )

(0.2)8
5

= ( 0.2 ) = 0.008
3

PRACTICE TEST 1

\$363

⎛ 1⎞ ⎛ 1⎞ 17. What is the ratio of ⎜ ⎟ to ⎜ ⎟ ? ⎝ 3⎠ ⎝ 3⎠ A. 9 B. 3 C. 1 D. 1:3 E. 1:27
⎛ 1 ⎞ equals 1 , while ⎛ 1 ⎞ ⎜ ⎟ ⎜ ⎟ ⎝ 3⎠ ⎝ 3⎠ 9 1 . 1 is nine times larger than 1 , equals 81 81 9 so the ratio is 9:1. ANSWER: A
2 4

2

4

20. What is the value of n? (1) n4 = 256 (2) n3 > n2
ANSWER: C (1) alone is insufficient because n could equal either 4 or -4. (2) alone is insufficient, because although it tells us that n > 1, it does not give a value for n. If the statements are combined, n = 4 is the only solution to the stated criteria.

18. A group of 7 fishermen chartered a boat for a day to fish for flounder. The boat costs x dollars per day to rent. If the group can find 3 more fishermen on the docks who are willing to come aboard and share the rental costs, how much less will the rental cost be per person in terms of x? A. B. C. D. E. x/70 x/35 3x/70 3x/10 3x/7

21. An employee at a company was given the task of making a large number of copies. He spent the first 45 minutes making copies at a constant rate on copier A, but copier A broke down before the task was completed. He then spent the next 30 minutes finishing the task on copier B, which also produced copies at a constant rate. How many total minutes would the task have taken had copier A not broken down? (1) Copier A produced twice as many copies in its first 5 minutes of operation as copier B produced in its first 15 minutes. (2) Copier B produces 10 copies per minute.
ANSWER: A (1) alone is sufficient because it gives the relative rates of the two machines; if copier A can produce twice as many copies as copier B can produce in three times the time, then it could have finished the task in onesixth the time it took copier B, or 5 minutes. (2) alone is insufficient because it does not allow you to determine the relative speeds of the two machines.

ANSWER: C The difference in cost is the difference between x/7 and x/10. x/7 - x/10 = (10x - 7x)/70 = 3x/70.

19. The size of a flat-screen television is given as the length of the screen’s diagonal. How many square inches greater is the screen of a square 34-inch flat-screen television than a square 27-inch flat-screen television? A. B. C. D. E. 106.75 213.5 427 729 1,156

22. If ab 0 0, is c an integer? (1) c = 5a – 2b (2) a = 2b
ANSWER: E (1) alone is insufficient because it could give values for c that are both integers and nonintegers. (2) alone is insufficient because it says nothing about c. If the statements are combined, a and b could still take values that make c either an integer (e.g., 1, 2) or a noninteger (e.g., 1/3, 1/6).

ANSWER: B The question specifies that the televisions are square, so the diagonals are part of 45–45–90 triangles. This means that the side of such a television is the diagonal divided by 2 . This would be an awkward number to deal with, but the question calls for areas, so you need to square the length of a side in order to get the area of the screen, thereby removing the square root. Set up the equation 1, 156 − 729 427 ⎛ 34 ⎞ ⎛ 27 ⎞ = = 213.5 ⎜ ⎟ −⎝ ⎜ ⎟ = ⎝ 2⎠ 2 2 2⎠
2 2

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23. x = 0.57y 9. If y denotes the thousandth digit in the decimal representation of x above, what digit is y ? (1) If x were rounded to the nearest tenth, the result would be 0.6. (2) If x were rounded to the nearest hundredth, the result would be 0.58.
ANSWER: E (1) alone is insufficient because it gives us no new information about y. (2) alone is insufficient because it tells us only that y ≥ 5, which is not sufficient to answer the question. Combining the statements yields no new information.

ANSWER: C If the truck travels 270 miles on 18 gallons, it is getting 270/18 = 15 miles per gallon. To travel 270 miles on 10 gallons, it would need to get 27 miles per gallon. 27 - 15 = 12.

24. Is integer y > 0? (1) –(2 + y) > 0 (2) (2 + y)2 > 0
ANSWER: A (1) alone is sufficient because this statement means that y < -3, which means that y is not greater than 0. (2) alone is insufficient, because the statement could work for values of y that are both greater and less than 0, such as 1 and -1.

27. The figure above represents a window, with the shaded regions representing openings for glass and the pale regions representing the wood panels between and around the glass. If the window is 4.5 feet high by 2.5 feet wide, and if each of the wooden panels is exactly 4 inches thick, what is the total surface area, in square inches, of glass in the window? (1 foot = 12 inches; figure not drawn to scale) A. B. C. D. E. 189 378 448 756 1,620

25. If 4 and 11 are the lengths of two sides of a triangular region, which of the following can be the length of the third side? I. 5 II. 13 III. 15 A. I only B. II only C. I and II only D. II and III only E. I, II, and III
ANSWER: B A leg of a triangle cannot be greater than or equal to the sum of the other two legs. This principle eliminates both I (11 > 5 + 4) and III (4 + 11 = 15). Therefore, II is the only acceptable length.

26. A certain truck uses 18 gallons of diesel fuel in traveling 270 miles. In order for the truck to travel the same distance using 10 gallons of diesel fuel, by how many miles per gallon must the truck’s fuel mileage be increased? A. B. C. D. E. 8 9 12 15 27

ANSWER: D For this problem, you could calculate the dimensions of each of the four pieces of glass, but it is probably simplest to calculate the area of glass as if the four pieces were just one rectangular area of glass. If the window is 4.5 feet high, then it is 4.5 ¥ 12 = 54 inches high. 54 inches minus the 3 ¥ 4 inches for the wooden panels means that the glass in the window is 54 - 12 = 42 inches high. The window is 2.5 feet wide = 30 inches; 30 inches minus 12 inches for the panels means that the glass is 18 inches wide. 42 ¥ 18 = 756 square inches. Note that the figure is not drawn to the dimensions given in the question.

28. If 3( x 2 + x ) − 7 = x 2 + 2( 4 + x 2 ) , then x = A. B. C. D. E. 5 6 9 15 25
You can restate the equation as

3x 2 + 3x − 7 = 3x 2 + 8, so 3x = 15, and x = 5.

PRACTICE TEST 1

\$365

29. Suzie’s Discount Footwear sells all pairs of shoes for one price and all pairs of boots for another price. On Monday the store sold 22 pairs of shoes and 16 pairs of boots for \$650. On Tuesday the store sold 8 pairs of shoes and 32 pairs of boots for \$760. How much more do pairs of boots cost than pairs of shoes at Suzie’s Discount Footwear? A. B. C. D. E. \$2.50 \$5.00 \$5.50 \$7.50 \$15.00

31. A hat company ships its hats, individually wrapped, in 8-inch by 10-inch by 12-inch boxes. Each hat is valued at \$7.50. If the company’s latest order required a truck with at least 288,000 cubic inches of storage space in which to ship the hats in their boxes, what was the minimum value of the order? A. B. C. D. E. \$960 \$1,350 \$1,725 \$2,050 \$2,250

ANSWER: B One approach to this question is to set up the two equations and then eliminate one variable to solve for the other. If s represents the prices of shoes and b represents the price of boots, then 22s + 16b = 650 and 8s + 32b = 760. To eliminate b, multiply both sides of the first equation by 2 and then subtract the second equation from the modified first equation, and you get 44s - 8s + 32b - 32b = 1,300 - 760; therefore, 36s = 540, and shoes cost \$15. Plug this value into one of the equations and you get b = \$20. \$20 - \$15 = \$5.

ANSWER: E An 8 ¥ 10 ¥ 12-inch box contains 960 cubic inches. 288,000 total cubic inches divided by 960 cubic inches per box equals 300 boxes. 300 boxes times \$7.50 per hat equals \$2,250.

32. Chauncy, an English bulldog, received 1,618 votes in the Mr. Bulldog USA competition, giving him approximately 20 percent of the vote. Approximately what percent of the remaining votes would he have needed to receive in order to win 30 percent of the total votes? A. B. C. D. E. 10% 12.5% 15% 17.5% 20%

30. For any 3 given numbers, which of the following is always equivalent to adding the 3 numbers together and then dividing the sum by 3? I. Ordering the 3 numbers numerically, from highest to lowest, and then selecting the middle number. II. Dividing each of the numbers by 3 and then adding the results together. III. Multiplying each number by 6, adding the resulting products together, and then dividing the sum by 9. A. B. C. D. E. I only II only I and II only II and III only None of the above

ANSWER: B If 1,618 was 20 percent of the vote, then there were approximately 8,090 votes (1,618/0.2 = 8,090). 30 percent of 8,090 would be 2,427. 2,427 - 1,618 = 809 additional votes that Chauncy would have needed in 809 order to reach 30 percent. = 8,090 − 1,618 0.125 = 12.5%.

33. If 8 skiers raced down a course multiple times in one day, and each skier used a different pair of skis on each run, what is the maximum number of different skis used by the 8 skiers during the day? (1) No skier shared any skis with any other skier. (2) Each skier made exactly 12 runs during the day.

ANSWER: B Choose any three numbers and test them on statements I, II, and III. You will quickly find that I and III are not always true. II is always true, because mathematically it and the process in the question are doing the same thing—summing the numbers and dividing by 3.

366#

ANSWER: C (1) alone is insufficient because it doesn’t say how many times each skier raced the course. (2) alone is insufficient because it does not exclude the possibility of sharing; there could have been 12 pairs of skis shared among the 8 skiers, or there could have been a total of 12 ¥ 8 = 96 skis, or any number in between. If the statements are combined, we see that the number has to be 12 ¥ 8 = 96 skis.

34. The symbol ⊗ represents one of the following operations: addition, subtraction, multiplication, or division. What is the value of 7 ⊗ 4? (1) 4 ⊗ 7 < 1 (2) 4 ⊗ 3 > 1
ANSWER: C (1) alone is insufficient, because the statement could be true if the symbol represents either subtraction or division. (2) alone is insufficient, because the statement could be true if the symbol represents multiplication, division, or addition. If the statements are combined, the only common operation is division, so the answer is 7/4.

ANSWER: A (1) alone is sufficient; it states that the absolute value of b is greater than the absolute value of a, which means that a − b is b +a a negative number regardless of whether a and b are both positive, both negative, or a mix of positive and negative (plug in numbers to verify); since a − b is a negative number, the b +a answer to the question has to be “yes.” (2) alone is insufficient, because if (a, b) equals (4, 2) then a − b = 1 and the answer is “yes,” b +a 3 a −b but if (a, b) equals (4, -3) then = 7, and b +a the answer is “no.”

37. The hold of a fishing boat contains only cod, haddock, and halibut. If a fish is selected at random from the hold, what is the probability that it will be a halibut or a haddock? (1) There are twice as many halibut as cod in the hold, and twice as many haddock as halibut. (2) Cod account for 1/7 of the fish by number in the hold.
ANSWER: D (1) alone is sufficient because it means that if there is one cod, there are two halibut and four haddock, so halibut and haddock account for 6/7 of the fish in the hold, giving a probability of 6/7 of selecting one of these fish. (2) alone is sufficient, because the probability of selecting a cod is the inverse of the probability of selecting one of the other two fish, or 6/7.

35. Salespeople at a certain car dealership are paid a \$250 commission on every car they sell up to their monthly quota, and \$500 for every car they sell over the quota. What is the monthly sales quota at this dealership? (1) One salesperson exceeded the quota by 8 cars and received a total monthly commission of \$7,500. (2) One salesperson achieved only half of the quota; he received a commission of \$1,750 and a warning that he will be fired unless he meets the next month’s quota.
ANSWER: D (1) alone is sufficient; we know the 8 cars over the quota will receive a total of \$4,000 in extra commission (8 ¥ \$500), so divide the remaining money by \$250 per car to determine the quota—\$3,500/\$250 = 14 cars. (2) alone is sufficient; \$1,750 at \$250 per car means that he sold 7 cars, and if 7 is half of the quota, then the quota is 14.

36. If a ≠ −b , is a − b < 1? b +a (1) b 2 > a 2 (2) a − b > 1

PRACTICE TEST 1

\$367

PRACTICE TEST 1

VERBAL

1. Studies have shown that companies that present seminars on workplace safety to their employees actually have higher rates of workplace accidents than companies that do not present such seminars to their employees. Despite this finding, it is still in the best interests of companies and their employees for companies to present these seminars. Which of the following, if true, provides the strongest support for the argument that the companies should continue to present these seminars? A. Companies that present workplace safety seminars to their employees are likely to be in manufacturing industries or segments of the service sector that present more opportunities for workplace accidents than the average company. B. A fast-food chain determined that the rate of workplace accidents remained the same at its franchises after all employees had viewed a 30-minute workplace safety video. C. Workers are ultimately responsible for their own safety, and no amount of workplace education can alter their behavior. D. A business research institute determined that workplace accidents reduce the productivity of manufacturing businesses by as much as 8 percent per year. E. Many companies mistakenly believe that presenting workplace safety seminars to their employees relieves the company of legal liability in the event that employees are injured on the job.
ANSWER: A To strengthen the argument, the answer must refute the apparent connection between workplace safety seminars and higher rates of accidents; answer A provides a plausible explanation for this phenomenon.

2. For hundreds of years, pearl divers have gathered pearls directly from mollusks on the sea floor. This is an extremely risky profession, exposing the divers to risks of drowning, air embolism, and shark attacks. Still, as long as society demands authentic cultured pearls, these brave divers must continue to risk their lives. Which of the following statements, if true, most seriously weakens the conclusion above? A. Shark attacks on pearl divers have decreased steadily over the last three decades because of declining shark populations. B. Cultured pearls are generally considered more beautiful than those made by artificial means. C. Robotic pearl harvesters can gather pearls faster and at less cost than human divers, although they may disturb aquatic communities. D. Part of the value of cultured pearls derives from the exotic way in which they are obtained. E. With the proper equipment and training, a diver employing scuba gear can harvest three times as many pearls per hour as can a free air diver.
ANSWER: C This answer provides an alternative means by which society can obtain cultured pearls without exposing divers to risk.

3. An electronic company’s two divisions showed consistent performance over the last two years. In each year, the audiovisual department accounted for roughly 30 percent of the company’s sales and 70 percent of the company’s profits over the period, while the home appliance division accounted for the balance.

368#

Which of the following statements regarding the last two years can be inferred from the statement above? A. The audiovisual market is growing faster than the home appliance division. B. The home appliance division has realized lower profits per dollar of sales than has the audiovisual division. C. Total dollar sales for each division has remained roughly constant for the last five years. D. The company has devoted more money to research and development efforts in the audiovisual division than in the home appliance division. E. To maximize profitability, the company should focus its resources on the home appliance division.
ANSWER: B If the home appliance division accounted for 70 percent of sales but only 30 percent of profits, it is clearly generating less profit per dollar of sales than is the audiovisual division.

ANSWER: A This answer provides a substantial reason—the operation’s risk of serious complications and death—for doctors to refrain from recommending the gastric bypass surgery.

5. This passage is primarily interested in which of the following? A. Investigating the factors that brought about the Marvel revolution and the Silver Age of comic books B. Reviewing the factors that brought about the end of the Golden Age of comic books C. Comparing and contrasting two eras in the history of comic books D. Condemning the horror comic book for its corrupting influence on the nation’s youth E. Evaluating the historical legacy of William Gaines’s EC Comics
ANSWER: B The introductory paragraph brings up the subject of the factors that brought the Golden Age to an end, and the next three paragraphs discuss these factors.

4. Gastric bypass surgery has been shown to be effective at helping extremely obese people lose weight. Some patients have lost as much as 300 pounds after undergoing the surgery, thereby substantially prolonging their lives. Despite the success of the treatment, most doctors have not embraced the surgery as a weight loss option. Which of the following statements, if true, best accounts for the lukewarm reaction of the medical community to gastric bypass surgery? A. Gastric bypass surgery carries a high risk of serious complications, including death. B. Obesity is one of the leading contributors to heart disease and hypertension, two leading causes of death. C. Obesity rates among the American population have been increasing consistently for the last three decades. D. Many patients report that losing weight through diets is ineffective, since they usually gain the weight back within six months. E. Most health insurance plans will cover the cost of gastric bypass surgery for morbidly obese patients at high risk of heart disease.

6. According to the passage, which of the following was true of the creators of superhero comic books in the postwar years? A. They sought to head off the censorship of the Comics Code Authority by voluntarily prohibiting stories dealing with sexuality, drugs, or criminal behavior. B. They introduced characters such as Superman and The Spirit. C. They unintentionally laid the groundwork for the transition from the Golden Age of comic books to the Silver Age. D. They focused increasingly on flashy artwork and less on well-developed stories. E. They responded to the competitive pressure from horror comic books by increasing the amount of violence in their stories.
ANSWER: E The passage states, “The creators of superhero comic books, not wanting to be left behind, responded by matching their protagonists against darker criminals in more violent encounters.”

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7. According to the passage, what can we infer to be the central message of Fredric Wertham’s The Seduction of the Innocent? A. Adults reading violent comic books were as likely to be corrupted by them as young people were. B. The horror comic books of the late 1940s were inferior to the superhero comic books that gained popularity during World War II. C. Comic books were leading the nation’s youth into crime, violence, and drug abuse. D. Creating a regulatory board to censor the comic book industry would drive the worst offenders out of the business. E. Comic books would never be able to convey stories of any serious literary merit.
ANSWER: C The sentence preceding the mention of Wertham’s book states that he believed that comic books “were leading the nation’s youth into crime, violence, and drug abuse.”

9. In what light does the passage depict the efforts by Fredric Wertham to bring about regulation of the comic book industry? A. As a fanatical crusade brought about by Wertham’s inner demons B. As a witch-hunt roughly analogous to the concurrent anti-Communist hearings by the House Committee on Un-American Activities C. As a reasonable response to an industry that had gone too far D. As an angry response to a trend in the subject matter of the comic book industry E. As an inappropriate response to a phenomenon that was not actually hurting anyone
ANSWER: D The passage describes the trend toward horror comics in neutral terms, and it states that horror comics “aroused the anger” of Wertham.

8. According to the final paragraph of the passage, what may we infer about the comic book companies of the Silver Age? A. They were able to create popular comic books despite the regulations of the Comics Code Authority. B. They achieved commercial success because of the popularity of characters such as Spider-Man, the Hulk, and the Fantastic Four. C. They repeated the same mistakes as the comic book companies of the Golden Age. D. They failed to succeed because of the numbing effect of the Comics Code Authority regulations. E. Marvel Comics was the only major comic book company to survive from the Golden Age into the Silver Age.
ANSWER: A The last paragraph states that the CCA regulations had a numbing effect on comic book publishers, but it concludes with the statement that the industry recovered in the Silver Age. Since the passage did not state that the CCA regulations were repealed, we can infer that the companies succeeded despite the regulations.

10. According to the passage, which of the following statements can be made about the content of Weird Tales and The Crypt of Terror? A. Their adult-oriented content was not suitable for young readers. B. Their grim and gritty content was a market response to the demands of soldiers home from World War II. C. They frequently depicted violence and criminal behavior, but shied away from sexuality or drug abuse. D. Their sales surpassed those of previous bestselling titles such as Superman or Batman. E. The publication of Weird Tales #1 coincided with the end of the Golden Age of comic books.
ANSWER: B The second paragraph states: “When these soldiers came home, they still wanted to read comic books, but they sought out more adult content. William Gaines of EC Comics was happy to meet the market demand with such grim and gritty titles as Weird Fantasy and The Crypt of Terror.”

11. The way in which the mighty blue whale and the other baleen whales—the finback, gray, humpback, and right whales—eats was discovered by careful observation by biologists. A. eats was discovered by B. eat was discovered through

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C. eats were discovered by means of D. eat were discovered by E. eat was discovered resulting from
ANSWER: B The two subject-verb phrases in question here are “The way . . . was discovered” and “whales . . . eat”; only B and E present these verb forms properly. The construction “discovered resulting from” in E is awkward and unidiomatic; B is the best answer.

the presence of “by” in the phrase does not make sense with the rest of the sentence. B is the clearest and most idiomatic choice. 14. No less remarkable than the invention of

nuclear power has been the way the technology has prompted governments to reevaluate the nature of international relations. A. No less remarkable than the invention of nuclear power B. What was as remarkable as the invention of nuclear power C. Inventing nuclear power has been none the less remarkable than D. The invention of nuclear power has been no less remarkable as E. The thing that was as remarkable as inventing nuclear power
ANSWER: A A is grammatically correct and idiomatic, and it is stylistically preferable to the other choices.

12. The eighteenth-century author Jonathan Swift once suggested in a satiric essay Irish farmers could eat their children to address the twin problems of overpopulation and lack of food. A. Irish farmers could eat their children to address the twin problems of overpopulation and lack of food B. that the twin problems of overpopulation and lacking food could be addressed by the eating of children by Irish farmers C. of the twin problems of Irish farmers, overpopulation and a lack of food, could be addressed by the eating of their children D. that Irish farmers could address the twin problems of overpopulation and lack of food by eating their children E. that Irish farmers , facing overpopulation and lacking food, could address the twin problems through eating their children
ANSWER: D A and C fail to conform to the idiomatic construction “{subject} suggested that . . .”; B is awkward and is weakened by its use of the passive voice. In E, it is unclear that “twin problems” necessarily refers to overpopulation and lack of food. D is the clearest statement.

15. Unlike the recognition of ethical lapses in others, many people are disinclined to perceive the same flaws in themselves. A. Unlike the recognition of ethical lapses in others, many people are disinclined to perceive the same flaws in themselves. B. Unlike the perception of ethical flaws in themselves, many people are willing to recognize these same flaws in others. C. Many people, willing to recognize ethical lapses in others, are disinclined to perceive the same flaws in themselves. D. Many people are disinclined to perceive the same flaws in themselves, but are willing to perceive ethical lapses in others. E. Although willing to recognize ethical lapses in others, many people in themselves are disinclined to perceive the same flaws.
ANSWER: C A and B incorrectly compare “people” with “recognition” and “perception,” respectively. In D, it is unclear what “the same flaws” is referring to. The construction “many people in themselves” in E is unidiomatic. C is the best answer.

13. The stock market collapse of 1929 had farreaching consequences for the national economy, causing a nationwide collapse in home values, putting millions out of work, and by erasing the investment savings of one-fifth of the population. A. B. C. D. E. and by erasing and erasing and having erased and erased by erasing

ANSWER: B To maintain a parallel structure with “causing” and “putting,” the verb in the final clause should be “erasing” without “by”;

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16. The Elk City garbage dumps are so full that Elk City has been forced to pay a large sum to Caribou City to accept much of Elk City’s garbage. The Elk City mayor has proposed paying for this garbage relocation by imposing a tax on manufacturing businesses in Elk City. MegaCorp, the largest manufacturing business in the area, protests that this tax is unfair because businesses should not have to pay for a garbage problem that has been created by homeowners. Which of the following, if true, most weakens MegaCorp’s argument? A. MegaCorp already pays more than \$10,000 per year in taxes and fees to Elk City. B. MegaCorp employs more than 60 percent of the employed residents of Elk City. C. A recycling program would address the garbage problem more effectively by reducing the overall quantity of waste. D. MegaCorp’s manufacturing processes produce more than 90 percent of the total waste that goes into Elk City’s garbage dumps. E. Caribou City is happy to receive the extra garbage because the fees it collects from Elk City have helped to address a shortfall in education funding.
ANSWER: D If MegaCorp produces the majority of the waste that goes into the overfull garbage dumps, the company cannot validly claim that the problem was “created by homeowners.”

A. Several new materials developed for the Apollo space program were later adapted to provide basic components of the modern computer and electronics industries. B. The missile defense system in question will not require the development of any new technologies. C. Space-based missile defense programs may be the only way to defend civilian populations against preemptive nuclear attacks. D. Space-based missile defense programs, although more expensive than traditional land-based systems, are theoretically more effective than traditional land-based systems. E. The scientists employed on the project could make extraordinary advances in the capabilities of intercontinental ballistic missiles used by the army.
ANSWER: A The example given demonstrates that a past technology developed by the government that did not have immediate civilian economic applications was later adapted to provide important economic benefits.

18. The commissioner of a professional sports league dictated that teams could not put players on the field who had a greater than 20 percent chance of suffering a careerending spinal injury during competition. The commissioner justified this decision as a way to protect players from injury while protecting the league from lawsuits. Which of the following, if true, would most undermine the effectiveness of the commissioner’s new policy? A. Spinal injuries can result in paralysis, loss of fine motor skills, and even death. B. The previous year, more than seven players in the league suffered careerending spinal injuries. C. The players’ union agrees that the risk of injury is an inevitable part of playing the game at a professional level. D. There is no scientifically valid method for determining the likelihood of any player suffering a career-ending spinal injury at any given time. E. Players barred from playing because of this new regulation will be entitled to compensation for lost wages at a level determined by the commissioner’s office.

17. There are Congressmen who say that the development of a space-based missile defense system will provide economic benefits only to military contractors. This claim is not true. A space-based missile defense system, even if it has no current applications for civilian businesses, will still benefit civilian businesses because those businesses will be able to find profitable uses for the government-developed technology in the future. Which of the following statements, if true, provides the most support for the argument that a space-based missile defense system could provide future economic benefits for civilian businesses?

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ANSWER: D If there is no valid way to determine which players have a 20 percent chance of suffering such an injury, there will be no way to enforce the commissioner’s new policy.

19. There are few things worse for a new parent than listening to a baby scream in hunger while a bottle of formula slowly warms up in a bowl of hot water. So why not just pop the bottle in the microwave and zap it in 20 seconds? Because microwaves heat fluids unevenly, and a hot pocket in the formula could seriously injure the baby. Which of the following is presupposed in the argument against heating formula in the microwave? A. Babies generally refuse to eat formula that has been heated in a microwave. B. Microwave radiation might break down some of the proteins in formula that are vital to a baby’s health. C. Different microwaves use different amounts of power, and consequently some models could heat a bottle to scalding temperature faster than others. D. Parents cannot be expected to consistently even out the temperature of a microwaved bottle by shaking it vigorously before giving it to the baby. E. Once formula has been heated, any leftover formula should be discarded, because otherwise the formula could spoil between feedings and make the baby sick.
ANSWER: D If parents could be expected to consistently even out the temperature of microwaved bottles, then the concern about hot pockets in the bottle would be unfounded. 20. Charlie’s Chainsaw Company has reason to

B. Charlie’s chief rival has recalled two of its products within the past year. C. Product recalls often result in a perception by customers that a given product is permanently defective, even after the defect has been remedied. D. The stocks of publicly traded companies that announce product recalls often drop upon the announcement, but they generally return to the pre-announcement level within 12 months. E. Three years ago a rival company went out of business because of large punitive damages awarded to a plaintiff who had been injured by a defective chainsaw.
ANSWER: E Answer E suggests that the company has a justifiable concern that if the product is not recalled, the company could be involved in a damaging lawsuit that could even lead the company into bankruptcy; this concern provides a strong economic incentive to recall the chainsaws. Answer A could be correct if the passage referred to a “moral decision” or just “the right decision,” but since the passage specifically refers to an “economic decision,” answer E is the best choice.

21. A dog enthusiast took home two puppies from the dog shelter. He fed one of the puppies super-premium canned dog food, while he fed the other a generic brand from the grocery store. The dog fed on the generic brand gained weight twice as fast as the dog fed the super-premium brand. Because of the difference in these results, the dog enthusiast concluded that the generic brand actually provided nutrition superior to that of the super-premium brand. Each of the following, if true, would weaken the evidence for the dog enthusiast’s conclusion except for which of the following? A. A dog will sometimes gain more weight when eating inferior-quality food because he must eat more of it to obtain the nutrients he needs. B. The dogs were of mixed breeds and appeared to be descended from dogs of different sizes. C. Both dogs ate all of the food given to them at each serving. D. The dog enthusiast did not give the two dogs equal amounts of their respective foods.
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believe that one of its models of saw is defective. A recall of all of the saws would cost more than \$5 million, and would probably result in a loss in market share over the next quarter because of bad publicity. Still, a recall is the right economic decision. Which of the following, if true, most supports the conclusion above? A. Defective chainsaws can seriously injure or even kill the people who use them.

E. The dog who received the super-premium dog food suffered from a digestive system disorder that hindered his growth.
ANSWER: C All of the other answers provide alternative reasons that the dogs might show different growth rates, but C offers no explanation for the observed difference in growth. 22. A council of ecologists in Hawaii have

D. by means of reducing poverty, cutting off the supply of illicit drugs, and through focusing on keeping kids in school E. to reduce poverty, cut off the supply of illicit drugs, and to focus on keeping kids in school
ANSWER: C The best answer should present each of the three points in the same grammatical construction, if possible. C presents each point as a gerund modified by a single adverb, which is grammatically correct and stylistically superior to the other options.

concluded that much of the currently uncontrolled invasive species on the island chain were arriving in the holds of cargo ships. A. have concluded that much of the currently uncontrolled invasive species on the island chain were arriving B. has concluded that many of the currently uncontrolled invasive species on the island chain arrived C. have concluded that many of the currently uncontrolled invasive species on the island chain have arrived D. concluded that many of the currently uncontrolled invasive species on the island chain would arrive E. has concluded that much of the currently uncontrolled invasive species on the island chain had arrived
ANSWER: B The subject of the sentence is “council,” so the plural verb “have concluded” in A and C is incorrect. The use of the conditional “would arrive” to describe species that are already “currently” on the island is illogical, so D is incorrect. E incorrectly uses “much” to describe the countable noun “species”; countable nouns require “many” instead of “much.”

24. As automobiles replaced horses as the primary means of transportation, it was widely anticipated that the time spent in transit by the average traveler would decrease. A. As automobiles replaced horses as the primary means of transportation, it was widely anticipated that B. Insofar as automobiles replaced horses as the primary means of transportation, it was anticipated widely C. With horses being replaced by automobiles as the primary means of transportation, there was wide anticipation that D. As the primary means of transportation replaced horses with automobiles, many anticipated that E. Automobiles replacing horses as the primary means of transportation produced anticipation widely that
ANSWER: A The underlined passage is grammatically correct and stylistically superior to the other choices.

23. Some people say that the answer to crime is to build more prisons, but more sensitive observers argue that instead we should address the sources of crime through reduced poverty, a cut off supply of illicit drugs, and by focusing on keeping kids in school. A. through reduced poverty, a cut off supply of illicit drugs, and by focusing on keeping kids in school B. by the reduction of poverty, cutting off the supply of illicit drugs, and to focus on keeping kids in school C. by reducing poverty, cutting off the supply of illicit drugs, and focusing on keeping kids in school

25. Intrigued by the new rules that favored quickness over strength, the decision of the coach was to give more playing time to the team’s smaller athletes. A. the decision of the coach was to give more playing time to the team’s smaller athletes B. the coach decided to give the team’s smaller athletes more playing time C. it was decided by the coach to give the team’s smaller athletes more playing time D. the team’s smaller athletes were given more playing time by the coach E. more playing time was given to the team’s smaller athletes by the coach

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ANSWER: B The introductory phrase “Intrigued by the new rules” makes sense only when it is applied to the coach, so B is the best answer.

26. At ground level, nitrous oxides are bad enough, but when up high, atmospherically they bond with free ions to create dangerous smog particles. A. but when up high, atmospherically they B. however, it is in the upper atmosphere in which it may C. but in the upper atmosphere, they D. however, but once in the upper atmosphere it is known to E. as in the upper atmosphere they
ANSWER: C The passage refers to “nitrous oxides” plural, so B and D are incorrect because they use the pronoun “it.” Answer E does not make sense given the preceding clause, and A is awkwardly worded, so C is the best choice.

ANSWER: D D provides an answer for the question of why, if feathered dinosaurs did exist, no evidence of their feathers has ever been found. Answer E also provides a partial answer— that the fossil record of dinosaurs is incomplete— but it is a weaker answer than D because it does not directly address the question of feathers.

28. Bob and Linda are tired of the freezing cold days in Glenmont, so they are considering retiring to either Sunny Glen or Buena Vista. Bob points out that Sunny Glen has an average annual temperature 8 degrees Fahrenheit higher than that of Buena Vista. Linda insists, however, that Buena Vista would be the better choice. Which of the following, if true, best accounts for Linda’s preference for Buena Vista? A. Different people experience cold in different ways, so what seems cold to Linda may seem pleasantly cool to Bob. B. Sunny Glen has a somewhat higher risk of hurricanes than does Glenmont. C. Buena Vista has a range of cultural offerings, including an opera, a ballet, and three jazz clubs. D. Living in a place that gets very hot, such as Sunny Glen, can have as many health risks as living in a place that gets very cold. E. While Sunny Glen is warmer than Buena Vista in the summer, it also has more freezing cold days in the winter.
ANSWER: E The passage specifically states that Bob and Linda are seeking to avoid freezing cold days, and answer E states that Buena Vista has fewer freezing cold days than Sunny Glen; this fact accounts for Linda’s preference for Buena Vista, despite Sunny Glen’s higher average temperature.

27. Paleontologists hypothesize that modern birds evolved from the family of dinosaurs that included Tyrannosaurus rex. This hypothesis would be strongly supported if evidence that dinosaurs from this family had a body covering resembling feathers could be found, but so far no such evidence has been found. Which of the following, if true, would most help the paleontologists explain why no evidence of feathered dinosaurs has yet been found? A. Fossilized dinosaurs have shown many birdlike characteristics, such as bone structure and winglike arms. B. If birds are in fact the descendants of dinosaurs, then it can be argued that the dinosaurs never really died out. C. Flying dinosaurs such as the Pteranodon, which is not thought to have been related to modern birds, do not appear to have had feathers. D. Soft tissues such as skin and feathers do not fossilize like bones, and therefore are far less likely to have left permanent evidence in the fossil record. E. The thousands of dinosaur fossils excavated by paleontologists represent only a tiny fraction of the billions of dinosaurs that once lived.

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29. Although many people would not believe it, the mosquito is actually the most dangerous animal in Africa. While the bite of the black mamba is invariably lethal when untreated, this dreaded snake kills only a few dozen people per year. Hippopotami, with their immense strength and foul dispositions, kill hundreds of people per year in rivers and lakes, but the mosquito is still more dangerous. Mosquitoes bite hundreds of millions of people in Africa every year, and they infect over a million each year with malaria, a disease that is often fatal. Which of the following questions would be most useful in evaluating the claim made above regarding the mosquito? A. Could a person survive an attack by a black mamba if that person received prompt medical attention? B. What criteria are used to determine which animal is the “most dangerous” animal? C. Could the incidence of mosquito bites be decreased through the judicious use of pesticides and insect repellent? D. Does malaria kill more people per year in Africa than tuberculosis? E. How does the percentage of people who survive hippopotamus attacks in Africa each year compare with the percentage of people who survive mosquito bites?
ANSWER: B The claim about mosquitoes is that “the mosquito is actually the most dangerous animal in Africa.” The argument then provides examples of other dangerous animals, but suggests that the mosquito is more dangerous because it attacks more people and infects a very large number of them with a potentially fatal disease. The answer to the question in choice B would allow us to determine whether the quantitative argument in the passage actually does make the mosquito the “most dangerous animal in Africa.” If it was determined that the “most dangerous animal” was the one most likely to kill a person in a single encounter, then the black mamba or the hippopotamus might be considered more dangerous than the mosquito. Choice E could be a follow-up to the question in B, but on its own it is less useful than B for evaluating the claim in the passage.

30. What appears to be the primary purpose of this passage? A. To educate readers about the health threats involved in the use of performance-enhancing drugs B. To analyze the ways in which professional athletes have eluded attempts to screen for performance-enhancing drugs C. To discuss the reasons why performanceenhancing drugs are a dangerous and persistent problem for society D. To complain about the inadequate efforts by government and professional sports organizations to eliminate the problem of performance-enhancing drugs E. To argue that athletes, both professional and amateur, should not use performanceenhancing drugs on the grounds that they are both dangerous and unfair
ANSWER: C The passage has two themes: presenting the dangers of performanceenhancing drugs, and then discussing the reasons why the problem is so hard to eliminate. The answer needs to address both of these themes. A and E address only the first of these themes, while B and D address only the second. C offers the most complete description of the passage’s purpose.

31. According to the passage, all of the following are known potential consequences of steroid use except for which of the following? A. B. C. D. E. Damage to reproductive organs Decreased blood pressure Increases in the user’s strength and speed Kidney tumors Increased risk of depression

ANSWER: B The article specifically states in the second paragraph that steroids “have been linked to . . . high blood pressure.” This is the opposite of what B suggests. There is support for all of the other answers in the passage.

32. The author’s attitude toward the problem of steroid abuse is best described as which of the following? A. B. C. D. E. Cautious but optimistic Judgmental but supportive Ambivalent but resigned Curious but subjective Concerned but pessimistic

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ANSWER: E The author is clearly concerned by the problem of steroid abuse; this attitude is seen in a statement such as: “This chemical epidemic is a pernicious threat to both the nation’s health and our collective sense of ‘fair play.’” The author’s pessimism is seen in the final sentence: “The sad fact is that unless the government and professional sports organizations are willing to get tough on the steroid problem, the use of performanceenhancing drugs in sports is not going to end.” A is incorrect because the author is not optimistic; B is incorrect because the author is not supportive; C is incorrect because the author is not ambivalent; and D does not capture the tone of the article.

B.

C.

D.

E.

cows that have not been given bovine growth hormone The relationship of a chess player to a competitor who uses psychological tricks in order to gain an advantage The relationship of a boxer in the lightweight class to a boxer in the heavyweight class The relationship of a person taking a standardized test according to the rules to a person taking the same test while using an illegal hidden calculator The relationship of a person entering a pig in an agricultural contest to a person entering a guinea pig in the same contest

33. Which of the following can be inferred about a long-distance race in which both athletes who use performance-enhancing drugs and those who do not use these drugs compete? A. The athletes using the drugs will be caught by the proper authorities and ejected from the race. B. The athletes using the drugs will have a better chance of winning the race. C. The athletes using the drugs will use steroid precursors that produce effects similar to those of androgenic drugs but are not technically steroids. D. The athletes using the drugs are more likely to be professionals in their sport than the athletes who do not use such drugs. E. The athletes using the drugs will be more likely to use any means possible to win the race, including intentional sabotage of the other racers’ equipment.
ANSWER: B The passage states: “the drugs really do work. Athletes who dope are simply stronger and faster than their competitors who play fair.” There is no substantial evidence for any of the other answers.

ANSWER: D D is the best answer because in both situations, the latter is using illegal means to gain an advantage over the former.

35. According to the passage, which of the following can be inferred about the “designer” steroid THG? A. It can increase masculine traits in users without setting off standard doping tests. B. It does not cause the health problems associated with traditional anabolic steroids. C. Even if professional sports organizations could detect THG, they would take no action against those who use it. D. It is a chemical permutation of progesterone, a hormone that has powerful effects on the human body. E. Because it is a “designer” steroid, it is more expensive than generic steroids.
ANSWER: A Referring to “designer” steroids, in the fifth paragraph the passage states: “Chemists have discovered that they can create new drugs that produce androgenic effects but do not set off the standard doping tests.” In the second paragraph, the passage states: “‘androgenic’ means that they increase masculine traits.” There is no substantial support in the passage for any of the other answers.

34. The relationship of an athlete who does not use performance-enhancing drugs to an athlete who does use such drugs is most similar to which of the following? A. The relationship of a farmer selling milk from cows that have been given bovine growth hormone, a legal drug that promotes greater than normal milk production, to a farmer selling milk from

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36. Which of the following best expresses the role of the third paragraph in the overall structure of the passage? A. It redirects the theme of the passage from presenting a problem to explaining the reasons for the problem’s severity. B. It introduces a new concept that defines the rest of the passage. C. It provides an answer to a question posed in the first two paragraphs. D. It refutes the central hypothesis of the second paragraph and poses a question that is answered in the following paragraphs. E. It narrows the focus of the passage from the general themes of the first two paragraphs to the more specific themes of the last two paragraphs.
ANSWER: A By posing the question “Why is this?” the third paragraph shifts the focus of the passage from a presentation of the problems caused by steroids to explanations of why large numbers of people use them despite the risks. Answer A captures this role best.

38. Since the average test score of students enrolled in charter schools were rising 7.5 percent in the spring, many educators concluded that the system was working. A. Since the average test score of students enrolled in charter schools were rising 7.5 percent in the spring, many educators concluded B. As the average test score of students enrolled in charter schools rose 7.5 percent in the spring, with many educators concluding C. Because the average test score of students enrolled in charter schools rose 7.5 percent in the spring, many educators concluded D. Because the average test score of students enrolled in charter schools were up 7.5 percent in the spring, many educators concluded E. With average test scores rising by 7.5 percent among students enrolled in charter schools, and many educators concluded
ANSWER: C “Score” is a single noun, so the statements “score . . . were rising” in A and “score . . . were up” in D suffer from noun-verb agreement errors. The constructions “as . . ., with” in B and “with . . ., and” in E do not convey the causal relationship between the first and second clauses of the sentence that the statements imply, so these choices are inferior to C, which is grammatically and stylistically acceptable.

37. His opponent having sprained his wrist, Andrew could have won by exploiting this weakness, but he chose not to do it. A. His opponent having sprained his wrist, Andrew could have won by exploiting this weakness, but he chose not to do it. B. Andrew could have won by exploiting this weakness after his opponent sprained his wrist, but he chose not to do so. C. Choosing not to do so, Andrew could have won after his opponent sprained his wrist by exploiting this weakness. D. After his opponent sprained his wrist, Andrew could have won by exploiting this weakness, but he chose not to do so. E. After his opponent sprained his wrist, Andrew could have, but chose not to do it, won by exploiting this weakness.
ANSWER: D The problem with A is that it is unclear what the “it” at the end applies to: winning or exploiting the weakness. E has the same problem. The statements in B and C are presented in an illogical order, so it is more difficult to understand the meaning of the sentence. Of the choices, D is the clearest and conforms best to standards of written English.

39. The police chief argued that first-time offenders who have no high school diploma but who have families with a record of crime will probably break the law again. A. who have no high school diploma but who have families with a record of crime B. without a high school diploma and families having a criminal record C. without a high school diploma whose families have a record of crime D. whose families have criminal records and lacking high school diplomas E. lacking high school diplomas and also having families having criminal records
ANSWER: C C is the clearest and most concise choice. A is less concise, and it is unclear why

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