Drue Gawel, Instructor
Drue@Druegawel.com
214.310.3978
Susan Langford, Instructor
Susan.langford3@gmail.com
972.571.5307
Norma Rodriguez
Recruiting Manager, MBA Programs norma.rodriguez@utdallas.edu Section 1 - Arithmetic v7.1
UTD GMAT
Math Prep Section 1
Introduction and Arithmetic
1
Instructor Background
Drue J Gawel
• M.S. Electrical Engineering
• B.S. Electrical Engineering, Computer Science
• M.Ed. Learning Sciences (The study of How People Learn).
• Work Experience
• Texas Instruments, Test Systems Engineer
• High School Mathematics Teacher, Dallas ISD
• Full Time Tutor, Mathematics and Science
Section 1 - Arithmetic v7.1
• Education
2
Instructor Background
Susan Langford
• Education
• Work Experience
•
•
•
•
•
•
•
•
•
Syncrude Canada, Power Distribution Design Engineer
Northern Telecom Canada, Product Manager
Intel USA, Program Manager
Nortel Australia, Technical Trainer
Telstra Australia, International Product Manager
Alliance Systems (now NEI), Program Manager
CollegeBound , General Manager and SAT/ACT Tutor
Plano ISD, High School Mathematics Teacher
Math Tutor
Section 1 - Arithmetic v7.1
• B.S. Electrical Engineering
3
Develop a Plan
• Evaluate where you are
• Take a Practice Test
• http://www.mba.com/the-gmat/download-free-test-preparationsoftware.aspx
• See what admissions scores are like for the colleges in the schools that you want to attend
• Develop a plan to get there.
• The UTD prep class is a good first step.
• Additional practice and practice tests will be required. How much depends upon your goal.
Section 1 - Arithmetic v7.1
• Figure out your goals
• Schedule your test in Advance
• Convenient Location
• Arrange your Life to be RESTED!!!!!
• Time of Day (morning or afternoon)
4
Course Objectives
• Cover basic mathematical concepts
• Increase your confidence by helping you understand your strengths and weaknesses so…
• You can plan your next steps in preparing for the test Section 1 - Arithmetic v7.1
• Help you identify your strengths and weaknesses
5
How To Get the Most From This Class
Make use of the slides for each day
EXAMPLE:
Percentages
Ratios / Proportions ??
Even/Odd Number Rules
Format
• Instruction on Topic
• Basic Practice on Topic
• Practice on your own
Section 1 - Arithmetic v7.1
The concepts covered will be listed. Make notes on which ones you master and which ones you need more practice on.
6
Math Resources Online
Repetition to help you review cards before you forget them. http://www.quizlet.com/ Online Flashcard system http://www.brightstorm.com/math/ (subscription service) http://majortests.com/ Has great practice problems http://www.kutasoftware.com/free.html Algebra worksheets and answers. Make sure you look for the free ones. http://wolframalpha.com/ Plug in any equation and get an answer for free. If you want a step by step solution, then a subscription is required.
Recommended Math Apps
“Math Facts Master” (iOS and Android) +, -, x, ÷ facts
“Dragon Box 2” (iOS and Android) for algebra basics – doesn’t cover everything but good start
Section 1 - Arithmetic v7.1
http://www.khanacademy.org/ https://ankiweb.net/ Online Flashcard system. Uses Spaced
7
Recommended Math Texts
CliffsNotes Math Review for Standardized Tests 2nd Edition
(2010) by Jerry Bobrow. For extra practice of the basics.
GMAT Math Resources Online
http://www.khanacademy.org/test-prep/gmat. Direct link to Khan Academy materials.
GMAT Math Resources – Recommended Texts
The Official Guide for GMAT Quantitative Review 2nd Edition (2009) Latest edition as of 6/12/12. Another may come out soon.
Manhattan GMAT 5th Edition Books 1-5 – excellent for those shooting for high scores. Advanced GMAT Quant by Manhattan GMAT 4th Edition. Good if you want to buy a single Manhattan GMAT book. The 5th edition set integrated
Quantitative practice throughout the other books.
Section 1 - Arithmetic v7.1
http://www.mba.com/the-gmat/download-free-test-preparation-software.aspx - A great resource for practice tests as well as practice problems.
8
Study Groups
• If interested in forming one, please stay after class.
• http://ctl.byu.edu/node/219 - Nice short summary
• http://web.duke.edu/arc/documents/How%20to%20Form%20a%
20Successful%20Study%20Group.pdf – Nice short summary
• http://www.lsa.umich.edu/advising/academicsupport/strategiesf orsuccess/collaboratingwithpeers - More in-depth details.
Section 1 - Arithmetic v7.1
• General information on forming study groups here:
9
•
•
•
•
•
37 questions, 75 minutes total
All multiple choice
Adaptive
Must answer a question to go on to the next one
Cannot go back to an earlier question
• Approximately 25% of questions are experimental
• About 22 Problem solving questions
• Some computation
• Some word problems
• About 15 Data Sufficiency Problems
• Determine how much info is needed to solve a problem
Section 1 - Arithmetic v7.1
GMAT Quantitative Section
10
Calculator – GMAT – None
None, Nada, Zip, Not allowed
Try not to use a calculator for anything (even balancing your checkbook) until you’ve completed the GMAT.
Section 1 - Arithmetic v7.1
So basic math is extremely important –
We will be going over shortcuts to speed your calculations, such as simplifying fractions before you multiply.
If your plan to solve a problem involves making many calculations, there is probably a different, faster way to approach the problem.
11
Math Sessions
Intro, Strategies & Arithmetic
Algebra
Coordinate Geometry
Geometry
Data Analysis
Word Problems
Data Sufficiency (GMAT)
Math Session(s)
1
2
3
3
4
4
1-4
Section 1 - Arithmetic v7.1
Topic
12
•
•
•
•
•
•
•
•
•
•
•
•
•
Problem Solving – Brief Intro
Types of Numbers
Order of Operations
Fractions
Decimals
Divisibility Rules
Prime Numbers
Prime Factorization
Exponents
Roots
Inequalities & Absolute Value
Percentages
Even/Odd Number Rules
Use this to keep track of those topics you have mastered or still need to practice.
Section 1 - Arithmetic v7.1
Arithmetic
13
Problem Solving
Approach Adapted from George Pólya’s How to Solve It (1945)
Understand the Problem
•
What exactly are you asked to find?
2. Develop a Plan
•
Is there something in the problem or answer choices that will help you solve it?
•
Is there more than one way to solve it? Which is the fastest?
3. Solve It
•
Carry out your plan. If that doesn’t work, use a different plan
•
Don’t know what to do? WRITE SOMETHING.
4. Review it
•
Ask yourself “Did I answer the question ASKED?” It is easy to lose track of what exactly was being asked.
•
When practicing, ask yourself if there was another way to solve it. Is there another way that would be faster? What did you learn that you didn’t know already? And how are you going to remember it?
Section 1 - Arithmetic v7.1
1.
14
Types of Numbers
Counting Numbers:
1, 2, 3,… (the numbers we use to count things)
Whole Numbers:
0, 1, 2, 3,...
Integers:
…-3, -2, -1, 0, 1, 2, 3,…
includes integers, decimals and any number that can be expressed as a fraction: 1/3, .125, -25, -8, 0.00005, etc.
Irrational numbers: numbers that can’t be expressed as a fraction. Ex: π, 2, 3, etc.
Prime Numbers :
Section 1 - Arithmetic v7.1
Rational Numbers:
positive integers are only divisible (without a remainder) by 1 and itself:
2, 3, 5, 7, 11… (Prime numbers start with 2)
Note: 1 is NOT a prime number
15
Order of Operations (PEMDAS)
(potentially tricky!)
What is 20 − 5 + 10 ?
B) 15
C) 25
D) 35
Section 1 - Arithmetic v7.1
A) 5
What is 35 ÷ 5 × 7 ?
A) 1
B) 13
C) 35
D) 49
16
Order of Operations
PEMDAS
Parenthesis
Exponents (including Square Roots) in order from left to right
• My Dear
Multiplication & Division in order from left to right
• Aunt Sally
Addition & Subtraction
Section 1 - Arithmetic v7.1
• Please
• Excuse
17
Order of Operations Examples
A quick reminder about exponents: 53 = 5 ∗ 5 ∗ 5 & (−3)2 = −3 ∗ (−3)
a) 15 − 6 − 4 −2
b) 2 − 17 ÷ 5
c) 60 ÷ 12 − −7 + 4
d 3
e) −5 −3 − 15
f) −2
g) 20 ÷ 5
2
−2 + 6
3
− −2
4
3
15 − 18
4
Section 1 - Arithmetic v7.1
4
g) −85 0 − −17 3
(Examples from ETS, The Official Guide to the GRE, 2nd Edition, 2012)
"UTD Arithmetic Practice" Order of Operations #1-12
18
Numerator
Denominator
Fractions ex. 19
4
Converting to Mixed
Mixed (Proper) Fraction ex. 4
3
4
Converting to Improper
Adding and Subtracting Fractions – Common Denominator ex. 3
8
2
8
+ =
1
4
1
3
5
8
ex. 2 + 3 =
ex.
5
8
2
3
+ =
1
4
15
16
+
24
24
2
3
ex. 5 − 1 =
=
31
24
=
7
1
24
Section 1 - Arithmetic v7.1
Improper Fraction
19
"UTD Arithmetic Practice" Fractions Add/Subtract #13-24
Fractions
Multiplying Fractions ex. 3
5
×
8
9
=
3×5
8×9
=
15
72
x x
Better yet – “Simplify before you multiply” ex.
3
5
×
8
9
=
3×5
8×9
1×5
8×3
=
=
5
24
Dividing Fractions : Multiply by the RECIPROCAL of the divisor (second number)
Ways to remember:
ex.
2
3
7
8
2
Dividing by a fraction?
Please don’t cry
Just flip it upside down
And multiply!
8
16
= 3 × 7 = 21
ex.
Any integer can be written as a fraction
Or KCF
Keep Change
4
5
÷8
9
=
ex. −7 =
−7
1
Flip
Section 1 - Arithmetic v7.1
A BENEFIT of doing this (CORRECTLY) is that then you don’t have to check if the number can be simplified after you multiply
20
Fractions
When multiplying or dividing Fractions, YOU MUST convert mixed numbers to improper fractions.
1
4
× =
Ex.
3
4
1
÷5
8
=
Fractions Practice
Reducing Fractions
Ex.
4
24
=
18+6
Ex.
8
1
6
6
7
Ex.
=
13+8
Ex.
4
×
35
18
=
1
1
5
3
= × =
5
3
Section 1 - Arithmetic v7.1
Ex.
3
2
7
21
Fractions - Examples
c)
1
2
1
3
− +
7
8
1
2
−
1
12
4 2
5
e) 3 − 2
1
6
b)
3
4
d)
3
−8
+
1
7
−2
5
÷
27
32
2
5
f) ÷ 4
"UTD Arithmetic Practice" Fractions Multiplication #25-30
"UTD Arithmetic Practice" Fractions Division #31-36
OGMAT EX: p. 155 #27, p. 158 #48, p. 165 #97
Section 1 - Arithmetic v7.1
a)
(Examples a)-d) from ETS,
The Official Guide to the
GRE, 2nd Edition, 2012)
22
Decimals
× 103
×1000
× 101
× 100
× 10−1
× 10
× 1
×
× 102
×100
1
.
9
3
1
10
Section 1 - Arithmetic v7.1
2
Thousandths
6
Hundredths
4
Tenths
,
Ones or Units
8
Tens
Thousands
Hundreds
Place values…
× 10−2 × 10−3
×
1
100
×
1
1000
23
Adding and Subtracting: line up the decimal points and fill in missing places with zeros.
EX. 1.0256 + 0.043
1.0256
+0.0430 is greater than
< is less than
≥ is greater than or equal to
≤ is less than or equal to
Absolute Value
Always positive (it is the distance a number is from zero)
4 =4
−4 = 4
− 4 = −4
− −4 = −4
Section 1 - Arithmetic v7.1
Inequalities & Absolute Value
31
Putting it Together True or False?
a) −5 < 3.1
g)
b)
h)
21
28
i)
- −23 = 23
j)
1
2
c) 7 ÷ 0 = 0
d) 0 <
−1
7
e) 0.3 <
f)
−1
87
1
3
k)
= −1
l)
=
2
1
17
59
3
59
2
= 596
- 25 < −4
(Examples from ETS, The Official Guide to the
GRE, 2nd Edition, 2012)
Section 1 - Arithmetic v7.1
16 = 4
−3
32
Section 1 - Arithmetic v7.1
Putting it Together - answers
33
Percent
What ()
is (=)
percent (÷ )
of (×)
=
OR
=
d) 15 is 30% of what number
b) 150% of 48
e) 11 is what % of 55
Section 1 - Arithmetic v7.1
a) 40% of 15
c) 0.6% of 800
(Examples from ETS, The Official Guide to the GRE, 2nd Edition, 2012)
"UTD Arithmetic Practice" Percent Problems # 83-92
OGMAT EX: p. 152 #6, p. 153 #11, p. 169 #123, p. 275 #3, p. 283 #91
34
Percent Change (Increase or Decrease) =
ℎ −
× 100 =
× 100
Ex. If an athlete’s weight decreased from 195 pounds to 182 pounds, what was the percent decrease in weight?
"UTD Arithmetic Practice" Percent Change Problems # 93-104
Section 1 - Arithmetic v7.1
Ex. If a person’s salary increased from $200 to $234 per week, what was the percent increase in salary?
Know these common percents and fraction equivalents
1
1
1
1
1
1 % 1 = 50% 1 = 4%
= 10%
= 5%
= 20%
= 25% = 33 3
10
20
5
4
3
2
25
35
•
•
•
•
•
Any number x even number = even number
Product of only odd numbers = odd number
Sum of 2 or more even numbers = even number
Sum of exactly 2 odd numbers = even number
Sum of an even and odd number = odd number
• OR just plug in actual odd/even #’s to get result
OGMAT EX: p. 158 #44, p. 275 #7, p. 277 #27
Section 1 - Arithmetic v7.1
Even/Odd Rules
36
Section 1 - Arithmetic v7.1
Odd/Even Rules Quiz
37
(Examples from ETS, The Official Guide to the GRE, 2nd Edition, 2012)
Section 1 - Arithmetic v7.1
Odd/Even Rules Quiz Answers
38
• “5.3 Problem Solving” (pages 149 – 185): 1, 2, 5, 8, 9, 15, 17,
19, 20, 21, 22, 24, 26, 27, 32, 33, 35, 39, 40, 41, 44, 46, 48, 51,
52, 57, 58, 63, 65, 74, 77, 80, 85, 87, 94, 95, 97, 100, 106, 110,
111, 116, 117, 122, 124, 127, 128, 133, 136, 138, 142, 146,
148, 149, 150, 151, 155, 156, 158, 163, 164, 170, 174, 176, 80,
181, 196, 199, 204, 217, 218, 221, 225, 226, 227 & 230
• “6.3 Data Sufficiency” (pages 269 – 291): 1, 2, 4, 7, 8, 10, 12,
13, 14, 15, 16, 18, 21, 22, 24, 26, 27, 28, 29, 31, 32, 37, 46, 54,
55, 57, 58, 59, 61, 62, 63, 64, 65, 75, 80, 83, 85, 91, 94, 95, 97,
98, 101, 103, 106, 107, 108, 111, 112, 114, 116, 118, 124, 126,
131, 133, 135, 136, 140, 147, 148, 150, 157, 159, 161, 162,
168, 170, 172, 173 & 144
Section 1 - Arithmetic v7.1
Arithmetic Examples from the
Official GMAT 13th Edition
39
UTD Arithmetic Practice
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Order of Operations - Evaluate each expression.
1)
9
1 − (−1) − 3
3)
25 × 2
(−2) × (−5)
2)
7
4) 5 − 2 + 9 + 5
5) 5 × (−2) + 4 + 1
6) 6 + 1 + (−9) − 2
7) (−10) × 5 − (8 + 6)
8)
9) (−4) × 7 − 3 − 1
11) −
(−6) + (−4) − (−3)
(−6) × 2
−3
10) (−10) + 10 × (−8) − 4
24
(−4) − (−2) − (−5)
12) 5 × (−10) +
3
−3
Fractions - Add/Subtract - Evaluate each expression.
13)
3
1
+
7
5
15) 4
1
3
1 2
+
4 7
16) 4
1
1
−2
7
6
5
6
18) 3
1
2
+4
2
5
17) 1 −
19)
14) 1 +
7
4
+
4
5
20)
1
5
−
4
3
UTD GMAT Prep Course
Gawel & Langford
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-1-
Arithmetic - page 40
Worksheet by Kuta Software LLC
21)
3
5
−
2
7
22)
3
1
+
5
3
23)
2
1
+2
3
6
24) 4
3 2
+
5 7
5
3
26) 5
1
× −4
3
27) 2
7
2
× −2
9
9
28) 4
2
1
× −1
3
10
29) −
5 7
×
4 6
30) −
7 2
×
8 9
Fractions - Multiplication - Find each product.
25) −2 ×
Fractions - Division - Find each quotient.
31)
9 1
÷
7 4
32)
33)
11 −13
÷
9
7
34) 2
35) 1
2 3
÷
9 5
36)
6 −7
÷
5
6
3
÷ −2
10
1 2
÷
3 5
Decimals - Add/Subtract - Evaluate each expression.
37) 5.1 − 0.7
38) (−2.8) − (−2.283)
39) (−3.3) + 7.8
40) 1.29 + (−5.9)
41) 1.2 + (−0.4)
42) 5 − (−5.56)
Decimals - Multiplication - Find each product.
43) 5 × 3.2
44) 0.3 × 1.8
UTD GMAT Prep Course
Gawel & Langford
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-2-
Arithmetic - page 41
Worksheet by Kuta Software LLC
45) 0.2 × 5
Decimals - Division - Find each quotient.
46) 6.1 ÷ 2.5
47) 4.4 ÷ 8
48) 2.8 ÷ 5
49) Through 54) intentionally left out
Factors - List all positive factors of each.
49) 55
50) 62
51) 65
52) 39
53) 42
54) 72
Factors - Write the prime factorization of each.
55) 50
56) 91
57) 63
58) 95
59) 88
60) 98
Exponents - Simplify. Your answer should contain only positive exponents.
61) b 0 ⋅ 4b −4
63) 3 x 3 ⋅ 4 x 3
62) 8n 0 ⋅ 6n 4 ⋅ 5n 3
64)
5x x 65)
67)
3k
66)
2k 4
4n
4
5 p3
6 p3
68) (5 x 3 )
4
2
70) (4v 4 )
4
5n 2
69) (7n 4 )
2
UTD GMAT Prep Course
Gawel & Langford
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-3-
Arithmetic - page 42
Worksheet by Kuta Software LLC
Simplify. Your answer should contain only positive exponents.
71) 2 x 0 ⋅ 2 x 3
72) 3m ⋅ 3m
73) 3r 2 ⋅ 2r 3 ⋅ 3r 3
74) 2n 4 ⋅ 3n 4
75) 3a 0 b 2 ⋅ a 2 b −4
76) 4 x −1 ⋅ 4 x 4 y 3 ⋅ 3 x 3
77) 3 x −1 y 2 ⋅ 2 x 4 y 2
78) 3a 3 b 3 ⋅ 2a −3 b −4
79)
81)
(2m 2) 4 ⋅ 2m 4n −1
80)
2m 0 n −4 x y −1 ⋅ ( x −3 )
−2
82)
2 yx3
(
2m 2 n −4 ⋅ 2m 2
2m 2 n 4
)
3
x −2 y 2 x −3 y 0 ⋅ ( x 2 y 0 )
2
Solve each problem and round to the nearest tenth or tenth of a percent
83) What is 260% of 61?
A) 158.6
C) 193.8
84) 48% of 101 is what?
B) 6300
D) 15860
A) 210.4
C) 4848
85) 62% of what is 114?
A) 7068
C) 81.8
86) 41 is 69% of what?
B) 70.7
D) 183.9
A) 55.8
C) 5580
87) 127% of what is 82.2?
A) 9301
C) 10439.4
B) 104.4
D) 64.7
B) 85%
D) 149.5%
91) 12% of $113 is what?
A) $13.56
C) $941.67
B) $1356
D) $11200
B) 28.3
D) 59.4
88) 66% of 151 is what?
A) 99.7
C) 158.9
89) What percent of 93.5 minutes is 110 minutes?
A) 1.49%
C) 117.6%
B) 40
D) 48.5
B) 228.8
D) 9966
90) 32% of $96 is what?
A) $300
C) $3072
B) $30.72
D) $3648
92) 7 inches is what percent of 114 inches?
A) 1628.6%
C) 6.1%
UTD GMAT Prep Course
Gawel & Langford
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-4-
B) 24.8%
D) 0.06%
Arithmetic - page 43
Worksheet by Kuta Software LLC
Find each percent change. Round to the nearest tenth of a percent. State if it is an increase or decrease.
93) From 98 to 20
A)
B)
C)
D)
79.6% increase
79.6% decrease
390% decrease
78% decrease
95) From 95 to 24
A)
B)
C)
D)
25.3% decrease
74.7% increase
71% increase
74.7% decrease
97) From 88 to 64
A)
B)
C)
D)
72.7% decrease
24% decrease
27.3% decrease
37.7% increase
99) From 14 hours to 17 hours
A)
B)
C)
D)
121.4% increase
21.4% increase
117.6% increase
3% increase
101) From $11 to $19
A)
B)
C)
D)
42.1% decrease
8% increase
72.7% increase
90.8% decrease
103) From 8 miles to 5 miles
A)
B)
C)
D)
62.5% decrease
3% increase
160% decrease
37.5% decrease
94) From 91 to 60
A)
B)
C)
D)
51.7% increase
65.9% decrease
34.1% increase
34.1% decrease
96) From 14 to 44
A)
B)
C)
D)
214.3% increase
30% increase
30% decrease
314.3% increase
98) From 19 to 53
A)
B)
C)
D)
34% increase
278.9% increase
178.9% increase
64.2% increase
100) From 4.9 grams to 13 grams
A)
B)
C)
D)
165.3% increase
22.3% increase
62.3% increase
8.1% increase
102) From 11 miles to 1 mile
A)
B)
C)
D)
9.1% decrease
1000% decrease
90.9% decrease
10% increase
104) From 17 minutes to 1 minute
A)
B)
C)
D)
1700% decrease
16% decrease
16% increase
94.1% decrease
UTD GMAT Prep Course
Gawel & Langford
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Arithmetic - page 44
Worksheet by Kuta Software LLC
Answers to
1) −9
5) −5
9) −32
22
13)
35
1
17)
6
11
21)
14
2) −1
6) −4
10) −94
1
14) 1
3
9
18) 7
10
14
22)
15
1
3
11
−1
24
77
−
117
4.4
0.8
1
1, 5, 11, 55
1, 2, 3, 6, 7, 14, 21, 42
2 ⋅ 52
2 3 ⋅ 11
25) −3
26)
29)
30)
33)
37)
41)
45)
49)
53)
55)
59)
63) 12 x 6
83) A
87) D
91) A
95) D
99) B
103) D
38)
42)
46)
50)
56)
60)
64)
4n 2
5
71) 4 x 3
3a 2
75) 2 b 79) 16m 12 n 3
67)
34)
68)
3) 5
7) −64
11) −8
15
15) 4
28
11
19) 2
20
5
23) 2
6
1
14
−21
27) −6
3
81
7
1
−
31) 5
36
7
3
1
−1
35) 2
20
27
−0.517
39) 4.5
10.56
43) 16
2.44
47) 0.55
1, 2, 31, 62
51) 1, 5, 13, 65
54) 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
7 ⋅ 13
57) 3 2 ⋅ 7
4
2 ⋅ 72
61) 4 b 5
3
65)
3
x
2k 3
25 x 6
69) 49n 8
72) 9m 2
76) 48 x 6 y 3
73) 18r 8
77) 6 y 4 x 3
8m 6
80) 24 n 84) D
88) A
92) C
96) A
100) A
104) D
x4
81)
2 y2
85) D
89) C
93) B
97) C
101) C
UTD GMAT Prep Course
Gawel & Langford
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4) 17
8) 4
12) −51
41
16) 1
42
5
20) 1
12
31
24) 4
35
2
28) −5
15
1
32) −1
35
5
36)
6
40) −4.61
44) 0.54
48) 0.56
52) 1, 3, 13, 39
58) 5 ⋅ 19
62) 240n 7
5
6
70) 256v 16
66)
74) 6n 8
6
78) b y2
82) 3 x 86) D
90) B
94) D
98) C
102) C
Arithmetic - page 45
Worksheet by Kuta Software LLC
GMAT/GRE “EXTRA” Arithmetic Exercises
UT Dallas Test Preparation
Tomas & Gawel
If k is an integer and 0.0010101 x 10K is greater than 1,000, what is the least possible value of K?
Simplify:
1)
3
√3
2)
4
√7
How many multiples of 4 are between 12 and 96, inclusive?
Order the following fractions:
−2 33 8 3 13 5
, , , , ,
3 50 11 5 27 8 (1 + √5) (1 – √5) =
104 doubles every 10 minutes… how many times does it double number in 1 hour? What does it equal?
How many minutes to go 120 miles at 400mph?
3
5
7
+
+
=
100 1000 100,000
What number when multiplied by 4/7 yields 6/7?
0.625 = 5/8… What does 0.0625 equal?
ܺ and ܻ are not BOTH odd… what Even/Odd options exist for ܺ ∗ ܻ and ܺ + ܻ ?
The average of 4 numbers = 150. Three are 240, 80, 110… what is the fourth?
Price increase 25%; then decrease 20%; what is relationship between the first and last price?
√16 + 16 =
22.4 ∗ 15 =
25% expected increase was actually 20% decrease; what is actual as % of expected?
What is the Ratio of 3/4 to 4 ∗ (3/4)
18 is 15% of 30% of what?
150mph speed = 4hr trip… at 200mph = ?hr
4x3y4 / 2xy3 =
Rank (0.08)2 and 1 / (0.08)2 and (1-0.08)2 and (1-0.08)2-1
3*(0.072) / 0.54 =
UTD GMAT Prep Course
Gawel & Langford
Arithmetic - page 46
GMAT/GRE “EXTRA” Arithmetic Exercises
UT Dallas Test Preparation
Tomas & Gawel
Approximate: [61.24 x (0.998)2] / √403
య
Approximate: √−89
(2 + 2√6) / 2 =
A fishing boat for 6 people costs $480, of which $150 is the down payment. If each of 6 contribute to down payment equally, how much more does each person still owe?
Sales compensation: $50 per unit + 10% of Total Sales; 6 units at $3,620 each unit; compensation?
Match Cannot be 0/Need Not be 0/Must be 0 with the appropriate expression:
-1/x; x + -x; x0
0, 4, 5, 2, 11, 8… median-mean = ?
N/T, quotient is S and remainder is V; what represents N?
UTD GMAT Prep Course
Gawel & Langford
Arithmetic - page 47
GMAT/GRE “EXTRA” Arithmetic Exercises
UT Dallas Test Preparation
Tomas & Gawel
ANSWERS
If k is an integer and 0.0010101 x 10K is greater than 1,000, what is the least possible value of K? 6
Simplify:
1)
3
√3
= √3 2)
4
√7
=
4√7
7
How many multiples of 4 are between 12 and 96, inclusive? 21+1 = 22
Order the following fractions:
−2 33 8 3 13 5
−2 13 3 5 33 8
, , , , , =
, , , , ,
3 50 11 5 27 8
3 27 5 8 50 11
ଶ
൫1 + √5൯൫1 – √5൯ = 1– √5 + √5 − ൫√5൯ = 1 − 5 = −4
If 104 doubles every 10 minutes… how many times does it double number in 1 hour? What does it equal? 6;
10ସ ∗ 2 = 10ସ ∗ 64 = 640,000
How many minutes to go 120 miles at 400mph?
ଵଶ௦ ௨௧௦
ೞ ቀ ଵ ௨ ቁ
ସ
ೠೝ
= 18 ݉݅݊ݏ݁ݐݑ
3
5
7
3
5
0
7
3507
+
+
=
+
+
+
=
= .03507
100 1000 100,000 100 1,000 10,000 100,000
100,000
ସ
ଷ
What number when multiplied by 4/7 yields 6/7? ∗ = ଶ
0.625 = 5/8… What does 0.0625 equal? = 0.625 (1/10) = 5/8 *(1/10) = 5/80 = 1/16
ܺ and ܻ are not BOTH odd… what Even/Odd options exist for ܺ ∗ ܻ and ܺ + ܻ and what are their outcomes?
Odd * Even = Even
Even * Odd = Even
Even * Even = Even
Odd + Even = Odd
Even + Odd = Odd
Even + Even = Even
The average of 4 numbers = 150. Three are 240, 80, 110… what is the fourth?
ଶସ ା ଼ ା ଵଵ ା ௫
ସ
= 150
x = 170
Price increase 25%; then decrease 20%; what is relationship between the first and last price? No change
To model – start with 100, increases to 125, then decreases to 100.
√16 + 16 = √32 = 4√2
22.4 ∗ 15 = 336
UTD GMAT Prep Course
Gawel & Langford
Arithmetic - page 48
GMAT/GRE “EXTRA” Arithmetic Exercises
UT Dallas Test Preparation
Tomas & Gawel
25% expected increase was actually 20% decrease; what is actual as % of expected?
To model – start with 100, expected was 125. Actual was 80.
Actual as percent of expected is 80 / 125 *100% = 16/25 *100% = 64%
What is the Ratio of 3/4 to 4 ∗ (3/4)
య
ర
య
ସ∗
ర
ଵ
ଵ
ସ
= ସ∗ଵ (ݐℎ݁ ݐℎݐݎݑ݂ ݁݁ݎℎ ܴܱ = )ݕ݂݈݅݉݅ݏ ݏ
య
ర
ସ∗ଷ/ସ
=
య
ర
ଷ
ଷ
ଵ
ଵ
= ସ ∗ ଷ = ସ
18 is 15% of 30% of what?
Translate into equation: 18 = 15/100 ∗ 30/100 ∗ ݔ
Solve for x:
18 ∗
ଵ ଵ
∗ ଷ =
ଵହ
004 = ݔ ݔ
150mph speed = 4hr trip… at 200mph = ?hr distance = rate * time = 150*4 = 600 miles time = distance/rate = 600 / 200 = 3 hours
4x3y4 / 2xy3 =
2x2y
Rank from least to greatest (0.08)2 and 1 / (0.08)2 and (1-0.08)2 and (1-0.08)2-1
(1-0.08)2-1, (0.08)2, (1-0.08)2, 1 / (0.08)2
3*(0.072) / 0.54 = .4
Approximate: [61.24 x (0.998)2] / √403 ~ [60 x 1] / 20 = 3
య
Approximate: √−89 ~ − 4.5
(2 + 2√6) / 2 = (1 + √6)
A fishing boat for 6 people costs $480, of which $150 is the down payment. If each of 6 contribute to down payment equally, how much more does each person still owe? $55
Sales compensation: $50 per unit + 10% of Total Sales; 6 units at $3,620; compensation? $2472
Match “Cannot be 0” / “Need Not be 0” / “Must be 0” with the appropriate expression:
-1/x
“Cannot be 0” x + -x “Must be 0” x0 “Cannot be 0”
0, 4, 5, 2, 11, 8… median-mean = ? median = (4+5)/2 = 4.5, mean = 5
N/T, quotient is S and remainder is V; what represents N? S*T+V
UTD GMAT Prep Course
Gawel & Langford
Arithmetic - page 49 