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Sat Math Difficult Questions

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Submitted By andrea8764
Words 3107
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x^2 表示 x 的平方,=!表示不等于。pi 表示圆周率 类型 1:
20. The least integer of a set of consecutive integers is -25. If the sum of these integers is 26, how many integers are in this set?
(A) 25
(B) 26
(C) 50
(D) 51
(E) 52 14. Exactly 4 actors try out for the 4 parts in a play. If each actor can perform any one part and no one will perform more than one part, how many different assignments of actors are possible? 16. Set X has x members and set Y has y members. Set Z consists of all members that are in either set
X or set Y with the exception of the k common members (k > 0). Which of the following represents the number of members in set Z ?
(A) x + y + k
(B) x + y - k
(C) x + y + 2k
(D) x + y - 2k
(E) 2x + 2y - 2k

20. There are 75 more women than men enrolled in Linden College. If there are n men enrolled, then, in terms of n, what percent of those enrolled are men?

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17. A merchant sells three types of clocks that chime as indicated by the check marks in the table above.
What is the total number of chimes of the inventory of clocks in the 90-minute period from 7:15 to
8:45 ?

18. If the 5 cards shown above are placed in a row so

is never at eithe end, how many different

arrangements are possible?

20. When 15 is divided by the positive integer k, the remainder is 3. For how many different values of k is this true?
(A) One
(B) Two
(C) Three
(D) Four
(E) Five

17. On the number line above, there are 9 equal intervals between 0 and 1. What is the value of x ? 19. If a, b. c, and f are four nonzero numbers, then all of the following proportions are equivalent
EXCEPT
(A) a/f=b/c
(B)f/c=b/a
(C) c/a=f/b
(D)a/c=b/f
(E)af/bc=1/1

8. If a and b are positive integers and

what is the value of ab ?

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(A) 6
(B) 12
(C) 18
(D) 24
(E) 36

16. After the first term, each term in a sequence is3 greater than 1/3 of the preceding term. If t is the first term of the sequence and t=!0. what is the ratio of the second term to the first term?

15. The Acme Plumbing Company will send a team of 3 plumbers to work on a certain job. The company has 4 experienced plumbers and 4 trainees. If a team consists of 1 experienced plumber and 2 trainees, how many different such teams are possible?
17.If p. r. and s are three different prime numbers greater than 2, and n = p * r * s, how many positive factors, including 1 and n. does n have?
18. If the sum of the consecutive integers from -22 to x, inclusive, is 72, what is the value of x?
(A) 23
(B) 25
(C) 50
(D) 75
(E) 94

17. For all positive integers j and k. let j \R\ k be defined as the whole number remainder when j is divided by k. If 13 \R\k = 2, what is the value of k ? 19, In a set of eleven different numbers, which of the following CANNOT affect the value of the median? (A) Doubling each number
(B) Increasing each number by 10
(C) Increasing the smallest number only
(D) Decreasing the largest number only
(E) Increasing the largest number only 15. A store charges $28 for a certain type of sweater. This price is 40 percent more than the amount it costs the store to buy one of these sweaters. At an end-of-season sale, store employees can purchase any remaining sweaters at 30 percent off the store's cost How much would it cost an employee to
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purchase a sweater of this type at this sale?
(A) $8.40
(B) $14.00
(C)$ 19.60
(D) $20.00
(E) $25.20
17.Alice and Corinne stand back-to-back. They each take 10 steps in opposite directions away from each other and stop. Alice then turns around, walks toward Corinne. and reaches her in 17 steps. The length of one of Alice's steps is how many times the length of one of Corinne's steps? (All of Alice's steps are the same length and all of Corinne's steps are the same length.)

14. If n and p are integers greater than 1 and if p is a factor of both n +3 and n + 10. what is the value of p?
(A) 3
(B) 7
(C)10
(D) 13
(E) 30 16. In a mixture of peanuts and cashews, the ratio by weight of peanuts to cashews is 5 to 2. How many pounds of cashews will there be in 4 pounds of this mixture? 14. How many integers greater than 20 and less than 30 are each the product of exactly two different numbers, both of which are prime?
(A) Zero
(B) One
(C) Two
(D) Three
(E) Four 20. If k is a positive integer, which of the following must represent an even integer that is twice the value of an odd integer?
(A) 2k
(B) 2k + 3
(C) 2k+ 4
(D) 4k+1
(E) 4k+ 2

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类型 2:

18. The shaded region in the figure above is bounded by the x‐axis, the line x = 4, and the graph of y = f(x).If the point (a, b) lies in the shaded region, which of the following must be true?
I. a < 4 II. b < a III. b < f(a)
(A) I only
(B) III only
(C) I and II only
(D) I and III only
(E) I. II, and III 19. At a bottling company, machine A fills, a bottle with spring water and machine B accepts the bottle only if the number of fluid ounces is between 11

7
1
and 12
If machine B accepts a bottle
8
8

containing n fluid ounces, which of the following describes all possible values of n ?

7. Dwayne has a newspaper route for which he collects k dollars each day. From this amount he pays out k/3 dollars per day for the cost of the papers, and he saves the rest of the money. In terms of k, how many days will it take Dwayne to save $1,000 ?

5 / 18

17. In the xy-coordinate plane, the graph of x = y*y -4 intersects line l at (0, p) and (5, t). What is the greatest possible value of the slope of l ?
18. Esther drove to work in the morning at an average speed of 45 miles per hour. She returned home in the evening along the same route and averaged 30 miles per hour. If Esther spent a total of one hour commuting to and from work, how many miles did Esther drive to work in the morning?
14. If (a + b)^0.5 = (a - b) ^-0.5, which of the following must be true?
(A) b = 0
(B) a + b = 1
(C) a - b = 1
(D) a^2 + b^2 = 1
(E) a^2 - b^2 = 1

15. The figure above shows the graphs of y = x*x and y = a - x*x for some constant a. If the length of
PQ is equal to 6, what is the value of a ?
(A) 6
(B) 9
(C) 12
(D) 15
18. During a sale, a customer can buy one shirt for x dollars. Each additional shirt the customer buys costs z dollars less than the first shirt. For example, the cost of the second shirt is x - z dollars. Which of the following represents the customer's cost, in dollars, for n shirts bought during this sale?

6 / 18

16. Let the function h be defined by h(x) = 14 + x^2/4. If h(2m) = 9m, what is one possible value of m?
16. If x is an integer greater than 1 and if y = x + 1/x, which of the following must be true?
I. y =! x II. y is an integer. III. xy > x^2
(A) I only
(B) III only
(C) I and II only
(D) I and III only
(E) I, II, and III
6. If m and k are positive and 10(m^2)*k^-1= 100m, what is m^-1! in terms of k ?
(A) k/10
(B) k/90
(C) k^0.5/10
(D) 1/10k
(E) 1/90k

8. The figure above shows the graph of a quadratic function f that has a minimum at the point (1,1). If f(b) = f(3), which of the following could be the value of b ?
(A) -3
(B) -2
(C) -1
(D) 1
(E) 5
16. If a + 2b is equal to 125 percent of 4b, what is the value of a/b?

7 / 18

15.Doug's biology experiment involved timing 12 hamsters in a maze. Each hamster received at least one practice before being timed. The scatter plot above shows the time each hamster took to complete the maze and the corresponding number of practices that each hamster received. Based on the data, which of the following functions best models the relationship between t, the number of seconds to complete the maze, and p, the number of practices?
(A) t(p) = 44
(B) t(p) = p
(C) t(p) = 44p
(D) t(p) = p/44
(E) t(p)= p+ 44

20. For all numbers .t and v. let the operation □ be defined by x □ v = xy - y If a and b re positive integers, which of the following can be equal to zero?
I. a □b
II. (a + b) □b
IIl. a □(a + b)
(A) I only
(B) II only
(C) IIl only
(D) I and ll
(E) I and IIl

8 / 18

18. In the figure above, ABCD is a rectangle. Points A and C lie on the graph of y = p*x^3?, where p is a constant. If the area of ABCD is 4, what is the value of p?

19. If k, n, x, and y are positive numbers satisfying x ^(-4/3)= k^-2 and y^(4/3) = n^2, what is
(xy)^(-2/3 in terms of n and k ?

(A) 1
(B) 1/2
(C) 3/2
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(D) 6/5
(E) 3

8. The price of ground coffee beans is d dollars for 8 ounces and each ounce makes c cups of brewed coffee. In terms of c and d. what is the dollar cost of the ground coffee beans required to make 1 cup of brewed coffee?

15. Ifx^2-y^2 = 10 and x +y = 5. what is the value of x - y ?

18. The average (arithmetic mean) of the test scores of a class of p students is 70. and the average of the test scores of a class of n students is 92. When the scores of both classes are combined, the average score is 86.
What is the value of p/n?

10 / 18

14. Which of the following is equivalent to h(m + 1) ?
(A) g(m)
(B) g(m) + l
(C) g(m)-1
(D) h(m)+1
(E) h(m)-1
7.Ahmad has containers of two different sizes. The total capacity of 16 containers of-one size is x gallons, and the total capacity of 8 containers of the other size is also x gallons, and x > 0. In terms of x, what is the capacity, in gallons, of each of the larger containers?
(A) 4x
(B) 2x
(C)x/2
(D)x/8
(E)x/16
18. Let the function f be defined by f(x) = x^2+ 18. If m is a positive number such that f(2m) = 2f(m), what is the value of

m?

19. The cost of maintenance on an automobile increases each year by 10 percent, and Andrew paid
S300 this year for maintenance on his automobile. If the cost c for maintenance on Andrew's automobile n years from now is given by the function c(n) = 300x^n, what is the value of x ?
(A) 0.1
(B) 0.3
(C) 1.1
(D) 1.3
(E) 30 16.If xy = 7 and x- y = 5. then x^2*y-xy^2=
(A) 2
(B) 12
(C) 24
(D) 35
(E) 70

17. Line m (not shown) passes through O and intersects AB between A and B. What is one possible value of the slope of line m ?
11 / 18

17. If k and h are constants and x^2+kx+7is equivalent to(x + 1)(x + h). what is the value of k ?
(A) 0
(B) 1
(C) 7
(D) 8
(E) It cannot be determined from the information given.

(A) 1
(B) 5
(C) 24
(D) 25
(E) 26

16. To celebrate a colleague's graduation, the m coworkers in an office agreed to contribute equally to a catered lunch that costs a total of y dollars. If p of the coworkers fail to contribute, which of the following represents the additional amount, in dollars, that each of the remaining coworkers must contribute to pay for the lunch?

12 / 18

类型 3
18. In the xy-coordinate plane, the distance between point B(10, 18) and point A(x, 3) is 17. What is one possible value of x ?

16. The pattern shown above is composed of rectangles. This pattern is used repeatedly to completely cover a rectangular region 12L units long and 10L units wide. How many rectangles of dimension L by
W are needed?
(A) 30
(B) 36
(C) 100
(D) 150
(E) 180

18. In the figure above, AB = BC and DE = EF = DF If the measure of /.ABC is 30° and the measure of
/.BDE is 50°, what is the measure of /DFA ?
(A) 30°
(B) 35°
(C) 40°
(D) 45°
(E) 50°

17. The three-dimensional figure above has two parallel bases and 18 edges. Line segments are to be drawn connecting vertex V with each of the other 11 vertices in the figure. How many of these segments will not lie on an edge of the figure?
13 / 18

15. In the figure above, what is the sum. in terms of n, of the degree measures of the four angles marked with arrows?
(A) n
(B) 2n
(O 180 - n
(D) 360 - n
(E) 360 - 2n

16. The figure above consists of two circles that have the same center. If the shaded area is 64pi square inches and the smaller circle has a radius of 6 inches, what is the radius, in inches, of the larger circle?

20. The figures above show the graphs of the functions f and g. The function f is defined by f(x) = x^3 - 4x. The function g is defined by g(x) = f(x + h) + k, where h and k it are constants. What is the value of hk?
(A) -6
(B) -3
(C) -2
(D) 3
(E) 6

14 / 18

15. The cube shown above has edges of length 2, and A and 8 are midpoints of two of the edges. What is the length of AB (not shown) ?

20.In the figure above, arc SBT is one quarter of a circle with center R and radius 6. If the length plus the width of rectangle ABCR is 8. then the perimeter of the shaded region is
(A) 8 - 3pi
(B) 10+3pi
(C) 14+3pi
(D) 1 + 6pi
(E) 12+6pi

16. In rectangle ABCD, point E is the midpoint of BC. If the area of quadrilateral ABED is 2/3, what is the area of rectangle ABCD ?
(A)1/2
(B) 3/4
(C) 8/9
(D) 1
(E)8/3

8.Rectangle ABCD lies in the xy -coordinate plane so that its sides are not parallel to the axes. What is the product of the slopes of all four sides of rectangle ABCD ?
(A) -2
(B) -1
(C)0
(D) 1
(E) 2

15 / 18

16. In the figure above, y+z=?
(A)180
(B)195
(C)215
(D)230
(E)245

18. The figure above shows part of a circle whose circumference is 45. If arcs of length 2 and length b continue to alternate around the ensure circle so that there are 18 arcs of each length, what is the degree measure of each of the arcs of length b ?
(A) 4°
(B) 6°
(C) 10°
(D) 16°
(E) 20°

20. If the five line segments in the figure above are all congruent, what is the ratio of the length of AC
(not shown) to the length of BD ?
(A) 2^0.5 to 1
(B) 3^0.5 to 1
(C) 2^0.5 to 2
(D) 3^0.5 to 2
(E)3^0.5 to 2^0..5

16 / 18

15. In the figure above, EBCD is a square and AE =8 What is the area of EBCD ?

18. In the figure above, if the legs of triangle ABC are parallel to the axes, which of the following could be the lengths of the sides of triangle ABC ?
(A) 2. 5.and 29^0.5
(B) 2. 5, and 7
(C) 3,3,and3*2^0.5
(D) 3, 4, and 5
(E) 4, 5, and 41^0.5

17 / 18

类型 4:
18. If the average (arithmetic mean) of x and y is k, which of the following is the average of x, y, and z? (A)(2k+z)/3
(B) (2k+z)/2
(C) (k+z)/3
(D) (k+z)/2
(E) 2(k+z)/3
IN A PRESCHOOL CLASS
Number
of Siblings
0
1
2
3

Number of Students
3
6
2
1

8.The table above shows how many students in a class of 12 preschoolers had 0,1, 2, or 3 siblings.
Later, a new student joined the class, and the average (arithmetic mean) number of siblings per student became equal to the median number of siblings per student. How many siblings did the new student have? (A) 0
(B) 1
(C) 2
(D) 3
(E) 4

18. The table above shows student enrollment at Weston High School from 1992 through 1996. If the median enrollment for the five years was 1351, and no two years had the same enrollment what is the greatest possible value for x ?

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