GMAT Practice Set 5 - Quant

1. What is the average of p, q, and r? (1) p + 3q - 2r = 5 (2) 4p + 2q + 7r = -5 A. Statement (1) by itself is sufficient to answer the question, but statement (2) by itself is not. B. Statement (2) by itself is sufficient to answer the question, but statement (1) by itself is not. C. Statements (1) and (2) taken together are sufficient to answer the question, even though neither statement by itself is sufficient. D. Either statement by itself is sufficient to answer the question. E. Statements (1) and (2) taken together are not sufficient to answer the question, requiring more data pertaining to the problem.

2. At a certain automobile dealership that sells only Tajimas and Franks, the number of nonhybrid Tajimas is 35 less than 3 times the number of hybrid Tajimas. 205 total Tajimas are currently owned by the dealership. If the ratio of hybrid Tajimas to nonhybrid Franks is 5:4 and there are 280 total automobiles owned by the dealership, how many hybrid Franks are there? A. 20 B. 27 C. 48 D. 60 E. 87

3. What is the remainder when

is divided by 10?

(1) x is a multiple of 3. (2) x is a multiple of 5. A. Statement (1) by itself is sufficient to answer the question, but statement (2) by itself is not. B. Statement (2) by itself is sufficient to answer the question, but statement (1) by itself is not. C. Statements (1) and (2) taken together are sufficient to answer the question, even though neither statement by itself is sufficient. D. Either statement by itself is sufficient to answer the question. E. Statements (1) and (2) taken together are not sufficient to answer the question, requiring more data pertaining to the problem.

4.

A.

B.

C.

D.

E.

5. The sum of x consecutive positive integers is 63. What is the value of x? (1) x

11

(2) x is odd. A. Statement (1) BY ITSELF is sufficient to answer the question, but statement (2) by itself is not. B. Statement (2) BY ITSELF is sufficient to answer the question, but statement (1) by itself is not. C. Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, even though NEITHER statement BY ITSELF is sufficient. D. EITHER statement BY ITSELF is sufficient to answer the question. E. Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question, requiring more data pertaining to the problem.

6. If the sides of a triangle have lengths x, y, and z, x + y = 30, and y + z = 20, then which of the following could be the perimeter of the triangle? I. 28 II. 36 III. 42 A. I only B. II only C. I and II only D. I and III only E. I, II, and III

7. A wholesaler needs to quickly sell some hats, so he reduced the price of the hats. By what percent did he reduce the price of the hats? (1) If a case of 144 hats is purchased from the wholesaler, the savings will be $51.84 as a result of the price reduction. (2) The price of a hat was reduced by 36 cents. A. Statement (1) BY ITSELF is sufficient to answer the question, but statement (2) by itself is not. B. Statement (2) BY ITSELF is sufficient to answer the question, but statement (1) by itself is not. C. Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, even though NEITHER statement BY ITSELF is sufficient. D. EITHER statement BY ITSELF is sufficient to answer the question. E. Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question, requiring more data pertaining to the problem.

8. A sphere is inscribed in a cube with an edge length of 20. What is the shortest possible distance from one of the vertices of the cube to the surface of the sphere? A. 10 B. C. 5 D. E.

9. The value of land increases by a% during June and decreases by b% during July. If the value of the land is the same at the end of July as at the beginning of June, what is b in terms of a?

A.

B.

C.

D.

E.

10. If it is true that -6 true? A. n

n

8

B. n = -6 C. n D. -10

-8 n

7

E. none of the above

10, which of the following must be

11. If 2|2 -x| = 5, what is the sum of all the possible values for x ? A. B. 2 C. D. 4 E. 5

2 3 4

12. If r, s, t, and w are all nonzero integers, is r s t w (1) rst2 2

(2) rst w

5

0?

0 3

0

A. Statement (1) BY ITSELF is sufficient to answer the question, but statement (2) by itself is not. B. Statement (2) BY ITSELF is sufficient to answer the question, but statement (1) by itself is not. C. Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, even though NEITHER statement BY ITSELF is sufficient. D. EITHER statement BY ITSELF is sufficient to answer the question. E. Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question, requiring more data pertaining to the problem.

5

13. If m = z , is m

1?

(1) 3 - (y- x)

x- (y- 3z)

(2) z

3

A. Statement (1) BY ITSELF is sufficient to answer the question, but statement (2) by itself is not. B. Statement (2) BY ITSELF is sufficient to answer the question, but statement (1) by itself is not. C. Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, even though NEITHER statement BY ITSELF is sufficient. D. EITHER statement BY ITSELF is sufficient to answer the question. E. Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question, requiring more data pertaining to the problem.

14. If

, is z

(1) x (2) |y|

8?

4 4

A. Statement (1) by itself is sufficient to answer the question, but statement (2) by itself is not. B. Statement (2) by itself is sufficient to answer the question, but statement (1) by itself is not. C. Statements (1) and (2) taken together are sufficient to answer the question, even though neither statement by itself is sufficient. D. Either statement by itself is sufficient to answer the question. E. Statements (1) and (2) taken together are not sufficient to answer the question, requiring more data pertaining to the problem.

+1

2

15. If (10a - 10a) / 3b = 10 b where a and b are both integers, what is the value of (a + b) ? A. 1 B. 2 C. 3 D. 4 E. 6

16. In 2010, City X urban planners expected the city's population to increase by 20% per year over the three years that followed. If that projection were to come true, the population in 2012 would be exactly triple the population in 2009. Which of the following is the approximate percent population increase in City X from 2009 to 2010? A. 20% B. 45% C. 72% D. 108% E. 124%

17. Let a represent the average of b consecutive integers and c represent the sum of d consecutive integers. If each of the following could be true EXCEPT A. a

c.

B. a

c.

C.

is an integer.

D. c is an integer. E. a is an integer.

, then

18. For all positive integers s and t, s @ t represents the remainder when s is divided by t. What is the sum of all the possible values of t for which 18 @ t = 2? A. 38 B. 28 C. 16 D. 12 E. 10

19. A fruit drink advertises that it has 5 percent apple juice. Children pour themselves another

cup of this fruit drink and then add

cup of fruit drink that has 50 percent apple juice.

Which is most nearly the percent of apple juice in the children's mixed drink? A. 12.5% B. 16.3% C. 17.5% D. 55.0% E. 65.0%

20. Pam and Cathy begin running at the same time on a straight path. Pam runs at 10 miles per hour, and Cathy runs at 8 miles per hour. After 45 minutes, Pam stops to stretch. If it takes Pam 30 minutes to stretch and Cathy continues to run during this time, how many minutes will it take Pam to catch up to Cathy assuming Pam resumes running at 10 miles per hour? A. 30 minutes B. 40 minutes C. 45 minutes D. 60 minutes E. 75 minutes

21. A jazz ensemble is holding auditions for new musicians. 11 musicians are auditioning, and 6 will be chosen for the ensemble. If 7 of the musicians are saxophone players and 4 of the musicians are clarinet players, how many different groups of 4 saxophone players and 2 clarinet players can be selected? A. 66 B. 192 C. 210 D. 420 E. 462

2

22. Is x

x - |y|?

(1) y

x

(2) x

0

A. Statement (1) BY ITSELF is sufficient to answer the question, but statement (2) by itself is not. B. Statement (2) BY ITSELF is sufficient to answer the question, but statement (1) by itself is not. C. Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, even though NEITHER statement BY ITSELF is sufficient. D. EITHER statement BY ITSELF is sufficient to answer the question. E. Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question, requiring more data pertaining to the problem.

23. A bakery currently has 5 pies and 6 cakes in its inventory. The bakery's owner has decided to display 5 of these items in the bakery's front window. If the items are randomly selected, what is the probability that the display will have exactly 3 pies?

A.

B.

C.

D.

E.

24. Is q divisible by 6? (1) 5q is divisible by 10. (2) 3 is a factor of q + 3. A. Statement (1) BY ITSELF is sufficient to answer the question, but statement (2) by itself is not. B. Statement (2) BY ITSELF is sufficient to answer the question, but statement (1) by itself is not. C. Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, even though NEITHER statement BY ITSELF is sufficient. D. EITHER statement BY ITSELF is sufficient to answer the question. E. Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question, requiring more data pertaining to the problem.

25. The circular base of a planter sits on a level lawn, and just touches two straight garden walls at points W and Y. The walls come together at point X, which is 15 inches from the center of the planter. What is the area of the base of the planter? (1) Both points Y and W are 9 inches from the center of the planter. (2) Point W is 12 inches from point X. A. Statement (1) by itself is sufficient to answer the question, but statement (2) by itself is not. B. Statement (2) by itself is sufficient to answer the question, but statement (1) by itself is not. C. Statements (1) and (2) taken together are sufficient to answer the question, even though neither statement by itself is sufficient. D. Either statement by itself is sufficient to answer the question. E. Statements (1) and (2) taken together are not sufficient to answer the question, requiring more data pertaining to the problem.

26. Mike just filled his truck's gas tank with 20 gallons of a mixture consisting of 10% additive and 90% gasoline. If his truck runs best on a mixture consisting of 20% additive and 80% gasoline, how many gallons of additive must he add into the gas tank for his truck to achieve optimum performance? A. 1.0 B. 1.5 C. 2.0 D. 2.5 E. 3.0

27. In the rectangular coordinate system, lines m and n cross at the origin. Is line m perpendicular to line n ? (1) If the slope of m is y and the slope of n is z, then -yz = 1. (2) m has a slope of -1, and n passes through the point (-x, -x). A. Statement (1) BY ITSELF is sufficient to answer the question, but statement (2) by itself is not. B. Statement (2) BY ITSELF is sufficient to answer the question, but statement (1) by itself is not. C. Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, even though NEITHER statement BY ITSELF is sufficient. D. EITHER statement BY ITSELF is sufficient to answer the question. E. Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question, requiring more data pertaining to the problem.

28. If the Board of Selectmen contains 4 positions, and if in the current election two candidates are running for each position, how many different combinations of candidates could be elected to the Board? A. 6 B. 8 C. 12 D. 16 E. 24

2

29. For all values of the integer x, is the product (x + 3)(x + 3x + 2) divisible by 4?

(1)

is an odd integer

(2) x is divisible by 16 A. Statement (1) BY ITSELF is sufficient to answer the question, but statement (2) by itself is not. B. Statement (2) BY ITSELF is sufficient to answer the question, but statement (1) by itself is not. C. Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, even though NEITHER statement BY ITSELF is sufficient. D. EITHER statement BY ITSELF is sufficient to answer the question. E. Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question, requiring more data pertaining to the problem.

30. If both x and y are positive integers that are divisible by 10, is 10 the greatest common factor of x and y? (1) x = 4y (2) x - 3y = 10 A. Statement (1) BY ITSELF is sufficient to answer the question, but statement (2) by itself is not. B. Statement (2) BY ITSELF is sufficient to answer the question, but statement (1) by itself is not. C. Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, even though NEITHER statement BY ITSELF is sufficient. D. EITHER statement BY ITSELF is sufficient to answer the question. E. Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question, requiring more data pertaining to the problem.

31.

is equivalent to

A. B. C. D. E.

32. All but 50 of the 1,000 plants at the annual flower show were sold. Of the plants sold, 30 percent were sold at a discount of 25 percent off the full price, and the remaining plants were sold at the full price of $12. What was the total revenue from the plant sales? A. $8,550 B. $8,835 C. $10,545 D. $11,100 E. $12,000

33. The total cost of manufacturing item A is equal to the sum of item A's fixed cost and variable cost. In January, the company was able to lower both costs due to improvements in its production process. If the variable cost of manufacturing A decreased by 5% in January, by what percent did the total cost of manufacturing item A change in January? (1) Before the changes in January, the fixed cost of manufacturing item A was five times the variable cost of manufacturing item A. (2) The fixed cost of manufacturing item A increased by 13% in January. A. Statement (1) BY ITSELF is sufficient to answer the question, but statement (2) by itself is not. B. Statement (2) BY ITSELF is sufficient to answer the question, but statement (1) by itself is not. C. Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, even though NEITHER statement BY ITSELF is sufficient. D. EITHER statement BY ITSELF is sufficient to answer the question. E. Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question, requiring more data pertaining to the problem.

2

34. If x and y are positive integers such that (2x)(5 y) = 2,500, 1

what is the value of (5y - )x ? A. 10 B. 25 C. 50 D. 500 E. 15,625

35. If two sides of a triangle are 12 and 8, which of the following could be the area of the triangle? I. 35 II. 48 III. 56 A. I only B. I and II only C. I and III only D. II and III only E. I, II, and III

36. Is x

10

10 ? 22

(1) x = 3 (2) x

3

20

A. Statement (1) BY ITSELF is sufficient to answer the question, but statement (2) by itself is not. B. Statement (2) BY ITSELF is sufficient to answer the question, but statement (1) by itself is not. C. Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, even though NEITHER statement BY ITSELF is sufficient. D. EITHER statement BY ITSELF is sufficient to answer the question. E. Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question, requiring more data pertaining to the problem.