GMAT Practice Set 6 - Quant

1. 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

2. A particular chainsaw requires a premixed combination of gasoline and oil in a 4 to 1 ratio. The chainsaw's default mixing recipe produces enough mix for two chainsaws. If the default mixing recipe were changed to yield enough mix for three chainsaws, how many quarts of oil would be needed? (1) 12 quarts of gas would be needed if the mixing recipe was changed to yield enough mix for four chainsaws. (2) 6 quarts of gas are used in the default mixing recipe. 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.

3. For the positive integers q, r, s, and t, the remainder when q is divided by r is 7 and the remainder when s is divided by t is 3. All of the following are possible values for the product rt EXCEPT A. 32 B. 38 C. 44 D. 52 E. 63

4. 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

5. If m and n are positive integers, each of the following could be equivalent to A.

EXCEPT

.

B.

.

C.

.

D.

.

E.

.

6. Is the positive integer z a prime number? (1) z and the square root of integer y have the same number of unique prime factors. (2) z and the perfect square y have the same number of unique factors. 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.

7. 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

8. Chris tosses all his spare change into a jar on his refrigerator. Once the jar is full, Chris counts out the coins and finds that he has only pennies, nickels, and dimes in the exact ratio of 1:4:8. How many nickels does he have? (1) There are exactly 650 coins in the jar. (2) The ratio of dimes to pennies is 8:1. 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.

9. In the diagram above, perpendicular to

. If

is a right angle, and has a length of 25 and

length of 4, what is the area of A. 125 B. 145 C. 240 D. 290 E. It cannot be determined

?

is has a

10. A chair store sold a certain chair to a collector for 40%more than the store had originally paid for the chair. When the collector tried to resell the chair to the store, the store bought it back at 60%of what the collector had paid. The shop then sold the chair again at a profit of 75%on its buyback price. If the difference between the chair's original cost to the shop and the amount the collector got from reselling it back to the shop is $176, for how much did the shop sell the chair the second time? A. $1,243 B. $1,439 C. $1,617 D. $1,851 E. $2,025

11. 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

12.

A. 1 B. 2 C. 3.01 D. 4 E. 6.02

13. Is Jill taller than Jack? (1) When Jill stands on her 5-inch pail, she is 3 inches taller than Jack. (2) Jill is 5 feet 4 inches tall. 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. Ms. Crabtree brought 30 identical pieces of candy to pass out to her kindergarten class. Every student will get the same number of pieces of candy, with no candy left over. Assuming that each piece of candy cannot be divided, how many pieces will each student receive? (1) If her class size were to double, Ms. Crabtree would not have enough candy for each student. (2) If half the class were absent, each student would receive two times as much candy. 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.

15. 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.

16. The ""length of integer x"" refers to the number of prime factors, not necessarily distinct, that x has. (If x = 60, the length of x would be 4 because 60 = 2 2 3 5.) What is the greatest possible length of integer z if z 1,080? A. 13 B. 10 C. 9 D. 7 E. 6

17. On average, Machine A will produce a completed item once every three minutes, and Machine B will produce a completed item once every seven minutes. The number of items Machine A produces in a 24-hour period is approximately what percent greater than the number of items Machine B would produce in that same period? A. 125% B. 133% C. 150% D. 166% E. 233%

18. Which of the following equations does not have at least one solution? A. (-3)-x = -3-x B. (-3)x = (-3)-x C. (-3)- x = -3x D. 3-x = (-3)x E. 3x = (-3)-x

19. 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.

20. The Smith horse farm has appaloosa, chestnut, and palomino horses. The appaloosa to chestnut ratio is 1:4 and the chestnut to palomino ratio is 1:2. The Windsor horse farm has appaloosa and chestnut horses in the ratio of 1:5. Together, the two farms have 45 chestnut horses. How many appaloosa horses does the Smith farm have? A. 5 B. 7 C. 8 D. 9 E. 11

21. All the paralegals at the Zindler law firm support either the family law attorneys, the estate planning attorneys, or both the family law and estate planning attorneys. Seventy percent of the paralegals work in only one area of practice, and 121 paralegals work in family law only. If 55 percent of the paralegals are in family law only, how many work in estate planning only? A. 26 B. 30 C. 33 D. 55 E. 79

22. 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.

23. The population of bacteria in a research lab doubles every 90 minutes. If 3 hours ago there were 2,000 bacteria in a petri dish, in approximately how many minutes will the population exceed 500,000 bacteria? A. 180 B. 270 C. 360 D. 450 E. 540

24. Which of the following must be true if the square root of X is a positive integer? I. X has an even number of distinct factors. II. X has an odd number of distinct factors. III. The sum of X's distinct factors is odd. A. I only B. II only C. I and III D. II and III E. I, II, and III

25. 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%

26. A new sales clerk in a department store has been assigned to mark sale items with red tags, and she has marked 30% of the store items for sale. However, 20% of the items that are supposed to be marked with their regular prices are now marked for sale, and 55% of the items that are supposed to be marked for sale are marked with regular prices. What percent of the items that are marked for sale are supposed to be marked with regular prices? A. 30% B. 35% C. 40% D. 45% E. 50%

27. 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.

28. Is the Skipper older than the Professor? (1) The Skipper is older than Ginger, who is older than Gilligan. (2) Gilligan is younger than the Professor. 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.

29. A 10-member student leadership committee consists of juniors and

seniors. Exactly 6 students will be selected

from this group to attend a national convention. What is the probability that at least 3 seniors are selected for the committee?

A.

B.

C.

D.

E.

30. Farmer Mack's ranch is currently home to 200 bunnies, whose population increases at a constant monthly rate. How many months will it take for the population of bunnies to double? (1) If the number of bunnies were to grow at twice the current rate, there would be 675 bunnies on the farm in three months. (2) Four months from now, there will be more than four times the current number of bunnies on the farm. 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. In which quadrant of the coordinate plane does the point (a, b) lie? (1) - a

-b

|b|

(2) |ab| + a|b| + |a|b + ab

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.

32. 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

33. If the sum of the digits of the positive two-digit number a is 3, what is the value of a ? (1) Triple the value of a is less than 66. (2) a 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.

34. If v, w, x, y, and z are non-negative integers, and a = 3w2v and b = 5z3y2x, is

a terminating decimal?

Note: A terminating decimal is any number that has only a finite number of nonzero digits (i.e. 45, 0.64, and 2.001 are terminating decimals). (1) w

y

(2) v

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.

35. A certain investment grows at an annual interest rate of 16%, compounded quarterly. Which of the following equations can be solved to find the number of years, x, that it would take for the investment to increase by a factor of 81? 4

A. 81 = 1.16 x B. 81 = 1.04x C. 3 = 1.16x 4

D. 3 = 1.04 x E.

3 = 1.04

x

36. Roger, Babe, and Will have hit a combined total of 256 home runs. How many home runs did Babe hit? (1) Roger, Babe, and Will hit home runs in the ratio of 1:5:10, respectively. (2) Will hit 80 more home runs than Babe. 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.