GMAT Practice Set 10 - Quantitative

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. If x is a positive integer and z = x! + (x + 2), is z prime? (1) x is odd. (2) 2

x

12

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. What was Joanne's average speed during her 4-hour run from Arlington to Burlington and back, if she did not stop to rest in Burlington? (1) It took Joanne 1.5 hours to reach Burlington. (2) The distance from Arlington to Burlington is 12 miles. 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. Which of the following must be true if integer and x, y, and z are all integers? I. z is odd. II.

0

III. xy

0

A. I only B. II only C. III only D. II and III E. I, II, and III

Explanation:

is a negative odd

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 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

7. Which of the following fractions has the greatest value?

A.

B.

C.

D.

E.

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

EXCEPT

.

B.

.

C.

.

D.

.

E.

.

9. If x

0, is xy

1?

(1) y = 0 (2) 0

x

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.

10. In a club baseball league, the number of coaches and players totals 240 and the ratio of players to coaches is 15 to 1. Each player is categorized under one of six levels. Level one players make up

of the total players, and levels five and six

account for

of the remainder. If levels two and three players

account for

of the total players, then the number of players

in level four is how many greater or fewer than the number of players in level one? A. 15 greater B. 18 greater C. 12 fewer D. 15 fewer E. 18 fewer

11. 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

12. Bobby has a bowl of marbles that contains 7 blue marbles, 5 red marbles, and 4 white marbles. If the first marble selected is not put back in the bowl, what is the probability of picking either a red marble twice in a row or a white marble twice in a row?

A.

B.

C.

D.

E.

13. Nine positive integers are contained in Set N. The median of Set N is the integer x, and all the values in Set N are 3x or smaller. What is the largest possible average (arithmetic mean) of set N? A. x B.

C.

D. E. 3x

14. 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.

15. Bruce and Anne can clean their house in 4 hours working together at their respective constant rates. If Anne's speed were doubled, they could clean their house in 3 hours working at their respective rates. How many hours does it currently take Anne to clean the house on her own? A. 6 B. 7 C. 8 D. 12 E. 14

16. A college student is studying a population of fungi for his senior thesis. The population of fungi grows at a constant rate, and at 4 p.m., he places 3,000 fungi in a petri dish. Although he is supposed to check the population at every hour, he falls asleep and does not wake up until 8 p.m., at which point the fungi population is 243,000. What was the fungi population at 7 p.m.? A. 24,000 B. 27,000 C. 60,000 D. 81,000 E. 90,000

17. 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.

18. In a set of positive integers {j, k, l, m, n, o}, in which j l m n o, is the mean larger than the median?

k

(1) The sum of n and o is more than twice the sum of j and k. (2) The sum of k and o is

the sum of l and m.

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.

19.

In the figure above, A, B, and C are all points on the circle. What is the area of triangle ABC ? (1) The circumference of the circle is 18 . (2)

o

measures 30 .

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.

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

21. 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

22. 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

23. What is the minimum value of the function g(y)? 2

(1) g(y) = (y - 6)

3

(2) g(8) = 64 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.

24. 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%

25. Jacob's farm utilizes a water pump that runs exactly 12 hours a day to irrigate crops. How much water can he pump to the fields in a third of a day? (1) Jacob's pump can provide 750 gallons of water in 30 hours. (2) Jacob's pump can provide 600 gallons of water in one day. 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. 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.

27. Fifteen hungry police officers are taking a break and will share a certain number of jelly, frosted, and sprinkled donuts. If no police officer can have more than 1 donut, and if no donut can be broken into pieces, how many different ways can the donuts be divided up among the hungry cops? (1) There is an equal number of each type of donut. (2) There are 4 jelly donuts. 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. A jury pool consists of 6 men and w women. If 2 jurors are selected from the pool at random, is the probability that 2 men will be selected higher than the probability that 1 man and 1 woman will be selected? (1) w

3

(2) w

6

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. 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

30. Working alone at a constant rate, Alan can paint a house in a hours. Working alone at a constant rate, Bob can paint of the same house in b hours. Working together, Alan and Bob can paint

of the house in c hours. What is the value of b in

terms of a and c?

A.

B.

C.

D.

E.

31. A certain drum is filled to one quarter of its capacity with a mixture consisting of water and oil. The proportion of oil in the drum is 50% by volume, and the capacity of the drum is 48 gallons. If the water evaporates from the drum at the rate of 1 gallon per hour and the amount of oil stays the same, what will be the concentration of water in the mixture in 2 hours? A. 32% B. 40% C. 48% D. 56% E. 64%

32. 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.

33. A cylinder has a base with a circumference of 20 meters and an equilateral triangle inscribed on the interior side of the base. A marker is dropped into the tank with an equal probability of landing on any point on the base. If the probability of the marker landing inside the triangle is length of a side of the triangle? A. B. C. D. E. 20

, what is the

34. 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

35. 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.

2 3 4

36. 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.