GMAT Practice Set 8 - Quantitative

1. If z = 25x125y, what is the value of z ? (1) y = 2 (2) 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. If n is an integer and

, which of the 2

following could be the value of (n + 3) ? A. -2 B. 1 C. 4 D. 11 E. 64

3. 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.

4. 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

5. On the Lamville Llamas baseball team last year, what was the average (arithmetic mean) number of home runs hit per player? (1) Last July, home runs from the top 4 players accounted for 80% of the team's homeruns, and the number of home runs for these players was 48 per person. (2) Last year, the Lamville Llamas had 20 players and hit a total of 240 home runs. 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.

Does line P (not pictured) intersect line segment QR in the coordinate plane shown above? (1) The slope of line P is -1. (2) The equation of line P is y = -x + 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.

7. 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

8. During winter break, Johnny sells 3 types of waffles at the ski resort: plain, strawberry, and banana. Last week, the ratio of plain to strawberry to banana waffles Johnny sold was 24:6:5. How many waffles did Johnny sell last week? (1) Johnny sold 624 strawberry waffles. (2) Johnny sold 4 times as many plain waffles as strawberry waffles. 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. Is a% of a% of b equal to a% less than b? (1) b(b + 1) = 1 (2) a(a + 100) = 10,000 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. The ACME company manufactured x brooms per month from January to April, inclusive. At the beginning of production on January 1, ACME had no brooms in its inventory. On the first of each month, during the following May to December, inclusive, it sold

brooms. If storage costs were $1 per month

per broom, approximately how much, in terms of x, did the ACME company pay for storage from May 2 to December 31, inclusive? A. $x B. $3x C. $4x D. $5x E. $14x

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. Which of the following, when squared, will yield a value greater than

A. B. C.

D.

E.

2 (.75)

?

13. At the Butterfly Scout Cookie Chow Down, each girl was given equal time to decorate as many cookies as possible. If the winner took an average of 20 seconds to decorate each cookie, how many cookies did the second-place finisher decorate? (1) The second-place finisher was only able to decorate at half the rate of the winner. (2) The winner decorated 15 more cookies than the secondplace finisher. 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. Bill owns a large collection of fishing lures consisting of tiny, small, medium, and large lures that weigh 1, 3, w, and 5 grams each, respectively. The medium lures weigh more than the small lures but less than the large lures. If the product of the lure weights that Bill sold to his friend is 216,000 grams, how many medium lures did he sell? A. 6 B. 5 C. 4 D. 3 E. 2

15. Bobby walks 4 miles to school and then walks back home again along the same route every day at a constant rate of 3 miles per hour. However, on the last day of school, Bobby walks to school at his usual rate but then sprints back home at a constant rate of 6 miles per hour. On his last day of school, what is Bobby's average speed for the entire trip in miles per minute?

A.

B.

C.

D.

E.

16. 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.

17. Jim has arrived late for his golf tee time with his friends. When he arrives at the course, he discovers that his friends have already walked 180 yards ahead on the course and that they are continuing to walk forward at a rate of 1.5 yards per second. A bystander with a golf cart takes pity on Jim and drives him to meet his friends at the rate of 4 yards per second. Once Jim meets his friends, he exits the cart and walks with them at their rate for the next 120 yards. What is Jim's approximate average speed for his total trip? A. 1.8 yards per second B. 2.0 yards per second C. 2.4 yards per second D. 2.7 yards per second E. 3.0 yards per second

18. 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.

19. What is the units digit of z if (385a)(225b) = z, where a and b are positive integers? (1) a = 3 (2) a + b = 11 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. 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

21. A set of numbers contains 7 integers and has an average (arithmetic mean) value as well as a median value of 23. If the largest value is equal to 15 more than 4 times the smallest number, what is the largest possible range for the numbers in the set? A. 33 B. 35 C. 38 D. 48 E. 75

22. 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

23. 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.

24. Dan and Craig stand back-to-back at point X. Dan begins to rollerblade in a straight line away from Craig at a rate of 4 miles per hour. Thirty minutes later, Craig begins to bicycle in a straight line in the exact opposite direction at a rate of 12 miles per hour. What is the positive difference, in hours, between the amount of time it takes Craig to cover the exact distance that Dan has covered and the amount of time it would take Craig to cover 50% more distance than Dan has covered? Round your answer to the nearest hundredth. A. .08 B. .16 C. .25 D. .50 E. .75

31 a4 +1b 90 25. In the correctly solved problem above, a and b are digits of their respective numbers. What is the value of the two-digit integer ba, where b is the tens digit and a is the units digit? A. 20 B. 45 C. 54 D. 64 E. 71

26. 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

27. 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

28. What was the total distance that Bill drove from Mount Pleasant to Springfield through Hollyberry? (1) The entire trip took Bill exactly four hours. (2) The segment from Mount Pleasant to Hollyberry took Bill two hours to complete at an average speed of 50 miles per hour. 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 certain language club has an equal number of native English and Spanish speakers. On a certain day,

of the

members were absent from the club meeting. Of the members there that day,

were native Spanish speakers. What is the

ratio of the number of native English speakers who were not at the meeting to the number of native Spanish speakers who were not at the meeting?

A.

B.

C.

D.

E.

30. 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%

31. If x- 1 is a positive integer, is x- 1 divisible by 3? 2

(1) (x + x)(x + 1) is divisible by 3. 2

(2) x(x -x) is divisible by 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.

32. 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.

33. Several students are studying together for an exam. 60% of the students who studied less than 10 hours a week feel unprepared. 80% of students who studied 10 hours or more each week feel prepared. If 75% of the students studied less than 10 hours per week, what percent of the students feel prepared for the exam? A. 20 B. 25 C. 30 D. 35 E. 65

34. 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

35. If x and y are integers, is

(1) x - y 2

(2) x y

2

?

0 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.

36. Jason is doing his weekend chores so he can collect his allowance. He needs to clean his room, mow the lawn, and put his clothes in the dryer after the washer finishes. If the washer is currently running and has 30 minutes remaining in its cycle, can Jason complete all the tasks before his mom comes home in exactly one hour? (1) Putting away the dishes will take Jason 33 minutes. (2) Cleaning his room and mowing the lawn will take Jason 20 minutes. 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.