GMAT Practice Set 4 - Quant

1. 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.

2. Angela begins walking at 4 mph around a circular track with a radius of 8 miles. Exactly 5 hours later, Matt leaves from the same point in the opposite direction jogging at 6 mph. For how many hours will Angela have been walking when Matt has passed and moved 10 miles beyond her? A. 1.6 - 1 B. 1.6

+4

C. 2 - 1 D. 2.6 - 2 E. 3.6 - 2

3. Does n = 1? (1) |n| = 4n - 6 (2) |n|

4n

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. 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

5. If z is a positive integer, is z + 1 a factor of 105? (1) z is a factor of 20. (2) 10 is a factor of z. 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 X and Y are single-digit positive integers, is X + Y a multiple of 6? (1) X + 4Y is an even integer. (2) If Y and X were combined into a two-digit number, YX, with Y as the tens digit and X as the units digit, then YX would be 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.

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. 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.

9. If a cylindrical tank were filled with water at a rate of 20 cubic feet per hour, the level of water in the tank would rise at a rate of 2 feet per hour. Which of the following best approximates the radius of the tank, in feet? A. 2 B. 3 C. 4 D. 5 E. 6

10. Pastry chef Pierre takes x hours to decorate a wedding cake. Pastry chef Francois takes y hours to decorate the same wedding cake. If Pierre works alone for z hours and is then joined by Francois until 20 cakes are decorated, for how long did the two pastry chefs work together?

A.

B.

C.

D.

E.

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. In triangle XYZ, if XZ = 5 and YZ = 9, XY could equal which of the following? I. 13 II. III. 4 A. I only B. II only C. I and II D. III only E. I, II, and III

13. Is

(1)

?

of 9 is less than the value of q.

(2) Two times the value of q is greater than

.

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. Fifty percent of all the students attending a school on a certain day arrived by 7:00 AM. How many students arrived by 7:00 AM on that day? (1) Fifteen students arrived between 7:00 AM and 8:00 AM, and

of that day's total attending students arrived by 8:00

AM. (2) Ten students arrived after 8:00 AM that 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.

15. If x and y are positive integers, each of the following could be the greatest common divisor of 30x and 15y EXCEPT A. 30x. B. 15y. C. 15(x + y). D. 15(x-y). E. 15,000.

16. 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.

17. At a certain resort, each of the 39 food service employees is trained to work in a minimum of 1 restaurant and a maximum of 3 restaurants. The 3 restaurants are the family buffet, the dining room, and the snack bar. Exactly 19 employees are trained to work in the family buffet, 18 are trained to work in the dining room, and 12 are trained to work in the snack bar. If 4 employees are trained to work in exactly 2 restaurants, how many employees are trained to work in all 3 restaurants? A. 2 B. 3 C. 4 D. 5 E. 6

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. Two sisters, Caryn and Missy, are each given an allowance by their parents in exchange for helping with household tasks. Caryn receives twice the hourly allowance that Missy receives, but Missy receives three times her hourly allowance for any hours she spends helping with laundry on Sundays. If both girls worked a whole number of hours this week and received the same dollar amount of allowance, which of the following must be true? I. Missy made more money on Sunday than did Caryn. II. Caryn worked fewer hours Monday through Thursday than did Missy. III. Missy worked at least one hour on Sunday. A. I only B. II only C. III only D. I and II only E. I and III only

20. Three is the largest number that can be divided evenly into 27 and the positive integer x, while 10 is the largest number that can be divided evenly into both 100 and x. Which of the following is the largest possible number that could be divided into x and 2,100? A. 30 B. 70 C. 210 D. 300 E. 700

21. How many consecutive zeros will appear at the end of 43! if that number is expanded out to its final result? A. 12 B. 11 C. 10 D. 9 E. 8

22. 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%

23. If x is y percent of 4z, where y of z, y is what percent of x ? A. 4z B. 25z C. D. E.

0 and z

0, then, in terms

24. The 39 parents participating in the Smithville PTA have been assigned to at least 1 of 3 committees: festival planning, classroom aid, and teacher relations. 21 parents are assigned to the festival planning committee, 18 parents are assigned to the classroom aid committee, and 19 parents are assigned to the teacher relations committee. If 5 parents are assigned to all 3 committees, how many parents are assigned to exactly 2 committees? A. 4 B. 6 C. 8 D. 9 E. 10

25. 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.

26. 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.

27. A group of 5 friends-Archie, Betty, Jerry, Moose, and Veronica-arrived at the movie theater to see a movie. Because they arrived late, their only seating option consists of 3 middle seats in the front row, an aisle seat in the front row, and an adjoining seat in the third row. If Archie, Jerry, or Moose must sit in the aisle seat while Betty and Veronica refuse to sit next to each other, how many possible seating arrangements are there? A. 32 B. 36 C. 48 D. 72 E. 120

28. St. Francis's gym coach is planning a kickball tournament for the 40 students in the fourth grade. How many teams are there if the coach wants to evenly divide the students to make sure there are more than 2 teams, with each team having more than 2 students? (1) If 17 fifth-graders are allowed to play in the tournament, one will have to serve as an alternate to evenly assign the fifth-graders to teams. (2) If 5 third-graders are allowed to play in the tournament, one will have to serve as an alternate to evenly assign the third-graders to teams. 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. The average (arithmetic mean) of the integers a, b, and c is 12. If the value of a is half the value of b, and the value of c is three times the value of b, what is the value of c-b ? A. 18 B. 16 C. 8 D. 4 E. 3

30.

What is the radius of the circle shown above? (1) The center of the circle is at point O. (2) The measure of minor arc PQ is 8. 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. 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

32. Bill is golfing with three friends and can either buy generic golf tees that are packaged by the dozen or the higher quality Aeroflight tees that come by the pair. What is the minimum number of Aeroflight tees Bill must purchase to ensure that he has at least 10 golf tees for each member of his foursome? A. 6 B. 4 C. 2 D. 1 E. 0

33. If x and y are integers, what is the value of

?

(1) y= (2) 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.

34. Integer s is equivalent to the sum of all the even multiples of 25 between 585 and 825, inclusive. What is the greatest prime factor of s? A. 19 B. 11 C. 7 D. 5 E. 3

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. 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.