GMAT Practice Set 3 - 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. On a certain farm, the onion and the pumpkin patch were each to receive x gallons of water for irrigation. The onion patch was 50 acres, and the pumpkin patch was 60 acres. Once it came time to deliver the water, the farmer decided to transfer y gallons of water from the onion patch to the pumpkin patch so that each would receive the same amount of water per acre. Which of the following is equivalent to y ? A. B. C. D. E.

3. If z is a positive integer, is the remainder of z divided by 10 equal to 4? (1) z is a multiple of 2. (2) The remainder when z is divided by 5 is 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.

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. For the positive integers s and t, 4s + 2t + 17 Is s a prime number? (1) s

t is a prime number

(2) s

t is an odd integer

5s + 2t + 14.

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, y, and z are integers, is x -y odd? 2

(1) x = z - 4y + 4 2

(2) y = z - 2z + 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.

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 is a two-digit prime number whose digits are the reverse of the two-digit prime number y, what is the value of x? (1) x - y = 54 (2) x + y = 88 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

9. If the function g(x) is defined by the equation g(x) = ax - 3x -b, where a and b are constants, g(5) = 0, and g(-2) = 0, then ab = A. -10 B. 10 C. 15 D. 100 E. It cannot be determined from the information given.

3

10. If *n* = xn + n(y + 2) - 2, where x and y are constants, and *3* = 4, what is the value of *-3* ? A. -12 B. -8 C. 0 D. 6 E. It cannot be determined from the information given.

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

2 2

2

12. If ab = 20 -a b , where both a and b are negative, then a = A. B. C. D. E.

13. What is the value of a + b if a, b, and c are integers? (1) 3a5b = 225 4

c

c

(2) 9a5 -2b = 15

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 x and y are positive integers, does x-y = 0? (1) (z2)x = z2

y

2

(2) z = 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.

15. If x and y are integers and x + y following MUST be true? I. x

0

II. y

0

III. xy

0

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

x -y, which of the

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. Set S is defined by the following sequence: S0 = 4, S1 = 4, and Sn = Sn - 1 + 4 for all n

1.

What is the sum of the subset {S15, S16… S27}? A. 984 B. 1,024 C. 1,075 D. 1,092 E. 1,204

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.

4

4

19. If the sum of the squares of x and y is 3, and x = y + 25, 2

what is the value of x ? A. B. C. D. E.

20. If 4

10-3z 6z+10

8

A. 10 B. 5 C. 1 D. -5 E. -10

-3z

2z

100 500 = 1, what is the value of z?

2

21. The number 100 has how many factors? A. 28 B. 25 C. 24 D. 20 E. 16

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. Jim takes a seconds to swim c meters at a constant rate from point P to point Q in a pool. Roger, who is faster than Jim, can swim the same distance in b seconds at a constant rate. If Jim leaves point P the same time that Roger leaves point Q, how many fewer meters will Jim have swum than Roger when the two swimmers pass each other? A. B. C. D. E.

24. Attorneys are questioning 11 potential jurors about their ability to serve on a jury and decide a case fairly. Seven individuals will be selected to serve on the jury. If each potential juror has an equal chance of being selected, what is the probability that Tamara and Inga are chosen for the jury?

A.

B.

C.

D.

E.

25. If x and y are integers, is xy (1) x

0?

0

(2) y = x3 - x2 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 cake bakery sells white cakes, lemon cakes, and combination cakes that have one white layer and one lemon layer. Combination cakes currently comprise 20% of the bakery's inventory. The number of white cakes plus the number of combination cakes totals 98. If half of all the cakes are white cakes, how many of the cakes are lemon cakes? A. 12 B. 22 C. 30 D. 42 E. 48

28. If x, y, and z are all positive integers, what is the remainder when 7xyz is divided by 4? (1) yz = 3 (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.

29. The ratio of men to women in the Snyder community choir is 4 to 5. The ratio of men to women in the Leigh community choir is 5 to 6. If the two choirs merged, the ratio of men to women in the combined choir would be 22 to 27. If Snyder has 4 more men and 6 more women than Leigh, how many women are in the Snyder choir? A. 20 B. 24 C. 30 D. 32 E. 34

30. If the function g is such that g(x) = g(x- 1) -x + 2 and g(2) = 2, what is the value of g(5)? A. 1 B. 0 C. -1 D. -2 E. -4

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. If y is the average of x odd consecutive integers and , which of the following MUST be true? I. xy(z + 1) is even. II. x(z + y) is even. III. (x2 - x)yz is even. A. I only B. III only C. I and II D. II and III E. I, II, and III

33. If x and y are positive integers, is 4x- 7y (1) 16x (2) x

+1

0?

49y

y

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. Is x (1) x - y

0? -8

(2) x + y = -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.

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

x

36. If x is an integer and 5 x+1

(1) 5

x+1

(2) 5

1,000, what is the value of x?

500 -5

x

1,000

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.