GMAT Practice Set 7 - Quant

1. 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.

2. If the two-digit positive integer x is less than 99, what is the sum of the digits of x ? 3

(1) a is a two-digit odd integer. (2) x is divisible by the cube of a. 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. 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

4. 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

5. By what percentage will the virus population increase in one hour? (1) The virus population triples every 20 minutes. (2) The current population is 100,000 viruses. 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. In the rectangular coordinate system, are the points (v, w) and (x, y) equidistant from the origin?

(1)

(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.

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. In 1994, corn prices were six times wheat prices in Town X. Corn and wheat were sold in bushels. What was the ratio of Town X's total revenue from corn sales to total revenue from wheat sales in 1994? (1) Town T's price for each bushel of corn in 1994 was $500. (2) In the first half of 1994, Town X sold wheat bushels and corn bushels in the ratio of 4:1. In the second half of 1994, Town X sold corn bushels and wheat bushels in the ratio of 3:2. 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.

9. The length of arc AXB is 3 times the length of arc BZC, and the length of arc AYC is twice the length of arc AXB. What is the measure of angle BCA ? A. 18 B. 36 C. 54 D. 60 E. 108

10. 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

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 palindrome is a number that reads the same forward and backward, such as 242. How many even five-digit numbers are palindromes? A. 40 B. 400 C. 500 D. 5,000 E. 100,000

13. 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

14. 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

15. In the figure above, points A, B, C, and D are evenly 17

9

spaced. If point A equals 2 and point C equals 4 , what is the value of point D? 19

A. 2 B.

17 2 16

C. 5(2 ) 16

D. 3(2 ) E.

16 2

16. 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.

17. A.B. Cakes has two full-time cake decorators-Annie and Bonnie-to help with a wedding rush order. If Annie could complete the entire wedding order in six hours, how long would it take Annie and Bonnie working together to complete the order? (1) Annie works at a rate that is two-thirds as fast as Bonnie does. (2) Working alone, Bonnie could complete the job in four hours. 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. 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.

19. 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.

20. 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

21. 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

22. 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.

23. Randy can rebuild an automobile engine in a hours. Alvin can rebuild the same engine in b hours. If Randy and Alvin work together at their respective rates to rebuild the engine, which of the following represents the portion of the job that Randy will not have to complete?

A.

B.

C.

D.

E.

24. A dog breeder currently has 9 breeding dogs. 6 of the dogs have exactly 1 littermate, and 3 of the dogs have exactly 2 littermates. If 2 dogs are selected at random, what is the probability that both selected dogs are NOT littermates?

A.

B.

C.

D.

E.

25. 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.

26. 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

27. If the average allowance for all second-graders in School A is $2 per week, how many third-graders are there in School A? (1) The total money collected as allowance for all thirdgraders is $20 less than the total money collected as allowance for all second-graders. (2) The average allowance for third-graders is $3 per week. 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 summer camp has 25 children enrolled in its golf class, 25 children enrolled in its tennis class, and 8 children enrolled in both classes. If all the children in the summer camp are participating in at least one of the two classes, how many children are enrolled in only one of the two classes? A. 33 B. 34 C. 38 D. 40 E. 42

29. 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%

30. Three-twentieths of the members of a social club are retirees who are also bridge players, seven-twentieths of the members are retirees, and one-half of the members are bridge players. If 120 of the members are neither retirees nor bridge players, what is the total number of members in the social club? A. 240 B. 300 C. 360 D. 400 E. 480

31. Is the positive integer p a multiple of the positive integer q ?

(1)

is an integer.

(2)

is an integer.

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

, what is z ?

(1) y = 3 (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.

33. Chris started his trip to work by leaving his house and walking to the bus stop at a constant rate of x miles per hour. After reaching the bus stop, which is

the total distance to his

work, Chris got on a bus that travels at a constant y miles per hour for the remainder of the trip. If it took Chris t hours to reach his work, how many miles is Chris's work from where he lives?

A.

B.

C. D. 3x(y + t) + 2y(x + t) E.

34. T is a finite set of consecutive odd integers and contains at least three numbers. Is the median of T an odd integer? (1) If the smallest and largest numbers are removed from T, the median of the resulting set is an odd integer. (2) If the smallest and largest numbers are removed from T, the range of the resulting set is divisible by 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.

35. 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

36. A bag of jelly beans contains blue, red, green, and yellow jelly beans. How many pairs of matching colored beans are in the bag? (1) There are as many blue beans as there are red beans. (2) The bag contains 15 jelly beans. 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.