1. If , is z 8?

(1) x 4

(2) |y| 4

A. Statement (1) by itself is sufficient to answer thequestion, but statement (2) by itself is not.

B. Statement (2) by itself is sufficient to answer thequestion, but statement (1) by itself is not.

C. Statements (1) and (2) taken together are sufficient toanswer the question, even though neither statement byitself is sufficient.

D. Either statement by itself is sufficient to answer thequestion.

E. Statements (1) and (2) taken together are not sufficientto answer the question, requiring more data pertaining tothe problem.

2. On a certain farm, the onion and the pumpkin patch wereeach to receive x gallons of water for irrigation. The onion patchwas 50 acres, and the pumpkin patch was 60 acres. Once itcame time to deliver the water, the farmer decided to transfery gallons of water from the onion patch to the pumpkin patchso 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 10equal 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 thequestion but statement (2) by itself is not.

B. Statement (2) by itself is sufficient to answer thequestion but statement (1) by itself is not.

C. Statements (1) and (2) taken together are sufficient toanswer the question, even though neither statement byitself is sufficient.

D. Either statement by itself is sufficient to answer thequestion.

E. Statements (1) and (2) taken together are NOTsufficient to answer the question, requiring more datapertaining to the problem.

4. All but 50 of the 1,000 plants at the annual flower show weresold. Of the plants sold, 30 percent were sold at a discount of25 percent off the full price, and the remaining plants were soldat the full price of $12. What was the total revenue from theplant 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 5s + 2t + 14.Is s a prime number?

(1) s t is a prime number

(2) s t is an odd integer

A. Statement (1) BY ITSELF is sufficient to answer thequestion, but statement (2) by itself is not.

B. Statement (2) BY ITSELF is sufficient to answer thequestion, but statement (1) by itself is not.

C. Statements (1) and (2) TAKEN TOGETHER aresufficient to answer the question, even though NEITHERstatement BY ITSELF is sufficient.

D. EITHER statement BY ITSELF is sufficient to answerthe question.

E. Statements (1) and (2) TAKEN TOGETHER are NOTsufficient to answer the question, requiring more datapertaining to the problem.

6. If x, y, and z are integers, is x -y odd?

(1) x = z2- 4y + 4

(2) y = z2- 2z + 1

A. Statement (1) BY ITSELF is sufficient to answer thequestion, but statement (2) by itself is not.

B. Statement (2) BY ITSELF is sufficient to answer thequestion, but statement (1) by itself is not.

C. Statements (1) and (2) TAKEN TOGETHER aresufficient to answer the question, even though NEITHERstatement BY ITSELF is sufficient.

D. EITHER statement BY ITSELF is sufficient to answerthe question.

E. Statements (1) and (2) TAKEN TOGETHER are NOTsufficient to answer the question, requiring more datapertaining 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 theperimeter of the triangle?

I. 28II. 36III. 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 reverseof 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 thequestion but statement (2) by itself is not.

B. Statement (2) by itself is sufficient to answer thequestion but statement (1) by itself is not.

C. Statements (1) and (2) taken together are sufficient toanswer the question, even though neither statement byitself is sufficient.

D. Either statement by itself is sufficient to answer thequestion.

E. Statements (1) and (2) taken together are NOTsufficient to answer the question, requiring more datapertaining to the problem.

9. If the function g(x) is defined by the equation g(x) = ax2- 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.

10. If *n* = xn3 + 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 n 10, which of the following must betrue?

A. n 8

B. n = -6

C. n -8

D. -10 n 7

E. none of the above

12. If ab = 20 -a2b

2, where both a and b are negative, then a

2 =

A.

B.

C.

D.

E.

13. What is the value of a + b if a, b, and c are integers?

(1) 3a5b = 225c

(2) 9a54-2b = 15

c

A. Statement (1) by itself is sufficient to answer thequestion but statement (2) by itself is not.

B. Statement (2) by itself is sufficient to answer thequestion but statement (1) by itself is not.

C. Statements (1) and (2) taken together are sufficient toanswer the question, even though neither statement byitself is sufficient.

D. Either statement by itself is sufficient to answer thequestion.

E. Statements (1) and (2) taken together are NOTsufficient to answer the question, requiring more datapertaining to the problem.

14. If x and y are positive integers, does x-y = 0?

(1) (z2)x = z2y

(2) z 2 = z

A. Statement (1) by itself is sufficient to answer thequestion but statement (2) by itself is not.

B. Statement (2) by itself is sufficient to answer thequestion but statement (1) by itself is not.

C. Statements (1) and (2) taken together are sufficient toanswer the question, even though neither statement byitself is sufficient.

D. Either statement by itself is sufficient to answer thequestion.

E. Statements (1) and (2) taken together are NOTsufficient to answer the question, requiring more datapertaining to the problem.

15. If x and y are integers and x + y x -y, which of thefollowing 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

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 thequestion, but statement (2) by itself is not.

B. Statement (2) by itself is sufficient to answer thequestion, but statement (1) by itself is not.

C. Statements (1) and (2) taken together are sufficient toanswer the question, even though neither statement byitself is sufficient.

D. Either statement by itself is sufficient to answer thequestion.

E. Statements (1) and (2) taken together are not sufficientto answer the question, requiring more data pertaining tothe problem.

17. Set S is defined by the following sequence: S0 = 4, S

1 = 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 thequestion, but statement (2) by itself is not.

B. Statement (2) by itself is sufficient to answer thequestion, but statement (1) by itself is not.

C. Statements (1) and (2) taken together are sufficient toanswer the question, even though neither statement byitself is sufficient.

D. Either statement by itself is sufficient to answer thequestion.

E. Statements (1) and (2) taken together are not sufficientto answer the question, requiring more data pertaining tothe problem.

19. If the sum of the squares of x and y is 3, and x4 = y

4 + 25,

what is the value of x2?

A.

B.

C.

D.

E.

20. If 410-3z

86z+10

100-3z

5002z

= 1, what is the value of z?

A. 10

B. 5

C. 1

D. -5

E. -10

21. The number 1002 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 cup of this fruit drink and then add

another cup of fruit drink that has 50 percent apple juice.

Which is most nearly the percent of apple juice in the children'smixed 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 ratefrom 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 whenthe two swimmers pass each other?

A.

B.

C.

D.

E.

24. Attorneys are questioning 11 potential jurors about theirability to serve on a jury and decide a case fairly. Sevenindividuals will be selected to serve on the jury. If each potentialjuror has an equal chance of being selected, what is theprobability that Tamara and Inga are chosen for the jury?

A.

B.

C.

D.

E.

25. If x and y are integers, is xy 0?

(1) x 0

(2) y = x3 - x2

A. Statement (1) by itself is sufficient to answer thequestion but statement (2) by itself is not.

B. Statement (2) by itself is sufficient to answer thequestion but statement (1) by itself is not.

C. Statements (1) and (2) taken together are sufficient toanswer the question, even though neither statement byitself is sufficient.

D. Either statement by itself is sufficient to answer thequestion.

E. Statements (1) and (2) taken together are NOTsufficient to answer the question, requiring more datapertaining to the problem.

26. The circular base of a planter sits on a level lawn, and justtouches two straight garden walls at points W and Y. The wallscome together at point X, which is 15 inches from the center ofthe planter. What is the area of the base of the planter?

(1) Both points Y and W are 9 inches from the center of theplanter.

(2) Point W is 12 inches from point X.

A. Statement (1) by itself is sufficient to answer thequestion, but statement (2) by itself is not.

B. Statement (2) by itself is sufficient to answer thequestion, but statement (1) by itself is not.

C. Statements (1) and (2) taken together are sufficient toanswer the question, even though neither statement byitself is sufficient.

D. Either statement by itself is sufficient to answer thequestion.

E. Statements (1) and (2) taken together are not sufficientto answer the question, requiring more data pertaining tothe problem.

27. A cake bakery sells white cakes, lemon cakes, andcombination cakes that have one white layer and one lemonlayer. Combination cakes currently comprise 20% of thebakery's inventory. The number of white cakes plus the numberof combination cakes totals 98. If half of all the cakes are whitecakes, 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 remainderwhen 7xyz is divided by 4?

(1) yz = 3

(2) x is odd.

A. Statement (1) by itself is sufficient to answer thequestion but statement (2) by itself is not.

B. Statement (2) by itself is sufficient to answer thequestion but statement (1) by itself is not.

C. Statements (1) and (2) taken together are sufficient toanswer the question, even though neither statement byitself is sufficient.

D. Either statement by itself is sufficient to answer thequestion.

E. Statements (1) and (2) taken together are NOTsufficient to answer the question, requiring more datapertaining to the problem.

29. The ratio of men to women in the Snyder community choir is4 to 5. The ratio of men to women in the Leigh community choiris 5 to 6. If the two choirs merged, the ratio of men to womenin the combined choir would be 22 to 27. If Snyder has 4 moremen and 6 more women than Leigh, how many women are inthe 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 thecurrent election two candidates are running for each position,how many different combinations of candidates could beelected 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 0?

(1) 16x + 1

49y

(2) x y

A. Statement (1) by itself is sufficient to answer thequestion but statement (2) by itself is not.

B. Statement (2) by itself is sufficient to answer thequestion but statement (1) by itself is not.

C. Statements (1) and (2) taken together are sufficient toanswer the question, even though neither statement byitself is sufficient.

D. Either statement by itself is sufficient to answer thequestion.

E. Statements (1) and (2) taken together are NOTsufficient to answer the question, requiring more datapertaining to the problem.

34. Is x 0?

(1) x - y -8

(2) x + y = -8

A. Statement (1) BY ITSELF is sufficient to answer thequestion, but statement (2) by itself is not.

B. Statement (2) BY ITSELF is sufficient to answer thequestion, but statement (1) by itself is not.

C. Statements (1) and (2) TAKEN TOGETHER aresufficient to answer the question, even though neitherstatement by itself is sufficient.

D. Either statement BY ITSELF is sufficient to answer thequestion.

E. Statements (1) and (2) TAKEN TOGETHER are NOTsufficient to answer the question, requiring more datapertaining to the problem.

35. If two sides of a triangle are 12 and 8, which of the followingcould be the area of the triangle?

I. 35II. 48III. 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 is an integer and 5x 1,000, what is the value of x?

(1) 5x+1

500

(2) 5x+1

- 5x

1,000

A. Statement (1) by itself is sufficient to answer thequestion but statement (2) by itself is not.

B. Statement (2) by itself is sufficient to answer thequestion but statement (1) by itself is not.

C. Statements (1) and (2) taken together are sufficient toanswer the question, even though neither statement byitself is sufficient.

D. Either statement by itself is sufficient to answer thequestion.

E. Statements (1) and (2) taken together are NOTsufficient to answer the question, requiring more datapertaining to the problem.