1. 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.

2. At a certain automobile dealership that sells only Tajimasand Franks, the number of nonhybrid Tajimas is 35 less than3 times the number of hybrid Tajimas. 205 total Tajimas arecurrently owned by the dealership. If the ratio of hybrid Tajimasto nonhybrid Franks is 5:4 and there are 280 total automobilesowned by the dealership, how many hybrid Franks are there?

A. 20

B. 27

C. 48

D. 60

E. 87

3. 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.

4.

A.

B.

C.

D.

E.

5. The sum of x consecutive positive integers is 63. What is thevalue of x?

(1) x 11

(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 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 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

7. A wholesaler needs to quickly sell some hats, so he reducedthe price of the hats. By what percent did he reduce the price ofthe hats?

(1) If a case of 144 hats is purchased from the wholesaler,the savings will be $51.84 as a result of the price reduction.

(2) The price of a hat was reduced by 36 cents.

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.

8. A sphere is inscribed in a cube with an edge length of 20.What is the shortest possible distance from one of the verticesof the cube to the surface of the sphere?

A. 10

B.

C. 5

D.

E.

9. The value of land increases by a% during June anddecreases by b% during July. If the value of the land is thesame at the end of July as at the beginning of June, what is b interms of a?

A.

B.

C.

D.

E.

10. 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

11. If 2|2 -x| = 5, what is the sum of all the possible values for x?

A.

B. 2

C.

D. 4

E. 5

12. If r, s, t, and w are all nonzero integers, is r2s

3t4w

5 0?

(1) rst2 0

(2) rst 2 w

3 0

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.

13. If m = z5, is m 1?

(1) 3 - (y- x) x- (y- 3z)

(2) z 3

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.

14. 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.

15. If (10a+1

- 10a) / 3b = 102b where a and b are both integers,

what is the value of (a + b) ?

A. 1

B. 2

C. 3

D. 4

E. 6

16. In 2010, City X urban planners expected the city'spopulation to increase by 20% per year over the threeyears that followed. If that projection were to come true, thepopulation in 2012 would be exactly triple the populationin 2009. Which of the following is the approximate percentpopulation increase in City X from 2009 to 2010?

A. 20%

B. 45%

C. 72%

D. 108%

E. 124%

17. Let a represent the average of b consecutive integers and

c represent the sum of d consecutive integers. If , then

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.

18. For all positive integers s and t, s @ t represents theremainder when s is divided by t. What is the sum of all thepossible values of t for which 18 @ t = 2?

A. 38

B. 28

C. 16

D. 12

E. 10

19. 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%

20. Pam and Cathy begin running at the same time on astraight path. Pam runs at 10 miles per hour, and Cathy runsat 8 miles per hour. After 45 minutes, Pam stops to stretch. Ifit takes Pam 30 minutes to stretch and Cathy continues to runduring this time, how many minutes will it take Pam to catch upto Cathy assuming Pam resumes running at 10 miles per hour?

A. 30 minutes

B. 40 minutes

C. 45 minutes

D. 60 minutes

E. 75 minutes

21. A jazz ensemble is holding auditions for new musicians.11 musicians are auditioning, and 6 will be chosen for theensemble. If 7 of the musicians are saxophone players and 4 ofthe musicians are clarinet players, how many different groups of4 saxophone players and 2 clarinet players can be selected?

A. 66

B. 192

C. 210

D. 420

E. 462

22. Is x2

x - |y|?

(1) y x

(2) x 0

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.

23. A bakery currently has 5 pies and 6 cakes in its inventory.The bakery's owner has decided to display 5 of these items inthe bakery's front window. If the items are randomly selected,what is the probability that the display will have exactly 3 pies?

A.

B.

C.

D.

E.

24. Is q divisible by 6?

(1) 5q is divisible by 10.

(2) 3 is a factor of q + 3.

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.

25. 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.

26. Mike just filled his truck's gas tank with 20 gallons of amixture consisting of 10% additive and 90% gasoline. If histruck runs best on a mixture consisting of 20% additive and80% gasoline, how many gallons of additive must he add intothe gas tank for his truck to achieve optimum performance?

A. 1.0

B. 1.5

C. 2.0

D. 2.5

E. 3.0

27. In the rectangular coordinate system, lines m and n cross atthe origin. Is line m perpendicular to line n ?

(1) If the slope of m is y and the slope of n is z, then -yz = 1.

(2) m has a slope of -1, and n passes through the point (-x,-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 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.

28. 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

29. For all values of the integer x, is the product (x + 3)(x2 + 3x

+ 2) divisible by 4?

(1) is an odd integer

(2) x is divisible by 16

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.

30. If both x and y are positive integers that are divisible by 10,is 10 the greatest common factor of x and y?

(1) x = 4y

(2) x - 3y = 10

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.

31. is equivalent to

A.

B.

C.

D.

E.

32. All but 50 of the 1,000 plants at the annual flower showwere sold. Of the plants sold, 30 percent were sold at adiscount of 25 percent off the full price, and the remainingplants were sold at the full price of $12. What was the totalrevenue from the plant sales?

A. $8,550

B. $8,835

C. $10,545

D. $11,100

E. $12,000

33. The total cost of manufacturing item A is equal to thesum of item A's fixed cost and variable cost. In January, thecompany was able to lower both costs due to improvements inits production process. If the variable cost of manufacturing Adecreased by 5% in January, by what percent did the total costof manufacturing item A change in January?

(1) Before the changes in January, the fixed cost ofmanufacturing item A was five times the variable cost ofmanufacturing item A.

(2) The fixed cost of manufacturing item A increased by 13%in January.

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.

34. If x and y are positive integers such that (2x)(52y) = 2,500,

what is the value of (5y -1)x ?

A. 10

B. 25

C. 50

D. 500

E. 15,625

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. Is x 1010

?

(1) x = 322

(2) x 320

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.