__Quantitative__:

Problem-solving: Solve these problems and indicate the best of the answer choices given. All numbers used are real numbers.

1. If a = 3 and b = -2, what is the value of a2 + 3ab – b2? (A) 5

(B) -13

(C) -4

(D) -20 (E) 13

2. 34 is what percent of 80? (A) 34%

(B) 40%

(C) 42.5%

(D) 44.5% (E) 52%

3. Jack and Kevin play in a basketball game. If the ratio of points scored by Jack to points scored by Kevin is 4 to 3, which of the following could NOT be the total number of points scored by the two boys?

(A) 7

(B) 14

(C) 16

(D) 28

(E) 35

4. Factor the following expression: x2 + x – 12 (A) (x – 4) (x + 4)

(B) (x – 2) (x + 6)

(C) (x + 6) (x – 2)

(D) (x – 4) (x + 3) (E) (x + 4) (x – 3)

5. The average of six numbers is 4. If the average of two of those numbers is 2, what is the average of the other four numbers?

(A) 5

(B) 6

(C) 7 (D) 8 (E) 9

6. What is the next-highest prime number after 67? (A) 68

(B) 69

(C) 71

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(D) 73 (E) 76

7. Solve: 0.25 x 0.03 = (A) 75

(B) 0.075

(C) 0.75

(D) 0.0075 (E) 7.5

8. Dean’s Department Store reduces the price of a $30 shirt by 20%, but later raises it again by 20% of the sale price. What is the final price of the shirt?

(A) $24.40

(B) $32

(C) $30 (D) $28.80 (E) $26.60

9. How many 3-inch segments can a 4.5-yard line be divided into? (A) 15

(B) 45

(C) 54

(D) 64 (E) 84

10. Sheila, Janice, and Karen, working together at the same rate, can complete a job in 3 1/3 days. Working at the same rate, how much of the job could Janice and Karen do in one day?

(A) 1/5

(B) 1/4 (C) 1/3 (D) 1/9 (E) 1/8

11. Dave can deliver four newspapers every minute. At this rate, how many newspapers can he deliver in 2 hours?

(A) 80

(B) 160

(C) 320 (D) 400 (E) 480

12. 46 ÷28 = (A) 2

(B) 8

(C) 16

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(D) 32 (E) 64

13. Ifa=4,b=3,andc=1,then a(b−c) = b(a+b+c)

(A) 4/13 (B) 1/3 (C) 1/4 (D) 1/6 (E) 2/7

14. What is 20% of 12 , expressed as a percentage? 5

(A) 48% (B) 65% (C) 72% (D) 76% (E) 84%

15. Archie’s gas tank is 1/3 full. If Archie adds 3 gallons of gas to the tank, it will be 1⁄2 full. What is the capacity in gallons of Archie’s tank?

(A) 28

(B) 12

(C) 20 (D) 16 (E) 18

Data sufficiency: This Data Sufficiency problem consists of a question and two statements, labeled (1) and (2), in which certain data are given. You have to decide whether the data given in the statements are sufficient for answering the question, using only the data given in the statements and your knowledge of mathematics and everyday facts (such as the number of days in July or the meaning of counterclockwise).

16. Does Jonathan get paid more than Deborah? (1) Alice gets paid more than Deborah.

(2) Jonathan makes less money than Alice.

(A) Statement (1) ALONE is sufficient, but statement (2) is not sufficient.

(B) Statement (2) ALONE is sufficient, but statement (1) is not sufficient.

(C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

(D) EACH statement ALONE is sufficient.

(E) Statements (1) and (2) TOGETHER are NOT sufficient.

17. Is the integer a less than the integer b? (1) a3 < b3

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(2) a2 < b2

(A) Statement (1) ALONE is sufficient, but statement (2) is not sufficient.

(B) Statement (2) ALONE is sufficient, but statement (1) is not sufficient.

(C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

(D) EACH statement ALONE is sufficient.

(E) Statements (1) and (2) TOGETHER are NOT sufficient.

18. Is the perimeter of a given rectangle greater than 8 inches?

(1) The two shorter sides of the rectangle are 2 inches long.

(2) The length of the rectangle is 2 inches greater than the width of the

(A) Statement (1) ALONE is sufficient, but statement (2) is not sufficient.

(B) Statement (2) ALONE is sufficient, but statement (1) is not sufficient.

(C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

(D) EACH statement ALONE is sufficient.

(E) Statements (1) and (2) TOGETHER are NOT sufficient.

19. Is a an integer? (1) a > 0

(2)42 +32 =a2

(A) Statement (1) ALONE is sufficient, but statement (2) is not sufficient.

(B) Statement (2) ALONE is sufficient, but statement (1) is not sufficient.

(C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

(D) EACH statement ALONE is sufficient.

(E) Statements (1) and (2) TOGETHER are NOT sufficient.

20. What is the value of the integer P? (1) P is an integer multiple of 2, 4, and 5. (2) 40 < P < 70

(A) Statement (1) ALONE is sufficient, but statement (2) is not sufficient.

(B) Statement (2) ALONE is sufficient, but statement (1) is not sufficient.

(C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

(D) EACH statement ALONE is sufficient.

(E) Statements (1) and (2) TOGETHER are NOT sufficient.

21. Brian is dividing 50 marbles into 3 groups. How many marbles are in the largest of the three groups?

(1) The sum of the two smaller groups of marbles is equal to the largest group of marbles. (2) The smallest group contains 6 marbles.

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(A) Statement (1) ALONE is sufficient, but statement (2) is not sufficient.

(B) Statement (2) ALONE is sufficient, but statement (1) is not sufficient.

(C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

(D) EACH statement ALONE is sufficient.

(E) Statements (1) and (2) TOGETHER are NOT sufficient.

22. Is b a positive number? (1) 1,452(b) > 0

(2) –b < 0

(A) Statement (1) ALONE is sufficient, but statement (2) is not sufficient.

(B) Statement (2) ALONE is sufficient, but statement (1) is not sufficient.

(C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

(D) EACH statement ALONE is sufficient.

(E) Statements (1) and (2) TOGETHER are NOT sufficient.

23. Is x greater than y? (1) x > 2y

(2) x – y > 0

(A) Statement (1) ALONE is sufficient, but statement (2) is not sufficient.

(B) Statement (2) ALONE is sufficient, but statement (1) is not sufficient.

(C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

(D) EACH statement ALONE is sufficient.

(E) Statements (1) and (2) TOGETHER are NOT sufficient.

24. What is the average test score of Angela, Barry, Carl, Dennis, and Edward? (1) The average of the test scores of Barry, Carl, and Edward is 87.

(2) The average of the test scores of Angela and Dennis is 84.

(A) Statement (1) ALONE is sufficient, but statement (2) is not sufficient.

(B) Statement (2) ALONE is sufficient, but statement (1) is not sufficient.

(C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

(D) EACH statement ALONE is sufficient.

(E) Statements (1) and (2) TOGETHER are NOT sufficient.

25. If y is an integer, is it an odd number?

(1)y3 ≥0

(2) y is either an odd number or a negative number

(A) Statement (1) ALONE is sufficient, but statement (2) is not sufficient.

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(B) Statement (2) ALONE is sufficient, but statement (1) is not sufficient.

(C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

(D) EACH statement ALONE is sufficient.

(E) Statements (1) and (2) TOGETHER are NOT sufficient.

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