15 Math Section ------------------------------------------------------------------------------------------------------------ Q1: A grocer has 400 pounds of coffee in stock, 20 percent of which is decaffeinated. If the grocer buys another 100 pounds of coffee of which 60 percent is decaffeinated, what percent, by weight, of the grocer’s stock of coffee is decaffeinated? A. 28% B. 30% C. 32% D. 34% E. 40% Answer: ------------------------------------------------------------------------------------------------------------ Q2: If 2 different representatives are to be selected at random from a group of 10 employees and if p is the probability that both representatives selected will be women, is p > 2 1 ? (1) More than 2 1 of the 10 employees are women. (2) The probability that both representatives selected will be men is less than 10 1 . A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. B. Statement (2) ALONE is sufficient, but statement (1) alone 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. Answer: ------------------------------------------------------------------------------------------------------------ Q3: If the population of a certain country is 120,256,000 and its land area is 2,998,000 square kilometers, then the population per square kilometer is closest to which of the following? A. 4 B. 6 C. 20 D. 40 E. 60 Answer: ------------------------------------------------------------------------------------------------------------ Q4: 16 1.6(10 ) 4.8(10 ) 3 9 = A. 30(105 ) B. [3(10)]6 C. 305 D. 30(106 ) E. 3(1012) Answer: ------------------------------------------------------------------------------------------------------------ Q5: If vmt ? 0, is v 2 m 3 t -4 > 0? (1) m > v 2 (2) m > t -4 A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. B. Statement (2) ALONE is sufficient, but statement (1) alone 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. Answer: ------------------------------------------------------------------------------------------------------------ Q6: B C xo yo zo A D In the figure shown, line segment AD is parallel to line segment BC. What is the value of x? (1) y = 50 (2) z = 40 A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. B. Statement (2) ALONE is sufficient, but statement (1) alone 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. Answer: ------------------------------------------------------------------------------------------------------------ 17 Q7: A certain university will select 1 of 7 candidates eligible to fill a position in the mathematics department and 2 of 10 candidates eligible to fill 2 identical positions in the computer science department. If none of the candidates is eligible for a position in both departments, how many different sets of 3 candidates are there to fill the 3 positions? A. 42 B. 70 C. 140 D. 165 E. 315 Answer: ------------------------------------------------------------------------------------------------------------ Q8: The points R, T, and U lie on a circle that has radius 4. If the length of arc RTU is 3 4p , what is the length of line segment RU? A. 3 4 B. 3 8 C. 3 D. 4 E. 6 Answer: ------------------------------------------------------------------------------------------------------------ Q9: For all integers n, the function f is defined by f (n) = a n , where a is a constant. What is the value of f (1)? (1) f (2) = 100 (2) f (3) = -1,000 A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. B. Statement (2