12 Math Section ------------------------------------------------------------------------------------------------------------ Q1: If k is negative, which of the following must also be negative? A. (-k)2 B. (-1) k C. 1 - k D. k + 1 E. k - 1 Answer: ------------------------------------------------------------------------------------------------------------ Q2: On Saturday morning, Malachi will begin a camping vacation and he will return home at the end of the first day on which it rains. If on the first three days of the vacation the probability of rain on each day is 0.2, what is the probability that Malachi will return home at the end of the day on the following Monday? A. 0.008 B. 0.128 C. 0.488 D. 0.512 E. 0.640 Answer: ------------------------------------------------------------------------------------------------------------ Q3: Each of the 45 boxes on shelf J weighs less than each of the 44 boxes on shelf K. What is the median weight of the 89 boxes on these shelves? (1) The heaviest box on shelf J weighs 15 pounds. (2) The lightest box on shelf K weighs 20 pounds. 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: ------------------------------------------------------------------------------------------------------------ Q4: What is the total value of Company H’s stock? (1) Investor P owns ¼ of the shares of Company H’s total stock. (2) The total value of Investor Q’s shares of Company H’s stock is $16,000. 13 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: ------------------------------------------------------------------------------------------------------------ Q5: If (y+3)(y-1) – (y-2)(y-1) = r(y-1), what is the value of y? (1) r2 = 25 (2) r = 5 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: If x and k are integers and (12x )(42x+1) = (2k )(32 ), what is the value of k? A. 5 B. 7 C. 10 D. 12 E. 14 Answer: ------------------------------------------------------------------------------------------------------------ Q7: If x < 0, then √(-x •x) is A. -x B. -1 C. 1 D. x E. √x Answer: ------------------------------------------------------------------------------------------------------------ Q8: A thin piece of wire 40 meters long is cut into two pieces. One piece is used to form a circle with radius r, and the other is used to form a square. No wire is left over. Which of the following represents the total area, in square meters, of the circular and the square regions in terms of r? 14 A. πr 2 B. πr 2 + 10 C. πr 2 + ¼ π 2 r 2 D. πr 2 + (40-2πr)2 E. πr 2 + (10- ½ πr)2 Answer: ------------------------------------------------------------------------------------------------------------ Q9: If r is a constant and an = r•n for all positive integers n, for how many values of n is an < 100? (1) a50 = 500 (2) a100 + a105 = 2,050 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,