1 Math Section ------------------------------------------------------------------------------------------------------------ Q1: A certain company’s profit in 1996 was 15 percent greater than its profit in 1995, and its profit in 1997 was 20 percent greater than its profit in 1996. The company’s profit in 1997 was what percent greater than its profit in 1995? A. 5% B. 18% C. 33% D. 35% E. 38% Answer: ------------------------------------------------------------------------------------------------------------ Q2: If every car sold last week at a certain used-car dealership was either a coupe or a sedan, what was the average (arithmetic mean) sale price for all the cars that were sold at the dealership last week? (1) The average sale price for the sedans that were sold at the dealership last week was $10,600. (2) The average sale price for the coupes that were sold at the dealership last week was $8,400. 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: Pat, Kate, and Mark charged a total of 162 hours to a certain project. If Pat charged twice as much time to the project as Kate and 1/3 as much time as Mark, how many more hours did Mark charge to the project than Kate? A. 18 B. 36 C. 72 D. 90 E. 108 Answer: ------------------------------------------------------------------------------------------------------------ Q4: What is the greatest prime factor of 2100 - 296? 2 A. 2 B. 3 C. 5 D. 7 E. 11 Answer: ------------------------------------------------------------------------------------------------------------ Q5: If b, c, and d are constants and x 2 + bx + c = (x + d) 2 for all values of x, what is the value of c? (1) d = 3 (2) b = 6 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 a, b, k, and m are positive integers, is a k a factor of b m ? (1) a is a factor of b. (2) k = m 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: ------------------------------------------------------------------------------------------------------------ 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: 3 ------------------------------------------------------------------------------------------------------------ Q8: R S T Q U P V W Note: Figure not drawn to scale. In the figure above, the area of square region PRTV is 81, and the ratio of the area of square region XSTU to the area of square region PQXW is 1 to 4. What is the length of segment RS? A. 5 B. 5.5 C. 6 D. 6.5 E. 7 Answer: ------------------------------------------------------------------------------------------------------------ Q9: If t