13 Math Section ------------------------------------------------------------------------------------------------------------ Q1: The population of City X is 50 percent of the population of City Y. The population of City X is what percent of the total population of City X and City Y? A. 25% B. 33 3 1 % C. 40% D. 50% E. 66 3 2 % Answer: ------------------------------------------------------------------------------------------------------------ Q2: Guy’s net income equals his gross income minus his deductions. By what percent did Guy’s net income change on January 1, 1989, when both his gross income and his deductions increased? (1) Guy’s gross income increased by 4 percent on January 1, 1989. (2) Guy’s deductions increased by 15 percent on January 1, 1989. 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: Each participant in a certain study was assigned a sequence of 3 different letters from the set {A, B, C, D, E, F, G, H}. If no sequence was assigned to more than one participant and if 36 of the possible sequences were not assigned, what was the number of participants in the study? (Note, for example, that the sequence A, B, C is different from the sequence C, B, A.) A. 20 B. 92 C. 300 D. 372 E. 476 Answer: 14 ------------------------------------------------------------------------------------------------------------ Q4: Of the total amount that Jill spent on a shopping trip, excluding taxes, she spent 50 percent on clothing, 20 percent on food, and 30 percent on other items. If Jill paid a 4 percent tax on the clothing, no tax on the food, and an 8 percent tax on all other items, then the total tax that she paid was what percent of the total amount that she spent, excluding taxes? A. 2.8% B. 3.6% C. 4.4% D. 5.2% E. 6.0% Answer: ------------------------------------------------------------------------------------------------------------ Q5: If x and y are positive, is x 3 > y? (1) x > y (2) x > y 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: The infinite sequence a1, a2,…, an,… is such that a1 = 2, a2 = -3, a3 = 5, a4 = -1, and an = an-4 for n > 4. What is the sum of the first 97 terms of the sequence? A. 72 B. 74 C. 75 D. 78 E. 80 Answer: ------------------------------------------------------------------------------------------------------------ Q7: For a certain race, 3 teams were allowed to enter 3 members each. A team earned 6 – n points whenever one of its members finished in nth place, where 1 n 5. There were no ties, disqualifications, or withdrawals. If no team earned more than 6 points, what is the least possible score a team could have earned? A. 0 15 B. 1 C. 2 D. 3 E. 4 Answer: ------------------------------------------------------------------------------------------------------------ Q8: At a certain food stand, the price of each apple is ¢ 40 and the price of each orange is ¢ 60. Mary selects a total of 10 apples and oranges from the food stand, and the average (arithmetic mean) price of the 10 pieces of fruit is ¢ 56. How many oranges must Mary put back so that the average price of the pieces of fruit that she keeps is ¢ 52? A. 1 B. 2 C. 3 D. 4 E. 5 Answer: -----------------------------------------