单选题 Directions: Questions 9-20 have three different formats. Unless a question has its own directions that specifically state otherwise, each question has five answer choices, exactly one of which is correct.
单选题 In the figure below, what is the value of a+ b+ c?
【正确答案】 B
【答案解析】The unmarked angle opposite the 60° angle also measures 60°, and the sum of the measures of all six angles in the diagram is 360°. So, 360 =a+ b+ c+20+60+60 =a+b+c+ 140. Subtracting 140 from each side, we get that a + b + c = 220.
单选题 What is the value of n if410× 642 = 162×4n?
  • A. 6
  • B. 10
  • C. 12
  • D. 15
  • E. 30
【正确答案】 C
【答案解析】410 × 642= 410×(43)2= 410× 46= 416.
Also, 162 × 4n = (42)2 × 4n = 44 × 4n = 44+n.
So, 416 = 44+n and 16 = 4 + n. Then n = 12.
单选题 Twenty children were sharing equally the cost of a present for their teacher. When 4 of the children decided not to contribute, each of the other children had to pay $1.50 more. How much did the present cost, in dollars?
  • A. 50
  • B. 80
  • C. 100
  • D. 120
  • E. 150
【正确答案】 D
【答案解析】Let x be the amount in dollars that each of the 20 children were going to contribute; then 20x represents the cost of the present. When 4 children dropped out, the remaining 16 each had to pay (x + 1.50) dollars. So, 16(x+ 1.5) =20x[*]16x+24=20x[*]24=4x[*]x=6, and so the cost of the present was 20 × 6 = 120 dollars. Alternative Solution. Since each of the 16 remaining children had to pay an extra $1.50, the extra payments totaled 16 × $1.50 = $24. This is the amount that would have been paid by the 4 children who dropped out, so each of the 4 would have paid $6. The cost of the gift was 20 × $6 = $120.
填空题 Directions: For the following question, enter your answer in the box. Of the 200 seniors at Monroe High School, exactly 40 are in the band, 60 are in the orchestra, and 10 are in both. How many seniors are in neither the band nor the orchestra?
多选题 Directions: For the following question, consider each of the choices separately and select all that apply. Benjamin's average (arithmetic mean) on the six biology tests he took last semester was 89. On each of his first five tests, his grade was between 90 and 100, inclusive. Which of the following could have been his grade on his sixth test? Indicate all such grades. A. 15 B. 25 C. 35 D. 45 E. 55 F. 85 G. 75 [H] 85 [I] 95
【正确答案】 C、D、E、F、G
【答案解析】On the six tests, Benjamin earned a total of 6 × 89 = 534 points. On his first five tests, he earned at least 5 × 90 = 450 points, but no more than 5 × 100 = 500 points. So his grade on the sixth test was at least 534 - 500 = 34 and at most 534 - 450 = 84. Only answer choices C, D, E, F, and G are between 34 and 84.