【正确答案】 C

【答案解析】By the triangle inequality (KEY FACTS J12 and J13), · The third side must be less than 9 + 10 = 19. (Ⅲ is false.) · The third side must be greater than 10 -9 = 1. (Ⅰ is false.) · Any number between 1 and 19 could be the length of the third side. (Ⅱ is true.) The answer is C.

【正确答案】 D

【答案解析】Check each choice. (A) If x = 5, [*]= 2. (B) This one is more difficult; the only possibility if x = 1, in which case [*] = 0. If you don't see that immediately, keep Choice B under consideration, and test the rest. (C) If x = 1, [*] = 1. (D) For positive x, [*] is always greater than 1 but less than 2; [*] cannot be an integer—that's it. If you didn't reason that out, check Choice E. [*] is an integer if x = 6. You should have eliminated at least Choices, A, C, and E.

【正确答案】 A

【答案解析】a+10%(a)=a+.1a=1.1a. Also, b -10%(b) = b -.1b = .9b. Then, 1.1a = .9b, and [*] **If after increasing a and decreasing b the results are equal, a must be smaller than b. So, the ratio of a to b must be less than 1. Eliminate Choices C, D, and E. Now, either test Choices A and B or just guess. To test B, pick 2 numbers in the ratio of 9 to 10—90 and 100, for example: 90 increased by 10% is 99. 100 decreased by 10% is 90. They're not equal. Eliminate Choice B. The answer is Choice A. (110 decreased by 10% is 99.)

【正确答案】 C

【答案解析】Since, in 1990, 2p pounds of potatoes cost [*] dollars, p pounds cost half as much: [*][*] or 25%, as much as the cost in 1980, which represents a decrease of 75%. **In this type of problem it is often easier to use TACTIC 2, Chapter 11. Assume that 1 pound of potatoes cost $100 in 1980. Then in 1990, 2 pounds cost $50, so 1 pound cost $25. This is a decrease of $75 in the cost of 1 pound of potatoes, and [*]

【正确答案】 D

【答案解析】If the area of the square is 4, each side is 2, and the length of a diagonal is [*]. The area of a circle whose radius is [*] is [*]