单选题
If the lengths of two of the sides of a triangle are 9 and 10, which of the following could be the length of the third side? Ⅰ. 1 Ⅱ. 11 Ⅲ. 21
【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.
单选题
If x is a positive integer, which of the following CANNOT be an integer?
【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. 
= 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.