SAT Math Multiple Choice Practice Question 143: Answer and Explanation

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Question: 143

11. Which of the following must be true for x, given that x is a negative integer?

A. x -x
B. x x2
C. x x3
D. x 1/x
E. x x/2

Correct Answer: C


C. If x is negative, then -x and x2 are both positive. Therefore, both Choice (A) and Choice (B) are false. Choice (C) looks true: For example, (-1)3 = -1, and -1 -1, while (-2)3 = -8, and -2 -8. As usual, you should stop right there on the real test, but I'll check the last two choices just for fun. (D) doesn't work: For example, -2 isn't greater than or equal to -1/2. (E) is true for positive numbers, but not for negative numbers: 6 is greater than 3, but -6 is smaller than -3. Choice (C) it is.

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