SAT Math Multiple Choice Practice Question 87: Answer and Explanation

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Question: 87

21. If j2 > j, and j3 > j, but j2 > j3, then which of the following must be true?

A. j < -1
B. -1 < j < 0
C. 0 < j < 1
D. 1 < j < 2
E. j > 2

Correct Answer: B

Explanation:

B. The first two statements aren't unusual, but the third is a little weird. If you try a "normal" number, like 4, for j, then 42 = 16 and 43 = 64; notice that j2 isn't greater than j3, so you know j isn't a positive number greater than 2. What about a fraction, like 1/2? Then (1/2)2 = 1/4, and (1/2)3 = 1/8, and j2 > j3. But wait a minute: Now j2 and j3 are both smaller than j, which contradicts the first two statements. So how about a negative number, like -2? Well, (-2)2 = 4, which is greater than -2, but (-2)3 = -8, which isn't. So you're left with a negative fraction. Try -1/2: (-1/2)2 = 1/4, which is greater than -1/2; (-1/2)3 = -1/8, which is also greater than -1/2 because it's farther to the right on a number line. And, finally, 1/4 > -1/8, so the third condition is satisfied, too. Thus, you have your answer: j is any number between 0 and -1.

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