Official Guide Explanation:
Data Sufficiency #24




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Solution and Metadata

Question: 24
Page: 154
Difficulty: 4 (Moderately Easy)
Category 1: Arithmetic > Powers and Roots of Numbers > Powers
Category 2: Arithmetic > Real Numbers >

Explanation: In the expression r5s3t4, we know that t4 is positive; anything raised to an even power is positive. That leaves us to focus on r5s3.

Statement (1) is insufficient. If rt is negative, exactly one of the two variables must be negative, the other positive. If r is positive, r5 is positive, t is negative, and t4 is positive (as always). We dont' know anything about s. If r is negative, r5 is negative, and t4 is still positive. And we still don't know s.

Statement (2) is also insufficient. Here we learn that s and, by extension, s3, are negative, but we don't know whether r5 is positive or negative.

Taken together, the statements are still insufficient. We know that s3 is negative and t4 is positive, (1) doesn't give us enough information to determine whether r is positive or negative. Choice (E) is correct.

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