Official Guide Explanation:
Data Sufficiency #24

Background

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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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