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Official Guide Explanation:Data Sufficiency #24

Background

This is just one of hundreds of free explanations I've created to the quantitative questions in The Official Guide for GMAT Quantitative Review (2nd ed.). Click the links on the question number, difficulty level, and categories to find explanations for other problems.

These are the same explanations that are featured in my "Guides to the Official Guide" PDF booklets. However, because of the limitations of HTML and cross-browser compatibility, some mathematical concepts, such as fractions and roots, do not display as clearly online.

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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