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## Official Guide Explanation:Data Sufficiency #79

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: 79
Page: 158
Difficulty: 5 (Moderate)
Category 1: Arithmetic > Powers and Roots of Numbers > Powers
Category 2: Arithmetic > Real Numbers >

Explanation: This question tests positives and negatives. If n is positive, given that m and n are integers, mn must be an integer. Any integer raised to a positive integer power remains an integer. However, if n is negative, it is not an integer. For instance, if mn = 2-1, it's equal to (1/2). So really, the question is, "Is n positive?"

Statement (1) is insufficient. If nm is positive, it's possible that n is positive, but remember that any number raised to an even power is positive. So if m is even, it's possible that n is negative.

Statement (2) is also insufficient. Using the same reasoning as in the question, if nm is an integer, given that both variables are integers, all we know is that m must be positive.

Taken together, we still don't have enough information. From the statements, we learned that n is positive if m is odd, and that m is positive. These don't relate to each other at all, so choice (E) is correct.

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