Official Guide Explanation:
Data Sufficiency #79

Background

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Solution and Metadata

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 n^m 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 n^m 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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