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## Official Guide Explanation:Data Sufficiency #D44

Background

This is just one of hundreds of free explanations I've created to the quantitative questions in The Official Guide for GMAT Review (12th 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: D44
Page: 25
Difficulty: 5 (Moderate)
Category 1: Arithmetic > Powers and Roots of Numbers > Roots
Category 2: Algebra > Exponents >
Category 3: Arithmetic > Properties of Integers > Other

Explanation: Statement (1) is sufficient. If rt[m] is an integer, the expression ( rt[m])n can be phrased as, "an integer raised to a positive integer power." Any integer raised to a positive integer power must be an integer.

Statement (2) is insufficient. We know that m is an integer, but not that rt[m] is an integer. If rt[n] is an integer, n is the square of an integer. With this information, the expression ( rt[m])n can be phrased as, "the square root of an integer raised to a square of an integer power." While ( rt[3])4 would be an integer, ( rt[5])1 would not. Choice (A) is correct.

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