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## Official Guide Explanation:Data Sufficiency #162

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: 162
Page: 287
Difficulty: 6 (Moderately Difficult)
Category 1: Arithmetic > Powers and Roots of Numbers > Roots
Category 2: Algebra > Inequalities > other

Explanation: It's important to note that both n and k are positive. Because both are positive, meaning that all of the terms on both sides of the inequality are positive, we can simplify the inequality by squaring both sides:

rt[n + k] > 2 rt[n] ?

( rt[n + k])2 > (2 rt[n])2 ?

n + k > 4n ?

k > 3n ?

More simply, the question is asking whether k is greater than 3n.

Statement (1) answers that question directly, so it is sufficient.

Statement (2) is insufficient. Simplify it, and it says that k > 2n. If k is greater than 2n, it might be greater than 3n, but it might not be--it might be equal to 2.5n. Choice (A) is correct.

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