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## Official Guide Explanation:Data Sufficiency #51

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: 51
Page: 156
Difficulty: 6 (Moderately Difficult)
Category 1: Algebra > Inequalities > other
Category 2: Arithmetic > Powers and Roots of Numbers > Roots

Explanation: Since n is positive, we can square both sides of all of these inequalities without considering whether we need to reverse the sign (as we'd need to do if n were negative). The inequality in the question can be simplified:

( rt[n])2 > (100)2 ?

n > 10,000 ?

Statement (1) can be simplified the same way:

( rt[n - 1])2 > (100 - 1)2

n - 1 > 10,000 - 200 + 1

n > 9,802

If n is greater than 9,802, we don't know whether it is greater than 10,000.

Statement (2) can be simplified this way as well:

( rt[n + 1])2 > (100 + 1)2

n + 1 > 10,000 + 200 + 1

n > 10,200

If n is greater than 10,200, it must be greater than 10,000. The statement is sufficient, and choice (B) is correct.

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