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## Official Guide Explanation:Data Sufficiency #166

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: 166
Page: 288
Difficulty: 6 (Moderately Difficult)
Category 1: Algebra > Exponents >
Category 2: Arithmetic > Fractions >
Category 3: Algebra > Inequalities > other

Explanation: 0.01 = (1/100) = ((1/10))2, so the question is really asking:

Is ((1/10))n < ((1/10))2 ?

Or, is n < 2 ?

Statement (1) is sufficient: if n is greater than 2, n is not less than 2. Statement (2) is also sufficient, and can be simplified as follows:

((1/10))n - 1 < 0.1

((1/10))n - 1 < ((1/10))1

n - 1 < 1

n < 2

If n is less than 2, we can answer the question: n is less than 2. Choice (D) is correct.

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