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## Official Guide Explanation:Data Sufficiency #154

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: 154
Page: 287
Difficulty: 7 (Very Difficult)
Category 1: Algebra > Exponents >
Category 2: Arithmetic > Powers and Roots of Numbers > Powers
Category 3: Arithmetic > Ratio and Proportion >

Explanation: To write the question in equation form:

b - a ≥ 2(3n-2n) ?

Statement (1) is sufficient, but it requires some crafty algebra to show why:

3n + 1-2n + 1 = 3n(31) - 2n(21) = 2(1.5(3n) - 2n)

So, is 2(1.5(3n) - 2n) ≥ 2(3n-2n) ?

Divide both sides by 2:

1.5(3n) - 2n ≥ 3n-2n?

1.5(3n) ≥ 3n ?

Then divide by 3n:

1.5 ≥ 1 ?

Since 1.5 is greater than 1, we can conclusively answer the question.

Statement (2) is not enough information: it tells us nothing about b or a. Choice (A) is correct.

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