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## Official Guide Explanation:Data Sufficiency #121

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: 121
Page: 161
Difficulty: 6 (Moderately Difficult)
Category 1: Arithmetic > Powers and Roots of Numbers > Powers
Category 2: Algebra > Exponents >

Explanation: Statement (1) is insufficient. Substitute the equation into the inequality:

xy < yx?

(y2)y < y(y2)?

y2y < y(y2)?

2y < y2?

That simplifies the question somewhat, but without knowing more about y, it isn't enough to answer the question.

Statement (2) is insufficient, as it contains no information about x.

Taken together, the statements are sufficient. First, look at the simplifed result of (1):

Is 2y < y2?

If y > 2, the answer to this question will always be "yes." Because you know that y is positive, you can divide both sides by y, resulting in:

Is y > 2?

(2) answers that question directly, so the correct choice is (C).

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