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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 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: 51
Page: 277
Difficulty: 5 (Moderate)
Category 1: Algebra > Inequalities > other
Category 2: Arithmetic > Fractions >
Category 3: Arithmetic > Properties of Integers > Other

Explanation: In order for ((x)/(y)) to be greater than 1, x must be greater than y. (That's only because the question stipulates that both are positive; if they could be negative, that would open up more possibilities.) So, the question is: "Is x greater than y?"

Statement (1) is insufficient: x could be greater than y, but as long as the product is greater than 1, y could also be greater than x. Statement (2) is sufficient: add y to both sides of x - y > 0 and x > y, which directly answers the question. (B) is the correct choice.

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