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## Official Guide Explanation:Data Sufficiency #52

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: 52
Page: 156
Difficulty: 6 (Moderately Difficult)
Category 1: Algebra > Inequalities > other

Explanation: Statement (1) is insufficient: given the ranges of possible values for x and y, the product xy could be as small as 1(2) (less than 5) or as large as (3)(4) (greater than 5). Statement (2) is also insufficient: if x + y = 5, the product xy could less than 5, as in (1)(4), or greater than 5, as in (2)(3).

Taken together, the statements are still insufficient. If x = 1 and y = 4, both statements are true, and xy is less than 5. If x = 2 and y = 3, both statements are true, and xy is greater than 5. Since the answer could be "yes" or "no," the correct choice is (E).

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