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## Official Guide Explanation:Data Sufficiency #153

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: 153
Page: 287
Difficulty: 6 (Moderately Difficult)
Category 1: Algebra > Absolute Value >
Category 2: Algebra > Exponents >

Explanation: Statement (1) is sufficient: if x is negative, the absolute value of x is positive. Therefore, x|x| is the product of a positive and a negative: a negative. A positive number raised to any power remains positive, so 2x must be positive. A negative number is always less than a positive number, so the answer is "yes."

Statement (2) is also sufficient, and easier: knowing the value of x, you could find the value of each side of the equation, and compare them. It doesn't matter what the answer will be: since there's only one possible value for x, there's only one possible outcome. Choice (D) is correct.

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