Official Guide Explanation:
Data Sufficiency #153

Background

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Solution and Metadata

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 2^x 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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