Official Guide Explanation:
Data Sufficiency #1

Background

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Solution and Metadata

Question: 1
Page: 273
Difficulty: 4 (Moderately Easy)
Category 1: Algebra > Absolute Value >
Category 2: Arithmetic > Powers and Roots of Numbers > Powers

Explanation: To find the absolute value of x, you need the value of x--only the sign (positive or negative) doesn't matter. Statement (1) is insufficient: it has no insight as to the value of x, only that x is negative. (The absolute value of x is, by definition, positive, so if x is equal to the negative absolute value of x, x must be negative.)

Statement (2) is sufficient. There are two possible values for x: 2 and -2, but both have an absolute value of 2. The correct answer is (B).

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