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## Official Guide Explanation:Problem Solving #173

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: 173
Page: 176
Difficulty: 6 (Moderately Difficult)
Category 1: Algebra > Inequalities > other
Category 2: Arithmetic > Real Numbers >

Explanation: First, simplify the inequality. Add x2 to both sides: 1 ≥ x2. Since x2 cannot be negative (no number squared is negative) we can say that 0 ≤ x2 ≤ 1. The only way x2 can be within that range is if x itself is within that range, or within the negative equivalent of that range. For example, if x = (1/2), x2 = (1/4). If x= - (1/2), x2 = (1/4). So, the inequality that expresses the possible range of x is -1 ≤ x ≤ 1, choice (E).

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