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## Official Guide Explanation:Problem Solving #103

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.

Solution and Metadata

Question: 103
Page: 75
Difficulty: 6 (Moderately Difficult)
Category 1: Algebra > Solving Equations by Factoring >
Category 2: Algebra > Solving Quadratic Equations > Difference of Squares

Explanation: First, factor x3-x:

x3-x = x(x2-1) = x(x + 1)(x - 1)

Since the expression is set equal to (x - a)(x - b)(x - c), we can rewrite the expression to look more like that:

(x - 0)(x - (-1))(x - 1)

Thus, the values of a, b, and c are 0, -1, and 1. We know that a>b>c , so b is the middle number, 0. Choice (C) is correct.

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