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## Official Guide Explanation:

Problem Solving #97

**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.

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**Solution and Metadata**

**Question****: 97**

Page: 165

Difficulty: **5** (Moderate)

Category 1: Algebra > Solving Quadratic Equations > other

Category 2: Algebra > Solving Equations by Factoring >

**Explanation:** If the product of two terms is zero, that means that one or both of the terms must be equal to zero. So, if x(2x + 1) = 0, then either x = 0 or (2x + 1) = 0. In other words, x must be 0 or -(1/2). That's not enough information to answer the question, but that's why you're given a second equation. In that case, either (x + (1/2)) = 0 or (2x - 3) = 0, so x must be -(1/2) or (3/2). Since both equations must be true, the only possible x value is the one that appears as a solution in both cases: x= - (1/2), choice (B).

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