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## Official Guide Explanation:

Data Sufficiency #76

**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.

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**Solution and Metadata**

**Question****: 76**

Page: 158

Difficulty: **5** (Moderate)

Category 1: Algebra > Exponents >

Category 2: Arithmetic > Powers and Roots of Numbers > Powers

**Explanation:** Statement (1) is sufficient. If x^{2} is less than x, x cannot be negative--no matter what the value of x, x^{2} is positive, so if x were negative, x^{2} would be larger than x. If x is larger than 1, x^{2} is greater than x: 1.5^{2} = 2.25, 2^{2} = 4, etc. So, the only possible values for x that make x^{2} smaller than x are those between 0 and 1.

Statement (2) is not sufficient: in fact, it doesn't tell you anything except that x (and, by extension, x^{2}, are not equal to zero). If x is a positive or negative number, x^{2} will be positive, so if (2) is true, x could be any number. Choice (A) is correct.

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