Official Guide Explanation:
Data Sufficiency #76




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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 x2 is less than x, x cannot be negative--no matter what the value of x, x2 is positive, so if x were negative, x2 would be larger than x. If x is larger than 1, x2 is greater than x: 1.52 = 2.25, 22 = 4, etc. So, the only possible values for x that make x2 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, x2, are not equal to zero). If x is a positive or negative number, x2 will be positive, so if (2) is true, x could be any number. Choice (A) is correct.

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