Official Guide Explanation:
Data Sufficiency #16




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Solution and Metadata

Question: 16
Page: 274
Difficulty: 6 (Moderately Difficult)
Category 1: Arithmetic > Properties of Integers > Factors and Multiples

Explanation: With statements regarding properties of numbers, it's useful to treat them like algebraic equations. In Statement (1): if ((x)/2) is an integer, then ((x)/2) = \func{integer}, and x = 2(\func{integer}). Twice an integer is always an integer, so x must be an integer.

Statement (2) can work the same way: if 2x is an integer, then 2x = integer, and x = ((\func{integer})/2). If the integer is even, x is an integer; if it is odd, x is not an integer, so the statement is insufficient. The correct choice is (A).

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