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## Official Guide Explanation:Data Sufficiency #31

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.

Question: 31
Page: 155
Difficulty: 7 (Very Difficult)
Category 1: Arithmetic > Powers and Roots of Numbers > Roots
Category 2: Arithmetic > Properties of Integers > Other

Explanation: As usual, think of other ways to phrase the question: in this case, you want to know whether x is a perfect square.

Statement (1) is sufficient. If rt[4x] is an integer, then its equivalent, 2 rt[x], is an integer. Thus, rt[x] must be one of two things: an integer, or one - half an integer, such as (3/2). However, if x is a number such as (3/2), x is not an integer: x in this case would be ((3/2))2 = (9/4). Since x must be an integer, we can rule out this second group, and reason that x must be an integer.

Statement (2) is not sufficient. If rt[3x] is not an integer, then its equivalent, rt[3] rt[x] must not be an integer. If x = 4, then rt[3x] is not an integer, and rt[x] is an integer, 2. However, if x = 2, then rt[3x] is not an integer, and rt[x] is not an integer. Since rt[x] could be either an integer or a non - integer, the statement isn't sufficient. Choice (A) is correct.

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