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## Official Guide Explanation:Data Sufficiency #109

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: 109
Page: 161
Difficulty: 5 (Moderate)
Category 1: Arithmetic > Powers and Roots of Numbers > Roots
Category 2: Algebra > Equations >

Explanation: Since both statements are equations that isolate z, first solve for z in the initial equation:

x = ((y)/(z2))

xz2 = y

z2 = ((y)/(x))

z= rt[((y)/(z))]

Each one of those steps is equivalent to the initial equation, so we can compare the equations in the statements to any of them.

Statement (1) is sufficient: multiply both sides by z and the result is z2 = ((y)/(x)), which is equivalent to the initial equation. Statement (2) is also sufficient: it is identical to the final version of the initial equation. Choice (D) is correct.

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