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## Official Guide Explanation:Data Sufficiency #106

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.

Solution and Metadata

Question: 106
Page: 160
Difficulty: 6 (Moderately Difficult)
Category 1: Algebra > Solving Equations by Factoring >
Category 2: Arithmetic > Fractions >

Explanation: First, do what you can to simplify the equation:

((x)/(m))(m2 + n2 + k2) = xm + yn + zk

((x)/(m))m2 + ((x)/(m))n2 + ((x)/(m))k2 = xm + yn + zk

xm + ((x)/(m))n2 + ((x)/(m))k2 = xm + yn + zk

((x)/(m))n2 + ((x)/(m))k2 = yn + zk

It's not pretty, but it's a little simpler.

Statement (1) is insufficient: if ((z)/(k)) = ((x)/(m)), the equation can be further simplified:

((x)/(m))n2 + ((z)/(k))k2 = yn + zk

((x)/(m))n2 + zk = yn + zk

((x)/(m))n2 = yn

Statement (2) is also insufficient, though the equation can be simplified in the same way:

((y)/(n))n2 + ((x)/(m))k2 = yn + zk

yn + ((x)/(m))k2 = yn + zk

((x)/(m))k2 = zk

Taken together, the statements are sufficient. If ((z)/(k)) = ((x)/(m)) = ((y)/(n)), then

((x)/(m))n2 + ((x)/(m))k2 = yn + zk is the same as:

((y)/(n))n2 + ((z)/(k))k2 = yn + zk

yn + zk = yn + zk

That's true, so the answer to the question is "yes," and the correct choice is (C)

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