Official Guide Explanation:
Data Sufficiency #106




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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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