Official Guide Explanation:
Data Sufficiency #109




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Solution and Metadata

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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