Official Guide Explanation:
Data Sufficiency #162




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Solution and Metadata

Question: 162
Page: 287
Difficulty: 6 (Moderately Difficult)
Category 1: Arithmetic > Powers and Roots of Numbers > Roots
Category 2: Algebra > Inequalities > other

Explanation: It's important to note that both n and k are positive. Because both are positive, meaning that all of the terms on both sides of the inequality are positive, we can simplify the inequality by squaring both sides:

rt[n + k] > 2 rt[n] ?

( rt[n + k])2 > (2 rt[n])2 ?

n + k > 4n ?

k > 3n ?

More simply, the question is asking whether k is greater than 3n.

Statement (1) answers that question directly, so it is sufficient.

Statement (2) is insufficient. Simplify it, and it says that k > 2n. If k is greater than 2n, it might be greater than 3n, but it might not be--it might be equal to 2.5n. Choice (A) is correct.

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