Official Guide Explanation:
Data Sufficiency #121




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Solution and Metadata

Question: 121
Page: 161
Difficulty: 6 (Moderately Difficult)
Category 1: Arithmetic > Powers and Roots of Numbers > Powers
Category 2: Algebra > Exponents >

Explanation: Statement (1) is insufficient. Substitute the equation into the inequality:

xy < yx?

(y2)y < y(y2)?

y2y < y(y2)?

2y < y2?

That simplifies the question somewhat, but without knowing more about y, it isn't enough to answer the question.

Statement (2) is insufficient, as it contains no information about x.

Taken together, the statements are sufficient. First, look at the simplifed result of (1):

Is 2y < y2?

If y > 2, the answer to this question will always be "yes." Because you know that y is positive, you can divide both sides by y, resulting in:

Is y > 2?

(2) answers that question directly, so the correct choice is (C).

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