Official Guide Explanation:
Data Sufficiency #80




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Solution and Metadata

Question: 80
Page: 279
Difficulty: 5 (Moderate)
Category 1: Arithmetic > Ratio and Proportion >
Category 2: Algebra > Inequalities > other

Explanation: Since both variables must be positive, we can simplify the inequality by cross - multiplying:

((r)/(s)) < ((s)/(r))?


Again, since both variables must be positive, the only way that s2 is greater than r2 is if s itself is greater than r. So really, the question is simply:

rStatement (1) is sufficient. Simplify by multiplying both sides by 3:

((r)/(3s)) = (1/4)

((r)/(s)) = (3/4)

Given the ratio of r to s, we know which is greater, so we can answer the question.

Statement (2) is also sufficient. If s is 4 greater than r, it is greater than r. Choice (D) is correct.

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