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## Official Guide Explanation:Data Sufficiency #80

Background

This is just one of hundreds of free explanations I've created to the quantitative questions in The Official Guide for GMAT Review (12th ed.). Click the links on the question number, difficulty level, and categories to find explanations for other problems.

These are the same explanations that are featured in my "Guides to the Official Guide" PDF booklets. However, because of the limitations of HTML and cross-browser compatibility, some mathematical concepts, such as fractions and roots, do not display as clearly online.

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))?

r22?

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.