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## Official Guide Explanation:Data Sufficiency #105

Background

This is just one of hundreds of free explanations I've created to the quantitative questions in The Official Guide for GMAT Quantitative Review (2nd 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: 105
Page: 160
Difficulty: 5 (Moderate)
Category 1: Algebra > Equations >

Explanation: Statement (1) is not sufficient: whether r is positive depends on whether t is positive, which we don't know. Statement (2) is also not sufficient, as again, we know nothing about t.

Taken together, the statements are sufficient. The two equations can be combined to form one. If r + t = 7, then t = 7 - r, which can be substituted into the equation in (1). If rt = 12 and t = 7 - r, then:

r(7 - r) = 12

7r - r2 = 12

-r2 + 7r - 12 = 0

r2-7r + 12 = 0

(r - 3)(r - 4) = 0

r = 3 or r = 4

In either case, r is positive, so choice (C) is correct.

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