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Official Guide Explanation:Data Sufficiency #83

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: 83
Page: 280
Difficulty: 5 (Moderate)
Category 1: Algebra > Simplifying Algebraic Expressions >

Explanation: When you see an expression with the same variables appearing in multiple places, it's probably something you can factor. This is the case with Statement (1):

ab + cd + ac + bd = 6

a(b + c) + d(b + c) = 6

(b + c)(a + d) = 6

As it is, that's not enough information to find b + c; we need a + d. Statement (2) offers a + d, but without the connection offered by (1), that's irrelevant.

Taken together, the statements are sufficient: if (b + c)(a + d) = 6 and a + d = 4, then 4(b + c) = 6, or b + c = (3/2). Choice (C) is correct.

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