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## Official Guide Explanation:Problem Solving #107

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: 107
Page: 75
Difficulty: 5 (Moderate)
Category 1: Algebra > Simplifying Algebraic Expressions >
Category 2: Algebra > Linear Equations-One Unk >

Explanation: It may look like the two fractions (3/(x)) and ((y)/4) can be added to create ((3 + y)/(x + 4)), but they can't, not without a common denominator. Instead, solve each of the first two equations for the variable in each, then plug in to ((3 + y)/(x + 4)):

(3/(x)) = 2

2x = 3

x = (3/2)

((y)/4) = 3

y = 12

((3 + y)/(x + 4)) = ((3 + 12)/((3/2) + 4)) = (15/((3/2) + (8/2))) = (15/((11/2))) = 15((2/11)) = (30/11), choice (D).

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