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## Official Guide Explanation:Problem Solving #115

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.

Solution and Metadata

Question: 115
Page: 76
Difficulty: 5 (Moderate)
Category 1: Algebra > Linear Equations-Two Unk >
Category 2: Algebra > Equations >

Explanation: This question throws you a curve with the addition of y to Fred's age at the end, but until that point, it's very much the other questions you've seen with two people's ages. As usual, translate each statement into algebra:

d + f = y

d = f + 12

Then substitute one equation into the other, and solve:

(f + 12) + f = y

2f + 12 = y

2f = y - 12

f = ((y - 12)/2)

Now that Fred's age is established in terms of y, add the "y years from now:"

f + y = ((y - 12)/2) + y = ((y - 12)/2) + ((2y)/2) = ((y - 12 + 2y)/2) = ((3y - 12)/2) = ((3y)/2) - (12/2) = ((3y)/2) - 6, choice (D).

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