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## Official Guide Explanation:Problem Solving #91

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: 91
Page: 165
Difficulty: 4 (Moderately Easy)
Category 1: Algebra > Linear Equations-Two Unk >

Explanation: If the price of a map is m and the price of a book is b , we can set up two equations:

12m + 10b = 38

20m + 15b = 60

We're looking for b - m, the difference in the prices of each type of product.

The easiest way to combine the two equations is to start by multiplying the first by (3/2), so that both equations contain a 15b:

18m + 15b = 57

We can now subtract this equation from the second:

2m = 3

m = 1.5

Substitute m into the second equation to find b:

20(1.5) + 15b = 60

30 + 15b = 60

15b = 30

b = 2

The difference, then, is 2 - 1.5 = 0.5, choice (B).

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