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## Official Guide Explanation:Problem Solving #195

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: 195
Page: 180
Difficulty: 5 (Moderate)
Category 1: Arithmetic > Ratio and Proportion >
Category 2: Word Problems > Rate Problems > other

Explanation: Say that the current price of the towels is x. That means that, when increased, the price of the towels will be x + 1. The number of towels that can be purchased for \$120 when the price is x is (120/(x)), and the number of towels that can be purchased when the price is increased is (120/(x + 1)). Since 10 fewer towels can be purchased for \$120 at the higher price, we can set up an equation:

(120/(x)) - 10 = (120/(x + 1))

((120 - 10x)/(x)) = (120/(x + 1))

(120 - 10x)(x + 1) = 120x

120x - 10x2 + 120 - 10x = 120x

-10x2-10x + 120 = 0

x2 + x - 12 = 0

(x + 4)(x - 3)

x = 3 or x= - 4

Since towels can't have negative prices, the price per towel must be \$3, choice (C).

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