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## Official Guide Explanation:Problem Solving #204

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: 204
Page: 181
Difficulty: 6 (Moderately Difficult)
Category 1: Arithmetic > Ratio and Proportion >
Category 2: Word Problems > Work Problems > 2 inputs
Category 3: Word Problems > Rate Problems > other

Explanation: If John and Mary were each paid x dollars, and worked 10 and (10 - 2) = 8 hours, respectively, their hourly rates were as follows. John's was: ((x)/10), and Mary's was ((x)/8). If Mary gave John y dollars of her payment, their respective rates were ((x + y)/10) and ((x - y)/8). Since those are equal, we can set up an equation to solve for x in terms of y:

((x + y)/10) = ((x - y)/8)

10(x - y) = 8(x + y)

10x - 10y = 8x + 8y

2x = 18y

x = 9y

We're looking for the amount John was paid in advance, which is equal to x, so the answer is 9y, choice (E).

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