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## Official Guide Explanation:Problem Solving #213

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: 213
Page: 183
Difficulty: 7 (Very Difficult)
Category 1: Algebra > Equations >
Category 2: Word Problems > Work Problems > 2 inputs
Category 3: Arithmetic > Fractions >

Explanation: If the reciprocal of r is equal to the sum of the reciprocals of x and y, we can write an equation as follows:

(1/(r)) = (1/(x)) + (1/(y))

(1/(r)) = ((y)/(xy)) + ((x)/(xy)) = ((x + y)/(xy))

r = ((xy)/(x + y)), choice (D).

You may notice that this is the same equation as the one for combined rate, where x and y stand in for the individual rates, and r is equivalent to the combined rate.

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