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## Official Guide Explanation:Problem Solving #130

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.

Question: 130
Page: 78
Difficulty: 6 (Moderately Difficult)
Category 1: Word Problems > Work Problems > 2 inputs
Category 2: Arithmetic > Ratio and Proportion >

Explanation: To find the ratio of X's time to Y and Z's time, you need both of those quantities. X's time is given, so find Y and Z's time, working together. The time it takes for two machines to do a job, working together, is ((AB)/(A + B)), where A and B are the amounts of time it takes for the two machines to do the job independently. So, A = 15 and B = 18, so the time is ((15(18))/(15 + 18)) = ((3(5)(18))/(3(5 + 6))) = (90/11). The ratio, then, is ((X)/(Y&Z)) = (12/((90/11))) = 12((11/90)) = ((6(2)(11))/(6(15))) = (22/15), choice (D).

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