Official Guide Explanation:
Problem Solving #192

 

 

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.

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Solution and Metadata

Question: 192
Page: 179
Difficulty: 6 (Moderately Difficult)
Category 1: Arithmetic > Ratio and Proportion >
Category 2: Word Problems > Rate Problems > other

Explanation: A three - way ratio is really just two two - way ratios jammed together. So, the original soap to alcohol ratio was 2:50. If that ratio is doubled, the new soap to alcohol ratio is 4:50. The original soap to water ratio was 2:100; if that ratio is halved, the new one is 1:100. However, if the new ratios are to be put back together, the common member (soap) must be the same number. So, we can change the new soap to water ratio from 1:100 to 4:400, making the new soap to alcohol to water ratio 4:50:400. In other words, there's 8 times as much water as alcohol, so if the new solution contains 100 cubic centimeters of alcohol, it will contain 100(8) = 800 cubic centimeters of water, choice (E).

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