Official Guide Explanation:
Problem Solving #192




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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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