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Ratio Problem !!

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Ratio Problem !!

by gmatpup » Tue Nov 08, 2011 6:30 pm
The ratio, by volume, of soap to alcohol to water in a certain solution is 2:50:100. The solution will be altered so that the ratio of soap to alcohol is doubled while the ratio of soap to water is halved. If the altered solution will contain 100 cubic cm of alcohol, how many cubic cm of water will it contain?

A. 50

B. 200

C. 400

D. 625

E. 800


It says the answer is E but I am completely lost. I thought I could plug in numbers but it is not working for me. Someone please explain :) thank you!
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by GMATGuruNY » Tue Nov 08, 2011 6:49 pm
gmatpup wrote:The ratio, by volume, of soap to alcohol to water in a certain solution is 2:50:100. The solution will be altered so that the ratio of soap to alcohol is doubled while the ratio of soap to water is halved. If the altered solution will contain 100 cubic cm of alcohol, how many cubic cm of water will it contain?

A. 50

B. 200

C. 400

D. 625

E. 800


It says the answer is E but I am completely lost. I thought I could plug in numbers but it is not working for me. Someone please explain :) thank you!
Let S = soap, A = alcohol, and W = water.

Original S:A = 2:50.
With the amount of soap doubled, new S:A = 4:50 = 2:25.

Original S:W = 2:100.
With the amount of soap halved, new S:W = 1:100 = 2:200.

Combining the ratios, new S:A:W = 2:25:200.
Since the actual amount of alcohol = 100, and S:A:W = 2:25:200 = 8:100:800, the actual amount of water = 800.

The correct answer is E.
Last edited by GMATGuruNY on Tue Nov 08, 2011 6:57 pm, edited 1 time in total.
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by gmatpup » Tue Nov 08, 2011 6:55 pm
WOW! That makes so much sense now... What I kept doing wrong was doubling BOTH or halving BOTH.. now I see what to do :) Thanks a million!!
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by neelgandham » Wed Nov 09, 2011 1:54 am
Hey gmatpup,

You might want to have a look at the below urls for different approaches to the same problem.

https://www.beatthegmat.com/soap-alcohol ... 94373.html
https://www.beatthegmat.com/ratio-of-soa ... 39493.html
https://www.beatthegmat.com/ratio-proble ... 77438.html
https://www.beatthegmat.com/og-problem-192-t70758.html
Anil Gandham
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by ariz » Wed Nov 09, 2011 11:12 am
Man you are all over this. I'd be surprise if you don't score at least 750 on the GMAT
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