Confusing Ratio!!

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sodha.rakesh: Junior | Next Rank: 30 Posts; Posts: 11; Joined: Sun Nov 21, 2010 8:07 pm; Thanked: 2 times

by sodha.rakesh » Tue Jan 25, 2011 6:59 am

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 centimeters of alcohol, how many cubic centimeters of water will it contain?

A. 50
B. 200
C. 400
D. 625
E. 800

IMO. E

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Source: Beat The GMAT — Problem Solving | Tue Jan 25, 2011 6:59 am

Target2009: Legendary Member; Posts: 574; Joined: Sat Oct 31, 2009 1:47 pmFollowed by: 5 members; Location: USA; Thanked: 29 times

by Target2009 » Tue Jan 25, 2011 7:16 am

its E:
See the detail solution : https://www.beatthegmat.com/og-problem-192-t70758.html

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Abhishek
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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Tue Jan 25, 2011 7:24 am

sodha.rakesh 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 centimeters of alcohol, how many cubic centimeters of water will it contain?

A. 50
B. 200
C. 400
D. 625
E. 800

IMO. E

Original S:A:W = 2:50:100.

Original S:A = 2/50.
To double this ratio, we multiply by 2:
2*(2/50) = 4/50 = 2/25 = 2:25.

So at this point the ratio of S:A:W = 2:25:100.

Original S:W = 2/100.
To halve this ratio, we multiply by 1/2:
(1/2)*(2/100) = 2/200 = 2:200.

So the final ratio of S:A:W = 2:25:200.

Since the actual amount of A = 100, every value in the ratio is multiplied by 4:
S:A:W = 2:25:200 = 8

800.
Thus, W = 800.

The correct answer is E.

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