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ratio of soap to alcohol to water

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by rookiez » Fri Jun 26, 2009 7:00 am
Que from OG11 PS 196

196. 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

OA is E

How to solve this and what does it mean for a ratio to be doubled or halved?
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by truplayer256 » Fri Jun 26, 2009 7:21 am
Soap= 2x
Alcohol= 50x
Water= 100x

Ratio of Soap to Alcohol= 2x/50x=1/25---> Doubled----> 2/25

Ratio of Soap to Water= 2x/100x=1/50---> Halved----> 1/100

Soap/100=2/25

Soap= 8 cubic centimeters.

8/Water= 1/100

Water= 800 cubic centimeters. E.
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by Robinmrtha » Fri Jun 26, 2009 7:22 am
Suppose soap =s
alcohol=a
water=w
Given,
s:a:w= 2:50:100

ratio of soap to alcohol is doubled means
s:a=2:50 X 2 =4:50 new ratio
again
ratio of soap to water is halved means
s:w=4:50 X 1/2 =1 :100
to combine the ratio make the s of both new ratio mentioned above equal
to do so...multiply the numerator and denominator of s:w by 4 = 1:100 X 4/4
=4:400
Now the altered ratio is s:a:w = 4:50:400
So alcohol is 100
i.e. 50x = 100
therefore x=2
now multiply corresponding ratio of w i.e. 400 with 2
gives 800

So the answer is E
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by rookiez » Fri Jun 26, 2009 8:47 am
Thanks Guys,
These solutions have helped me.

I mis-read the que many-a-times. It's now clear from your solutions.
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hi

by Jeff@TargetTestPrep » Sat Jul 14, 2018 6:42 pm
rookiez wrote:Que from OG11 PS 196

196. 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
The first thing we want to do is set up the ratio of the original solution, using variable multipliers.

soap : alcohol : water = 2x : 50x : 100x

We are given that the ratio of soap to alcohol is doubled. If we double the ratio we multiply the entire ratio by 2, so we have:

soap/alcohol = 2(2x/50x) = 4x/50x = 2x/25x

Next we are given that the ratio of soap to water is halved. If we halve the ratio, we multiply the entire ratio by 1/2, so we have:

soap/water = (1/2)(2x/100x) = 2x/200x

Now we can set up the ratio of the altered solution.

soap : alcohol : water = 2x : 25x : 200x

Lastly, we are given that the altered solution will contain 100 cubic centimeters of alcohol, thus:

25x = 100

x = 4

Thus, the altered solution will contain (200)(4) = 800 cubic centimeters of water.

Answer: E

Jeffrey Miller
Head of GMAT Instruction
[email protected]

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answer

by Karishma BL » Mon Jul 16, 2018 4:39 am
rookiez wrote:Que from OG11 PS 196

196. 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

OA is E

How to solve this and what does it mean for a ratio to be doubled or halved?
Note that a ratio A:B can be written as A/B.
When you double a ratio, you get 2A/B
When you halve a ratio, you get A/2B

Also note that A:B cannot be doubled as 2A:2B because this is the same as A:B. The ratio stays the same if you multiply/divide each term by the same number.

Soap : Alcohol : Water = 2: 50: 100

So Soap : Alcohol = 2:50 = 2/50
If you double it, you get Soap : Alcohol = 2*2/50 = 4/50

Also, Soap : Water = 2/100
If you halve it, you get 2/200

If alcohol is 100 i.e. 2*50, soap will be 2*4 = 8 (here, 2 is the multiplier)
If soap is 8 i.e. 4*2, water will be 4*200 = 800 cm3 (here, 4 is the multiplier)

Answer (E)

For more, check the ratios post I wrote for Veritas Prep: https://www.veritasprep.com/blog/2011/0 ... of-ratios/
Karishma
Private Tutor for GMAT
Contact: [email protected]
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