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ps - mixture

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by ccassel » Mon Apr 18, 2011 5:49 pm
How would you explain the answer to this question?

How many liters of pure alcohol must be added to a 100-liter solution that is 20% alcohol in order to produce a solution that is 25% alcohol?

A. 7/2
B. 5
C. 20/3
D. 8
E. 39/4

Answer is C
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by vineeshp » Mon Apr 18, 2011 6:11 pm
Thanks for the good numbers. :)

100-liter solution that is 20% alcohol. That means 20 litres of alcohol is there in 100 litres.

Now we need to add x litres of pure alcohol into the 100 litres solution such that
20 + x litres in 100 + x litres gives us 25 %.
(20 + x)/(100 + x) = 25/100 = 1/4
Cross multiplying,
(20 + x) * 4 = 100 + x
80 + 4x = 100 + x
4x-x = 100 -80
3x = 20
x = 20/3

C
Vineesh,
Just telling you what I know and think. I am not the expert. :)
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by Anurag@Gurome » Mon Apr 18, 2011 8:05 pm
ccassel wrote:How would you explain the answer to this question?

How many liters of pure alcohol must be added to a 100-liter solution that is 20% alcohol in order to produce a solution that is 25% alcohol?

A. 7/2
B. 5
C. 20/3
D. 8
E. 39/4

Answer is C
Let x liters of pure alcohol must be added to a 100-liter solution.
0.2 (100) + 1(x) = 0.25(100 + x)
75x = 500
x = 20/3

The correct answer is C.
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by ccassel » Tue Apr 19, 2011 8:56 am
Are these 2 different ways of solving the question?

What equations are you working from?

Thanks in advance.

Cheers,
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by Brent@GMATPrepNow » Tue Apr 19, 2011 9:23 am
ccassel wrote:How would you explain the answer to this question?

How many liters of pure alcohol must be added to a 100-liter solution that is 20% alcohol in order to produce a solution that is 25% alcohol?

A. 7/2
B. 5
C. 20/3
D. 8
E. 39/4

Answer is C
I find that it often helps to solve mixture problems by sketching each solution with the parts separated.
This makes it easy to see what happens when you combine solutions.
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by GMATGuruNY » Tue Apr 19, 2011 10:20 am
ccassel wrote:How would you explain the answer to this question?

How many liters of pure alcohol must be added to a 100-liter solution that is 20% alcohol in order to produce a solution that is 25% alcohol?

A. 7/2
B. 5
C. 20/3
D. 8
E. 39/4

Answer is C
The 100-liter solution contains 20 liters of alcohol.

We can plug in the answers, which represent the amount of pure alcohol that needs to be added.

Answer choice C: 20/3 of pure alcohol.
Total alcohol = 20 + 20/3 = 80/3 liters.
Total solution = 100 + 20/3 = 320/3 liters.
Alcohol/total = (80/3)/(320/3) = 1/4 = 25%.
Success!

The correct answer is C.

Another easy approach:
The 100-liter solution contains 20 liters alcohol, 80 liters non-alcohol.
The 80 liters of non-alcohol is not changing.
Since the final mixture must be 25% alcohol, the 80 liters of non-alochol must be 75% of the final mixture.
80 = .75x
x = 80/.75 = 320/3 liters.

Since the final mixture must be 320/3 liters, the amount of alcohol that must be added to the 100-liter solution = 320/3 - 100 = 20/3 liters.
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by ccassel » Tue Apr 19, 2011 12:04 pm
Total alcohol/Total Solution = % Alcohol in Solution. (Diagram helps enormously!)

Great solutions! Thanks for the tips.

Cheers,
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