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ps - mixture

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ccassel: Master | Next Rank: 500 Posts; Posts: 118; Joined: Wed Mar 16, 2011 1:44 pmFollowed by: 2 members; Location: Canada; GMAT Score:530

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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Source: Beat The GMAT — Problem Solving | Mon Apr 18, 2011 5:49 pm

vineeshp: Legendary Member; Posts: 965; Joined: Thu Jan 28, 2010 12:52 amFollowed by: 34 members; Thanked: 156 times; GMAT Score:720

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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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

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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ccassel: Master | Next Rank: 500 Posts; Posts: 118; Joined: Wed Mar 16, 2011 1:44 pmFollowed by: 2 members; Location: Canada; GMAT Score:530

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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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

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.

Attachments

Brent Hanneson - Creator of GMATPrepNow.com

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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 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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ccassel: Master | Next Rank: 500 Posts; Posts: 118; Joined: Wed Mar 16, 2011 1:44 pmFollowed by: 2 members; Location: Canada; GMAT Score:530

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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