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Liters added to solution ---chart possible?

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Liters added to solution ---chart possible?

by Goldfinger2001 » Wed Feb 23, 2011 12:47 am
How many liters of pure alcohol must be added toa 100 liter solution that is 20 percent alcohol in order to produce a soluton that is 25 percent alcohol?

a) 7/2
b) 5
c) 20/3
d) 8
e) 39/4

OA: C

When I take a look at the explaination, the formula gets clear, but its hard to memorize for me.
Is there no scheme for a chart / table I could draw to get a better overview regarding this problem? I tried to figure out a table/chart.. but that doesn't work...
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by anshumishra » Wed Feb 23, 2011 2:19 am
Goldfinger2001 wrote:How many liters of pure alcohol must be added toa 100 liter solution that is 20 percent alcohol in order to produce a soluton that is 25 percent alcohol?

a) 7/2
b) 5
c) 20/3
d) 8
e) 39/4

OA: C

When I take a look at the explaination, the formula gets clear, but its hard to memorize for me.
Is there no scheme for a chart / table I could draw to get a better overview regarding this problem? I tried to figure out a table/chart.. but that doesn't work...
In the beginning there is 20 liters of alcohol out of 100 liters of the soln

Let we added x liter of alcohol to make it 25% alcohol solution.

vloume of soln = 100 + x
volume of alcohol = 20 + x

since volume of alcohol is 25% of volume of the soln
=> (20+x) = (100+x)/4
=> 80 + 4x = 100 + x
=> 3x = 20
=> x = 20/3

C
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Anshu

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by anshumishra » Wed Feb 23, 2011 2:27 am
You may represent it in a table like this :

-----------------------------------------------------
Solution -------------- Alcohol -----------------

100 -------------------- 20 ----------------------

100+x ----------------- 20+x -------------------

..................................................................

Now, similarly; 20+x = 25% of 100+x = (100+x)/4
=> x = 20/3.
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by Goldfinger2001 » Wed Feb 23, 2011 3:07 am
Thanks anshumishra,
I like your approach!
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by sanju09 » Wed Feb 23, 2011 3:25 am
Goldfinger2001 wrote:How many liters of pure alcohol must be added toa 100 liter solution that is 20 percent alcohol in order to produce a soluton that is 25 percent alcohol?

a) 7/2
b) 5
c) 20/3
d) 8
e) 39/4

OA: C

When I take a look at the explaination, the formula gets clear, but its hard to memorize for me.
Is there no scheme for a chart / table I could draw to get a better overview regarding this problem? I tried to figure out a table/chart.. but that doesn't work...

Let x litres of pure alcohol must be added to a 100 litre solution that is 20 percent alcohol in order to produce a solution that is 25 percent alcohol. The alcohol contents in the new solution of x + 100 are x + 20 such that x + 20 = 25 percent of (x + 100)

Or x + 20 = ¼ (x + 100)

Or 4 x + 80 = x + 100

Or 3 x = 20

Or x = [spoiler]20/3


C[/spoiler]
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by GMATGuruNY » Wed Feb 23, 2011 6:22 am
Goldfinger2001 wrote:How many liters of pure alcohol must be added toa 100 liter solution that is 20 percent alcohol in order to produce a soluton that is 25 percent alcohol?

a) 7/2
b) 5
c) 20/3
d) 8
e) 39/4

OA: C

When I take a look at the explaination, the formula gets clear, but its hard to memorize for me.
Is there no scheme for a chart / table I could draw to get a better overview regarding this problem? I tried to figure out a table/chart.. but that doesn't work...
An easy and efficient approach would be to plug in the answer choices.

Answer choice C: 20/3 liters alcohol must be added
New amount of alcohol = 20 + 20/3 = 80/3.
Total solution = 100 + 20/3 = 320/3.
Alcohol/Solution = (80/3)/(320/3) = 1/4 = 25%.

The correct answer is C.
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