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Hard Solutions/Mixture Problem

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Hard Solutions/Mixture Problem

by rtaha2412 » Mon Nov 08, 2010 1:06 pm
Solution Y is 30 percent liquid X and 70 percent water. If 2 kilograms of water evaporate from 8 kilograms of solutions Y and 2 kilograms of solution Y are added to the remaining 6 kilograms of liquid, what percent of this new liquid solution is liquid X?

a 30%
b 33 1/3%
c 37 1/2%
d 40%
e 50%
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by MAAJ » Mon Nov 08, 2010 1:36 pm
Lets represent liquid Y:

Y = 0.3x + 0.7w

They don't say anything about weight so I'm assuming that each liquid weight proportional to its participation in the resulting solution. So if Y weights 8 kg then:

8kg = 0.3(8) + 0.7(8)
8kg = 2.4kg + 5.6kg (where 2.4kg is the weight of solution x and 5.6kg the weight of the water)

Then if we remove 2 kg of water:

(8-2) = 2.4 + (5.6-2)
6 = 2.4 + 3.6

Now we need to add 2kg of solution Y this is:

2 = 0.3(2) + 0.7(2)
2 = 0.6 + 1.4

Adding this 2 kg to the formula above we get:

6 + 2 = (2.4+0.6) + (3.6+1.4)
8 = 3 + 5

Now we need to find the percentage of X in the solution. This is:

3/8 = 37.5% = 37 1/2%

Correct Answer (C)
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by GMATGuruNY » Mon Nov 08, 2010 1:42 pm
rtaha2412 wrote:Solution Y is 30 percent liquid X and 70 percent water. If 2 kilograms of water evaporate from 8 kilograms of solutions Y and 2 kilograms of solution Y are added to the remaining 6 kilograms of liquid, what percent of this new liquid solution is liquid X?

a 30%
b 33 1/3%
c 37 1/2%
d 40%
e 50%
Using a little common sense, we can determine the correct answer quickly and without algebra.

The water that is being replaced is 2/8 = 25% of the total solution. This 25% is being replaced with solution Y. Thus, the percentage of each component of solution Y -- including the percentage of liquid X -- is going to increase by 25%.

Since liquid X is 30% of the original solution, its percentage in the new solution will increase by 25% to become 1.25*30 = 37.5%.

The correct answer is C.
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by MAAJ » Mon Nov 08, 2010 2:27 pm
GMATGuruNY wrote:
rtaha2412 wrote:Solution Y is 30 percent liquid X and 70 percent water. If 2 kilograms of water evaporate from 8 kilograms of solutions Y and 2 kilograms of solution Y are added to the remaining 6 kilograms of liquid, what percent of this new liquid solution is liquid X?

a 30%
b 33 1/3%
c 37 1/2%
d 40%
e 50%
Using a little common sense, we can determine the correct answer quickly and without algebra.

The water that is being replaced is 2/8 = 25% of the total solution. This 25% is being replaced with solution Y. Thus, the percentage of each component of solution Y -- including the percentage of liquid X -- is going to increase by 25%.

Since liquid X is 30% of the original solution, its percentage in the new solution will increase by 25% to become 1.25*30 = 37.5%.

The correct answer is C.
wow... this shortcut is nice TY!!!
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by saurabhmahajan » Mon Nov 08, 2010 11:24 pm
my way:

8 kg solution Y. in this 30% X so X = 2.4 kg
afetr removing 2 kg water again 2 kg added.
Again 2 kg of solution Y added, so 30% X now becomes = 0.6 kg
so total X= 2.4+0.6 = 3
now 3/8 = 37.5 %
Thanks and regards,
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by Zerks87 » Mon Jan 10, 2011 1:43 pm
GMATGuruNY wrote:
rtaha2412 wrote:Solution Y is 30 percent liquid X and 70 percent water. If 2 kilograms of water evaporate from 8 kilograms of solutions Y and 2 kilograms of solution Y are added to the remaining 6 kilograms of liquid, what percent of this new liquid solution is liquid X?

a 30%
b 33 1/3%
c 37 1/2%
d 40%
e 50%
Using a little common sense, we can determine the correct answer quickly and without algebra.

The water that is being replaced is 2/8 = 25% of the total solution. This 25% is being replaced with solution Y. Thus, the percentage of each component of solution Y -- including the percentage of liquid X -- is going to increase by 25%.

Since liquid X is 30% of the original solution, its percentage in the new solution will increase by 25% to become 1.25*30 = 37.5%.

The correct answer is C.
I really like this way but if you dont think to increase all the components of solution y other than the water by 25% than you can also think of it like this.

30% of 8 is 2.4. Therefore there are 2.4 kg's of solution Y in the 8 kg's of the combined solution. Since after removing 2 kg's of water there are only 6kg's of the solution, that means that solution y is 2.4/6 or 40% of the solution.

Since we are adding 2 kg's of the old solution, the percentage of solution y in in the new mixture cant increase and wont stay the same, eliminate A and E.

BUt it will also be skewed towards 40% of the solution since you are adding 2 kg's to a 6 kg solution. The only answer choice that satisfies this condition is C
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by kamalakarthi » Sat Mar 19, 2011 8:30 pm
Mitch,

I got the answer by substituting the numbers as per questions. However Can you please explain again the following " Thus, the percentage of each component of solution Y -- including the percentage of liquid X -- is going to increase by 25%. "
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by MM_Ed » Fri Aug 12, 2011 9:33 pm
X is never removed from the original 8 kg.
X in 8 kg of Y = 2.4 kg
X in 2 kg of Y = 0.6 kg
Total X = 3.0 kg
Final solution = 8 kg - 2 kg + 2 kg = 8 kg
% of X = 3/8 = 37.5%
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by ArunangsuSahu » Sun Jan 01, 2012 9:21 am
X W
2.4 5.6-----INITIAL
2.4 3.6-----AFTER EVAPORATION OF WATER
2.4+.6 3.6+1.4--AFTER ADDING 2 LITRES OF THE SOLN.
% OF X=3/8=37.5
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by him1985 » Mon Mar 12, 2012 4:45 am
C. 37.5% is the Answer

8 kg solution Y. in this 30% X so X = 2.4 kg
afetr removing 2 kg water again 2 kg added.
Again 2 kg of solution Y added, so 30% X now becomes = 0.6 kg
so total X= 2.4+0.6 = 3
now 3/8 = 37.5 %
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by ronnie1985 » Fri Mar 30, 2012 7:26 am
Should be solved using table to make it simpler and faster
37.5% is the answer.
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by Lifetron » Thu Jul 26, 2012 9:20 pm
37.5 !
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by elenaelena » Mon Jul 30, 2012 3:55 am
I wish it took me less time, but im glad to get it right!:)
The problem is easy,but takes time to realise what to do...took me 5 minutes:(
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by mparakala » Tue Dec 11, 2012 7:10 pm
out of 8kilogm water , 30% = 2.4 is liqx and 70% = 5.6 of water
then water evaporates -2.0
remaining 3.6
now 2 more of sol Y are added
so, 0.6 of liq x and 1.4 of water

total: 2.4 + 0.6 = 3 of liq x = a% of 8 (total)
= 37.5%

c
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by ritzzzr » Wed Feb 27, 2013 3:17 am
ans is 37.5%
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