Mixture

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heshamelaziry: Legendary Member; Posts: 869; Joined: Wed Aug 26, 2009 3:49 pmFollowed by: 3 members; Location: California; Thanked: 13 times

by heshamelaziry » Sat Oct 31, 2009 1:12 pm

Solution Y is 30 percent liquid X and 70 percent water. If 2 kilograms of water evaporate from 8 kilograms of solution Y and 2 kilograms of solution Y are added to the remaining 6 kilograms of liquid, what percent of this new solution is liquid X?

(A) 30%
(B) 30.3%
(C) 37.5%
(D) 40%
(E) 50%

Please provide solution

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Source: Beat The GMAT — Problem Solving | Sat Oct 31, 2009 1:12 pm

Testluv: GMAT Instructor; Posts: 1302; Joined: Mon Oct 19, 2009 2:13 pmFollowed by: 164 members; Location: Toronto; Thanked: 539 times; GMAT Score:800

by Testluv » Sat Oct 31, 2009 4:34 pm

Solution Y is 30 percent liquid X and 70 percent water. If 2 kilograms of water evaporate from 8 kilograms of solution Y and 2 kilograms of solution Y are added to the remaining 6 kilograms of liquid, what percent of this new solution is liquid X?

(A) 30%
(B) 30.3%
(C) 37.5%
(D) 40%
(E) 50%

Please provide solution

Hi heshamelaziry,

all we need to do on this one is take some time to understand the setup, break the problem down into parts, and then be organized while making the calculations (have to be organized b/c there are a lot of trap answer choices here that are intended to catch people that missed an operation).

Solution Y is 3/10 liquid X and 7/10 water.

We start with 8kg of the solution.
So the solution is 3/10 * 8 = 2.4kg of liquid X.
Therefore there are 8-2.4 = 5.6kg water.

From this we subtract the 2kg water that has evaporated, leaving 5.6-2= 3.6 kg water.

We now have 2.4 kg liquid X and 3.6 kg water.

To this we now add 2kg of solution. So that would be 0.6kg of liquid X and 1.4 kg of water that we are adding (solution is 3/10 liquid X and 7/10 water).

So we now have 2.4 +0.6 = 3 kg of liquid X.
And 3.6+1.4=5kg of water.
And we have 8kg in total.
So the percent of this new solution that is liquid X is: 3/8 =37.5%

Kaplan Teacher in Toronto

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mp2437: Master | Next Rank: 500 Posts; Posts: 177; Joined: Thu Aug 14, 2008 11:59 am; Thanked: 25 times

by mp2437 » Sat Oct 31, 2009 4:39 pm

You initially have 8 kg of solution Y. You are told that 70% is water (lets call it w), 30% is liquid x, so you have 5.6kg of w and 2.4kg of x.

Then you are told that 2kg of w is removed from the solution, leaving you with 5.6 - 2 = 3.6kg of w, and 2.4kg of x, for a total of 6kg.

Finally, they tell you that another 2kg solution of Y is added to the solution you have above. So out of the 2kg, 70%, or 1.4kg is w, and 30%, or 0.6kg, is x.

So previously you have 3.6kg water and 2.4kg of liquid x, now you add 1.4kg of water and 0.6kg of x.

total amount of water = 3.6 + 1.4 = 5 kg
total amount of liquid x= 2.4 + 0.6 = 3 kg.
total amount of solution = 5 + 3 = 8kg.

% of liquid in this new solution = 3 / 8 = 37.5%
Choice C.

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heshamelaziry: Legendary Member; Posts: 869; Joined: Wed Aug 26, 2009 3:49 pmFollowed by: 3 members; Location: California; Thanked: 13 times

by heshamelaziry » Sat Oct 31, 2009 4:57 pm

Testluv wrote:
Solution Y is 30 percent liquid X and 70 percent water. If 2 kilograms of water evaporate from 8 kilograms of solution Y and 2 kilograms of solution Y are added to the remaining 6 kilograms of liquid, what percent of this new solution is liquid X?

(A) 30%
(B) 30.3%
(C) 37.5%
(D) 40%
(E) 50%

Please provide solution
Hi heshamelaziry,

all we need to do on this one is take some time to understand the setup, break the problem down into parts, and then be organized while making the calculations (have to be organized b/c there are a lot of trap answer choices here that are intended to catch people that missed an operation).

Solution Y is 3/10 liquid X and 7/10 water.

We start with 8kg of the solution.
So the solution is 3/10 * 8 = 2.4kg of liquid X.
Therefore there are 8-2.4 = 5.6kg water.

From this we subtract the 2kg water that has evaporated, leaving 5.6-2= 3.6 kg water.

We now have 2.4 kg liquid X and 3.6 kg water.

To this we now add 2kg of solution. So that would be 0.6kg of liquid X and 1.4 kg of water that we are adding (solution is 3/10 liquid X and 7/10 water).

So we now have 2.4 +0.6 = 3 kg of liquid X.
And 3.6+1.4=5kg of water.
And we have 8kg in total.
So the percent of this new solution that is liquid X is: 3/8 =37.5%

I broke the problem down to these same parts, but did one wrong calculation.

THANKS

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