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If after 200 grams of water were added to the 24%-solution [#permalink]

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03 Aug 2009, 22:09

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65% (02:42) correct
35% (02:00) wrong based on 69 sessions

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If after 200 grams of water were added to the 24%-solution of alcohol, the strength of the solution decreased by one-third, how much of the 24%-solution was used?

A. 180 grams B. 220 grams C. 250 grams D. 350 grams E. 400 grams

There definitely is something wrong with this question....if the question is asking how much of the original solution was used...then it must be 400 gms...

I approach mixtures as weighted average problems. I define y to be the amount (in grams) of 24% before water was added. After adding water the solution is reduced by 1/3 and we have 2/3X24% strength of the new solutiion. The equation will be the following"

Another 10sec approach: decrease in concentration by 1/3 means increase in volume by 1/3. So, added water is 1/3 of new total volume and 24-% alcohol solution is 2/3 (twice as much as added water). Therefore, answer is 400g
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Another 10sec approach: decrease in concentration by 1/3 means increase in volume by 1/3. So, added water is 1/3 of new total volume and 24-% alcohol solution is 2/3 (twice as much as added water). Therefore, answer is 400g

HI Walker, decrease in concentration by 1/3 means increase in volume by 1/3 => this is very clear May question may sound stupid but how do you come to he fact that water added is 1/3 of new total?? Thx for your help

Another 10sec approach: decrease in concentration by 1/3 means increase in volume by 1/3. So, added water is 1/3 of new total volume and 24-% alcohol solution is 2/3 (twice as much as added water). Therefore, answer is 400g

Why do you all assume that the answer should be in grams? I also got 400 gram...but they ask about percentage...so they want to know how much 400 gram represent out of total 600 gram (after water is added)...which is 66.6%...there is a typo in choice B (it should be 66.6% instead of 36.6%)....

May question may sound stupid but how do you come to he fact that water added is 1/3 of new total??

Ok. Concentration decreases by 1/3. In other words, new volume is larger than old volume by 1/3 of new volume. Visually: XX - old volume, XXX - new volume.

Some example:

Concentration decrease by 4/5 (in 5 times). new volume is larger than old volume by 4/5 of new volume. Visually: X - old volume; XXXXX - new volume.
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...so they want to know how much 400 gram represent out of total 600 gram ....

They ask: "... how much of the 24%-solution was used?" It would be clear if we had 600g of solution and used 400g to prepare 1/3 reduced solution. Honesty, I don't think it is a real GMAT question.
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...so they want to know how much 400 gram represent out of total 600 gram ....

They ask: "... how much of the 24%-solution was used?" It would be clear if we had 600g of solution and used 400g to prepare 1/3 reduced solution. Honesty, I don't think it is a real GMAT question.

The new reduced solution consists of 2/3 of 24% solution (400g) and 1/3 of water (200g)...I thought they were asking about the composition of the new solution...that 24% solution represents 2/3 of the new reduced one...My interpretation was wrong (English is not my native language), especially given the fact that 66.6% is not among the choices...Thanks for clarifying it to me.

My interpretation was wrong (English is not my native language)...

I'm not a native English speaker too What I know GMAT is trying to use clear unambiguous language. I guess it is a poorly written GMAT-like question, although it has a good idea.
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My interpretation was wrong (English is not my native language)...

I'm not a native English speaker too What I know GMAT is trying to use clear unambiguous language. I guess it is a poorly written GMAT-like question, although it has a good idea.

As a non native speaker to a non native speaker, what % they ment? I am confused. I got 400 gram but the answers are %! Percent of what?! I really would like to know the answer if anyone has it...

As a non native speaker to a non native speaker, what % they ment? I am confused. I got 400 gram but the answers are %! Percent of what?! I really would like to know the answer if anyone has it...

Don't worry, it is not a GMAT question. The base of a GMAT question of 50-51 level is a TRICK not misunderstanding.
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If after 200 grams of water were added to the 24%-solution of alcohol, the strength of the solution decreased by one-third, how much of the 24%-solution was used?

A. 180 grams B. 220 grams C. 250 grams D. 350 grams E. 400 grams

Let the weight of 24% solution used be \(x\) grams, weight of alcohol in it would be \(0.24x\). As in final solution strength decreased be 1/3 thus it became 24*2/3=16%.

Set the equation: \(0.24x=0.16(x+200)\), the weight of 16% alcohol in \(x+200\) grams of new solution comes only from (equals to) 24% alcohol in \(x\) grams of strong (initial) solution, as there is 0 grams of alcohol in water (0% alcohol solution) --> \(0.08x=32\) --> \(x=400\).

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