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Ok Shabang, I'll try to explain this to you since it appears most people are away celebrating x-mas. Studying for the GMAT is how I'm celebrating X-mas this year.
I would pick numbers here and scan the answer choices (also think logically - the difference in the percentage of the solution declines by only 5% when added with the diluted solution - thus I would get rid of answer choices c,d,e - so I'm left with a and b) I chose b off the bat:
Pick 60 (ml, oz, whatever) as the total mixture - it works well with 3, 4, and 5.
You have a mixture that is 40% solution: 2:5=x:60 thus x = 24 solution : 60 total mixture
Using answer choice B 1/3 - plug it in. 1/3 of 60 is 20 so you're left with 40 oz of the solution. Thus the new solution is 2:5=x:40 x=16 solution: 40 total mixture. You're adding 20 oz of a diluted mixture. thus 1/4 = x/20 = 5 solution: 20 total mixture. Add them together you have: 21 solution : 60 total mixture or 21/60 = 35%.
I'm a little buzzed - I hoep ti amkes sense.
Last edited by Titleist on 25 Dec 2003, 16:04, edited 1 time in total.
Indeed, not easy to explain with words. My explanation is:
Let's say that the total original mixture A is 100ml
The original mixture A thus has 40ml of alcohol out of 100ml of solution
You want to replace some of that original mixture A with another mixture B that contains 25ml of alcohol per 100ml. Thus, the difference between 40ml and 25ml is 15ml per 100ml of mixture. This means that everytime you replace 100ml of the original mixture A by 100ml of mixture B, the original alcohol concentration will decrease by 15%. The question says that the new mixture, let's call it C, must be 35% alcohol, a decrease of only 5%. Therefore, 5 out of 15 is 1/3 and B is the answer. Was that clear?[/b]
Re: Mixture problem [#permalink]
19 May 2009, 23:23
I back solved it: Since it deals with percent, lets take 100 as the base.
When 1/4 - total mixrure is 40 + 25*4 / 500 = 140/500 ; this is not eq 35. When 1/3 - total mixture is 40 + 25*3/ 400 = 115/400 = 35% - this is the ans. When 1/2 - total mixture is 40 + 20*2/ 300 = 80/300 ; not eq 35% Similarly for D & E.
Re: Mixture problem [#permalink]
22 Jul 2011, 02:30
This post received KUDOS
A certain quantity of 40% solution is replaced with 25% solution such that the new concentration is 35%. What is the fraction of the solution that was replaced?
Or use our standard mixtures formula for replacements too. In a certain quantity of 40% solution, 25% solution is added to give 35% solution. w1/w2 = (A2 - Aavg)/(Aavg - A1) = (40 - 35)/(35 - 25) = 1/2 So quantity of 40% sol:25% solution = 2:1 This means the initial total solution was 3 and the fraction of 25% now in the mixture is 1. Therefore, 1/3 of the 40% solution was removed and replaced with 25% solution.
Re: A certain quantity of 40% solution is replaced with 25% [#permalink]
30 May 2014, 11:34
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