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If a portion of a half water/half alcohol mix is replaced [#permalink]
02 Sep 2010, 07:24

1

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15

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00:00

A

B

C

D

E

Difficulty:

65% (hard)

Question Stats:

52% (02:22) correct
48% (01:19) wrong based on 294 sessions

If a portion of a half water/half alcohol mix is replaced with 25% alcohol solution, resulting in a 30% alcohol solution, what percentage of the original alcohol was replaced?

If a portion of a half water/half alcohol mix is replaced with 25% alcohol solution, resulting in a 30% alcohol solution, what percentage of the original alcohol was replaced?

a 3% b 20% c 66% d 75% e 80%

Question can be solved algebraically or using allegation method.

Algebraic approach:

Initial solution is "half water/half alcohol mix" means it's 50% (0.5) alcohol solution.

Let the portion replaced be \(x\) and the volume of initial solution be 1 unit.

Then the amount of alcohol after removal of a portion will be \(0.5(1-x)\) and the amount of alcohol added will be \(0.25x\), so total amount of alcohol will be \(0.5(1-x)+0.25x\). On the other hand as in the end 30% alcohol solution was obtained then the amount of alcohol in the end was \(0.3*1\).

If a portion of a half water/half alcohol mix is replaced with 25% alcohol solution, resulting in a 30% alcohol solution, what percentage of the original alcohol was replaced?

a 3% b 20% c 66% d 75% e 80%

I think the answer B can be considered only if the question was rephrased as what percentage of alcohol was replaced in the original solution with water. (20/100*100). Else the answer should be E as explained by other above.

Yup. It is E indeed. - If V is volume of the mixture then V/2 is alc and V/2 is water. - Take Xml of the solution away (it takes X/2 alc with it). So the alc level now is (V-X)/2. - Add X ml back but this solution only has X/4 alc. So new alc content = (V-X)/2 + X/4 - New alc content = 3V/10 as it is 30%. Solving it gives X as 80%. More or less the same approach that Bunuel took. Thank you, Hemanth

I'm trying to apply a shortcut provided by KillerSquirrel in this thread mixture-55090.html, but getting a wrong answer Could you please elaborate this Mystery?

Re: mixture problem [#permalink]
23 Dec 2010, 19:11

10

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Expert's post

rtaha2412 wrote:

I do not know how to solve mixture problems. Please advise

If a portion of a half water/half alcohol mix is replaced with 25% alcohol solution, resulting in a 30% alcohol solution, what percentage of the original alcohol was replaced?

a 3% b 20% c 66% d 75% e 80%

Question on Mixtures can be easily solved using weighted averages concept discussed here: http://gmatclub.com/forum/tough-ds-105651.html#p828579 I would also recommend that you go through the complete theory from some standard book if you are not comfortable.

This question involves replacement rather than simply mixing two solutions hence it has one extra step at the end which I will discuss later.

First of all consider, you have a solution with 50% alcohol. Part of it is removed and mixed with a 25% alcohol solution. In effect, this is similar to mixing two solutions, one of 25% alcohol and other of 50% alcohol.

Attachment:

Ques1.jpg [ 3.8 KiB | Viewed 11689 times ]

So 25% alcohol solution volume : 50% alcohol solution volume is 20:5 which is 4:1. Since out of 5 parts of 50% alcohol solution, 4 parts were removed to replace them with 4 parts 25% alcohol solution, the portion of 50% alcohol solution replaced was 4/5 = 80%. The question asks: what percentage of original alcohol was replaced? Since the solution is homogenous, it you replace 80% of it, 80% of the original amount of alcohol in the solution will be replaced.

To understand this, lets say I have 100 liters of 50% alcohol solution. When I remove 80% of it, I remove 80 liters solution. In the solution I remove, I have 40 liters alcohol and 40 liters water. In the 20 liters solution that is remaining, 10 liters is alcohol and 10 liters is water. So amount of alcohol removed (and replaced) is 40/50 = 80% _________________

Re: mixture problem [#permalink]
24 Dec 2010, 11:50

rtaha2412 wrote:

I do not know how to solve mixture problems. Please advise

If a portion of a half water/half alcohol mix is replaced with 25% alcohol solution, resulting in a 30% alcohol solution, what percentage of the original alcohol was replaced?

a 3% b 20% c 66% d 75% e 80%

If you need additional instruction on these problem types, refer to the Jeff Sackmann Total Math handout p.158-159. He gives a more detailed explanation of Bunuel's method (which I think is the quickest approach to solving these problem types).

Re: Mixture problem-Can someone explain this [#permalink]
01 Oct 2011, 05:33

am I right? let x be water, y - alcohol. so we have - 0.5x+0.5y -0.25y=0.3x+0.3y x=1/4y x/y=1/4 so in a new solution y 's portion is 4/5 or 80% _________________

Happy are those who dream dreams and are ready to pay the price to make them come true

Re: mixture problem [#permalink]
30 May 2012, 20:21

VeritasPrepKarishma wrote:

rtaha2412 wrote:

I do not know how to solve mixture problems. Please advise

If a portion of a half water/half alcohol mix is replaced with 25% alcohol solution, resulting in a 30% alcohol solution, what percentage of the original alcohol was replaced?

a 3% b 20% c 66% d 75% e 80%

Question on Mixtures can be easily solved using weighted averages concept discussed here: http://gmatclub.com/forum/tough-ds-105651.html#p828579 I would also recommend that you go through the complete theory from some standard book if you are not comfortable.

This question involves replacement rather than simply mixing two solutions hence it has one extra step at the end which I will discuss later.

First of all consider, you have a solution with 50% alcohol. Part of it is removed and mixed with a 25% alcohol solution. In effect, this is similar to mixing two solutions, one of 25% alcohol and other of 50% alcohol.

Attachment:

Ques1.jpg

So 25% alcohol solution volume : 50% alcohol solution volume is 20:5 which is 4:1. Since out of 5 parts of 50% alcohol solution, 4 parts were removed to replace them with 4 parts 25% alcohol solution, the portion of 50% alcohol solution replaced was 4/5 = 80%. The question asks: what percentage of original alcohol was replaced? Since the solution is homogenous, it you replace 80% of it, 80% of the original amount of alcohol in the solution will be replaced.

To understand this, lets say I have 100 liters of 50% alcohol solution. When I remove 80% of it, I remove 80 liters solution. In the solution I remove, I have 40 liters alcohol and 40 liters water. In the 20 liters solution that is remaining, 10 liters is alcohol and 10 liters is water. So amount of alcohol removed (and replaced) is 40/50 = 80%

How have u used the weighted avg formula?

w1/w2 = (c2-avg) / (avg-c1)

if c1 = 25 and c2=50 and avg = 30 - here how do we calculate w1 and/ or w2? didnot understand this part "Since out of 5 parts of 50% alcohol solution, 4 parts were removed to replace them with 4 parts 25% alcohol solution, the portion of 50% alcohol solution replaced was 4/5 = 80%. "

Re: mixture problem [#permalink]
05 Jun 2012, 04:53

1

This post received KUDOS

Expert's post

kuttingchai wrote:

How have u used the weighted avg formula?

w1/w2 = (c2-avg) / (avg-c1)

if c1 = 25 and c2=50 and avg = 30 - here how do we calculate w1 and/ or w2? didnot understand this part "Since out of 5 parts of 50% alcohol solution, 4 parts were removed to replace them with 4 parts 25% alcohol solution, the portion of 50% alcohol solution replaced was 4/5 = 80%. "

Re: mixture problem [#permalink]
05 Jun 2012, 20:25

VeritasPrepKarishma wrote:

kuttingchai wrote:

How have u used the weighted avg formula?

w1/w2 = (c2-avg) / (avg-c1)

if c1 = 25 and c2=50 and avg = 30 - here how do we calculate w1 and/ or w2? didnot understand this part "Since out of 5 parts of 50% alcohol solution, 4 parts were removed to replace them with 4 parts 25% alcohol solution, the portion of 50% alcohol solution replaced was 4/5 = 80%. "

Re: If a portion of a half water/half alcohol mix is replaced [#permalink]
06 Oct 2013, 22:10

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Re: If a portion of a half water/half alcohol mix is replaced [#permalink]
16 Dec 2013, 05:22

zest4mba wrote:

If a portion of a half water/half alcohol mix is replaced with 25% alcohol solution, resulting in a 30% alcohol solution, what percentage of the original alcohol was replaced?

A. 3% B. 20% C. 66% D. 75% E. 80%

Quick way

Use Smart Numbers

Give 100 for the initial amount

Then you will have 50-0.25x = 30 x = 80

So % is 80/100 is 80%

Hence E is the answer Hope it helps Cheers! J

gmatclubot

Re: If a portion of a half water/half alcohol mix is replaced
[#permalink]
16 Dec 2013, 05:22

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