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If a portion of a half water/half alcohol mix is replaced

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Senior Manager
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Re: If a portion of a half water/half alcohol mix is replaced  [#permalink]

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New post 27 Oct 2018, 21:44
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%




Let the volume of solution be 100 ml

Given its a 50% water/505 alcohol solution.

So Alcohol=50ml and water = 50 ml

Now

50-0.50x(removing "x" ml of 50 % alcohol solution) + 0.25x(replacing with 25% alcohol solution) = 30(30%alcohol solution)

X= 80 ml

clearly origininal solution was 100 ml so its 80%

ALTERNATIVE APPROACH

Weighted average

We have 25 - 30 - 50 % alcohol solution

Ratio of 25% alcohol solution to 50% alchohol solution (W1/W2) = 50-30 / 30-25 = 4/1

Therefore we have 4 units of alcohol sulution of of 5 units of net solution
impues 4/5= 80%

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Re: If a portion of a half water/half alcohol mix is replaced  [#permalink]

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New post 25 Dec 2018, 16:57
gmat1011 wrote:
Hi Financier

It will work if you consider it as follows:

50% ---------------- 25%

------------30%---------

5%------------------20%

so ratio is 1:4 in final mixture

Earlier type 1 alcohol was 1

Now it is 1/5 ----> so loss of 4/5 = 80%...


Could someone please explain where 1/5 is coming from towards the end? I have been trying to figure out since past 30 mins but I haven't had any luck. Would immensely appreciate it!
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Re: If a portion of a half water/half alcohol mix is replaced  [#permalink]

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New post 09 Aug 2019, 19:22
Lets test 10 for total weight of solution

5 alcohol 5 water by weight (units are negligible)

x = amount we are replacing
We know that currently if we remove x units of the mix then half of x will be alcohol, the other half water.

This allows us to construct the following

(5-0.5x+0.25x)/10 = 3/10
50-2.5x=30
20=2.5x
x=8
Thus 8/10 = 0.8= 80%
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Re: If a portion of a half water/half alcohol mix is replaced  [#permalink]

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New post 29 Jan 2020, 02:37
(50 - 30)/ (30-25) = 4/1 so from 50/50 it came to 1/4 it lost 4/5 which is 80%
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If a portion of a half water/half alcohol mix is replaced  [#permalink]

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New post 21 Apr 2020, 01:28
Hi Guys,

I believe that the question should specify that we need to find 'what percentage of the original alcohol mix or the portion was replaced'. I think that just asking 'what percentage of the original alcohol was replaced' suggests that we need to find the percentage of alcohol from the original solution that was replaced, which would be 40%.

Unless, whenever the GMAT mentions 'alcohol', we take that a solution is being referred to.

Thank you.
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If a portion of a half water/half alcohol mix is replaced   [#permalink] 21 Apr 2020, 01:28

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