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M17-11

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M17-11 [#permalink]

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If there are 10 liters of a 20%-solution of alcohol, how much water should be added to reduce the concentration of alcohol in the solution by 75% ?

A. 25 liters
B. 27 liters
C. 30 liters
D. 32 liters
E. 35 liters
[Reveal] Spoiler: OA

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Official Solution:

If there are 10 liters of a 20%-solution of alcohol, how much water should be added to reduce the concentration of alcohol in the solution by 75% ?

A. 25 liters
B. 27 liters
C. 30 liters
D. 32 liters
E. 35 liters


Amount of alcohol in the original solution is \(0.2*10=2\) liters;

A 20% concentration of alcohol reduced by 75% means that the new solution should be a \(20-0.75*20=5 \%\) alcohol solution;

Since the amount of alcohol in the new solution is not changed, then 2 liters of alcohol must be 5% of the new solution, hence \(0.05*x=2\), which gives \(x=40\) liters.

So, we should add \(40-10=30\) liters of water.


Answer: C
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Re: M17-11 [#permalink]

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New post 21 Nov 2016, 09:15
Bunuel:

Let w be the no. of litres of water

0.2(10) + w = 0.05 (10+w)

What is wrong with this equation?

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Re: M17-11 [#permalink]

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New post 25 Apr 2017, 07:13
The solution contains 20% alcohol. Therefore, the amount of alcohol is 2l. We need to find out as to how much water must be added to reduce the concentration of alcohol by 75% or make the concentration 25% of the original one.

2/(10+x)=(1/4)*(1/5)
Solving for x , you will get the value as 30.
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New post 06 May 2017, 14:45
% after reduction= 20% * (100-75)%=5%
water added=x
before adding water, A=10 lit* 20%=2, w=10-2=8 lit
atq
2/(8+x) = 5/95
x=30 lit
ans:c

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Re: M17-11 [#permalink]

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New post 20 Aug 2017, 13:14
I think this is poorly worded. It is not very clear whether it is 10liters of alcohol or 10 liters in the entire solution

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New post 21 Aug 2017, 02:48
gmathopeful19 wrote:
I think this is poorly worded. It is not very clear whether it is 10liters of alcohol or 10 liters in the entire solution


This is a standard wording. 10 liters of a 20%-solution of alcohol, means that the entire solution is 10 liters and alcohol is 20% of that.
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Resources:
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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Kudos [?]: 128907 [0], given: 12183

Re: M17-11   [#permalink] 21 Aug 2017, 02:48
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