GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 20 Apr 2019, 09:28

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# How much water should be added to 10 liters of a 20%-solution of alcoh

Author Message
TAGS:

### Hide Tags

VP
Joined: 22 Nov 2007
Posts: 1030
How much water should be added to 10 liters of a 20%-solution of alcoh  [#permalink]

### Show Tags

Updated on: 22 Jul 2015, 10:24
3
25
00:00

Difficulty:

25% (medium)

Question Stats:

73% (02:05) correct 27% (02:33) wrong based on 256 sessions

### HideShow timer Statistics

How much water should be added to 10 liters of a 20%-solution of alcohol 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

Originally posted by marcodonzelli on 02 Mar 2008, 09:04.
Last edited by Bunuel on 22 Jul 2015, 10:24, edited 1 time in total.
Renamed the topic, edited the question, added the OA and moved to PS forum.
Director
Joined: 10 Sep 2007
Posts: 864
Re: How much water should be added to 10 liters of a 20%-solution of alcoh  [#permalink]

### Show Tags

02 Mar 2008, 10:51
2
1
In original Content of 10 litre, there is 2 litre alcohol and 8 litre water.

Question ask to reduce concentration of alcohol to 5% (reduce concentration from 20% by 75%).

So lets assume X litre water is added.

So alcohol remains 2, water is 8+X and total content is 10+X.

Now 2*100/(10+X) = 5 => X = 30

VP
Joined: 22 Nov 2007
Posts: 1030
Re: How much water should be added to 10 liters of a 20%-solution of alcoh  [#permalink]

### Show Tags

02 Mar 2008, 10:58
abhijit_sen wrote:
In original Content of 10 litre, there is 2 litre alcohol and 8 litre water.

Question ask to reduce concentration of alcohol to 5% (reduce concentration from 20% by 75%).

So lets assume X litre water is added.

So alcohol remains 2, water is 8+X and total content is 10+X.

Now 2*100/(10+X) = 5 => X = 30

very quickly: 2/(10+x)=1/20, x=30
Manager
Joined: 10 Mar 2014
Posts: 186
Re: How much water should be added to 10 liters of a 20%-solution of alcoh  [#permalink]

### Show Tags

22 Jul 2015, 09:34
marcodonzelli wrote:
How much water should be added to 10 liters of a 20%-solution of alcohol to reduce the concentration of alcohol in the solution by 75% ?
 25 liters
 27 liters
 30 liters
 32 liters
 35 liters

Hi Bunuel,

Could you please clarify 20%-solution of alcohol to reduce the concentration of alcohol in the solution by 75%?. I am getting confusion in this term.

Regards
Math Expert
Joined: 02 Sep 2009
Posts: 54376
Re: How much water should be added to 10 liters of a 20%-solution of alcoh  [#permalink]

### Show Tags

22 Jul 2015, 10:27
1
1
PathFinder007 wrote:
marcodonzelli wrote:
How much water should be added to 10 liters of a 20%-solution of alcohol to reduce the concentration of alcohol in the solution by 75% ?
 25 liters
 27 liters
 30 liters
 32 liters
 35 liters

Hi Bunuel,

Could you please clarify 20%-solution of alcohol to reduce the concentration of alcohol in the solution by 75%?. I am getting confusion in this term.

Regards

The question asks about the amount of water we should add to 10 liters of a 20%-solution of alcohol for the solution to become 5%-solution of alcohol (20% reduced by 75% is 5%).
_________________
Intern
Joined: 02 Mar 2015
Posts: 4
Re: How much water should be added to 10 liters of a 20%-solution of alcoh  [#permalink]

### Show Tags

22 Jul 2015, 13:08
1
The quantity of alcohol in the actual mixture is 2 litres (20% of 10 litres). Now it is said that the concentration is reduced by 75% or 3/4th of 20% which is 5%. Now in the new mixture this 2 litres alcohol is 5% of the total mixture therefore the total mixture would be 2 *20=40 litres. So 30 litres is added. (Note 5% is 1/20)
Intern
Joined: 11 Dec 2013
Posts: 7
Re: How much water should be added to 10 liters of a 20%-solution of alcoh  [#permalink]

### Show Tags

26 Jul 2015, 22:46
sudipnayak93 wrote:
The quantity of alcohol in the actual mixture is 2 litres (20% of 10 litres). Now it is said that the concentration is reduced by 75% or 3/4th of 20% which is 5%. Now in the new mixture this 2 litres alcohol is 5% of the total mixture therefore the total mixture would be 2 *20=40 litres. So 30 litres is added. (Note 5% is 1/20)

10 litres is containing 20% alcoholol...means 2 litres of alcohol and 8 litres of water.
Now the alchol percentage is to reduced by 75%..that means 75% of 20%...that means in the new solution, the content of alcohol should be 5%. (Reduction of 15%).
So that means, the 2 litres of alcohol will make 5% of new solution..
5%-->2 litres
100%-->40 litres..
That means an additional 30 litres (10 litres was initial solution)...and this additional 30 litres is only water.
To cross check--> in new solution..40 litres , 2 litres is alcohol and 38 litres is water.
2 litres = 5% and 38 litres=95%.

Regards
Naresh
Director
Joined: 05 Mar 2015
Posts: 999
Re: How much water should be added to 10 liters of a 20%-solution of alcoh  [#permalink]

### Show Tags

02 May 2016, 10:12
2
marcodonzelli wrote:
How much water should be added to 10 liters of a 20%-solution of alcohol 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

Let x ltr water to be added
2ltr alcohol to be represented as (20(1-3/4(new soln.=10+x)))

2=5%*(10+x)-------->x=30
Ans C
Senior Manager
Joined: 28 Jun 2015
Posts: 290
Concentration: Finance
GPA: 3.5
Re: How much water should be added to 10 liters of a 20%-solution of alcoh  [#permalink]

### Show Tags

26 Jul 2017, 23:05
1
marcodonzelli wrote:
How much water should be added to 10 liters of a 20%-solution of alcohol 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

Originally, the solution had 2L of alcohol and 8L of water. To reduce the concentration of alcohol by 75% means to bring down the alcohol level to 2L * 25% = 0.5L, so that the solution would contain 9.5L water and 0.5L alcohol.

$$\frac{8+x}{10+x} = \frac{95}{100}$$

$$800 + 100x = 950 + 95x$$

$$5x = 150$$

$$x = 30$$. Ans - C.
_________________
I used to think the brain was the most important organ. Then I thought, look what’s telling me that.
VP
Joined: 07 Dec 2014
Posts: 1179
How much water should be added to 10 liters of a 20%-solution of alcoh  [#permalink]

### Show Tags

27 Jul 2017, 11:21
marcodonzelli wrote:
How much water should be added to 10 liters of a 20%-solution of alcohol 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

let w=amount of water to be added
.2*10=.05(10+w)
w=30 liters
C
Senior SC Moderator
Joined: 22 May 2016
Posts: 2642
How much water should be added to 10 liters of a 20%-solution of alcoh  [#permalink]

### Show Tags

30 Jul 2017, 12:55
2
marcodonzelli wrote:
How much water should be added to 10 liters of a 20%-solution of alcohol 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

One iteration of a weighted average equation here is
(Concentration of A)(Vol A) + (Concen of B)(Vol B) = (Desired Concen)(Total vol = A+B)

This question is a bit unusual.

First, often, the desired concentration is given. Second, it might be hard to discern which value to reduce by 75 percent. In the equation above for this question,

A = 10 liters of soltion with 20% (=.20) alcohol
B = x liters of water with 0% (=0.0) alcohol

If water is zero percent alcohol, its percentage can't be reduced any further. The question therefore asks that 20 percent concentration be reduced by 75 percent:

(.20)(.25) = .05. The latter is the desired concentration of resultant solution.

In the equation, you don't have to insert second term on LHS. Doing so just makes clear that you are adding x, but its concentration of alcohol has no weight. So

(.20)10 + (0)x = (.05)(10 + x)

2 + 0x = .5 + .05x

1.5 = .05x

$$\frac{1.5}{.05}$$= x

x = 30

_________________
Listen, are you breathing just a little, and calling it a life?
-- Mary Oliver

For practice SC questions with official explanations that were posted and moderated by the SC Team,
go to SC Butler here: https://gmatclub.com/forum/project-sc-butler-get-2-sc-questions-everyday-281043.html
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9125
Location: Pune, India
Re: How much water should be added to 10 liters of a 20%-solution of alcoh  [#permalink]

### Show Tags

18 Sep 2017, 22:28
3
1
marcodonzelli wrote:
How much water should be added to 10 liters of a 20%-solution of alcohol 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

Responding to a pm:

Right now, we have a 20% solution of alcohol.
We need to reduce the concentration of alcohol by 75% i.e. reduce it by 15% to make it 5%.

So now, you have a 10 lt solution of 20% alcohol and you want to make it 5% alcohol by adding pure water (i.e. 0% alcohol)

w1/w2 = (A2 - Aavg)/(Aavg - A1) = (0 - 5)/(5 - 20) = 1/3

So for every 1 lt of original solution, you need 3 lt of water. So for 10 litres of original solution, you need 30 lt of water.

_________________
Karishma
Veritas Prep GMAT Instructor

Manager
Joined: 30 May 2012
Posts: 201
Location: United States (TX)
Concentration: Finance, Marketing
GPA: 3.3
WE: Information Technology (Consulting)
Re: How much water should be added to 10 liters of a 20%-solution of alcoh  [#permalink]

### Show Tags

28 Sep 2017, 09:31
How does one solve this using allegation approach? Bunuel, Abhishek009, VeritasPrepKarishma anyone?
Intern
Joined: 08 Sep 2011
Posts: 1
Re: How much water should be added to 10 liters of a 20%-solution of alcoh  [#permalink]

### Show Tags

05 Apr 2019, 13:55
Hi, why does this approach not work
20% of 10 litres of solution + x litres of water = 5% of (10+x) litres of solution

x being the added quantity of water
Intern
Joined: 28 Aug 2016
Posts: 9
Re: How much water should be added to 10 liters of a 20%-solution of alcoh  [#permalink]

### Show Tags

18 Apr 2019, 19:13
marcodonzelli wrote:
How much water should be added to 10 liters of a 20%-solution of alcohol 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

We can back-solve as well:

20% of 10 liters is 2 liters.
20% reduced by 75% is 5%.

If we check C -> 30 + 10 (initial liters) = 40 liters, 2/40 = 1/20 or 5%
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9125
Location: Pune, India
Re: How much water should be added to 10 liters of a 20%-solution of alcoh  [#permalink]

### Show Tags

18 Apr 2019, 20:30
marcodonzelli wrote:
How much water should be added to 10 liters of a 20%-solution of alcohol 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

Concentration of alcohol = 20% = C1
A reduction by 75% means the concentration of alcohol should become 5% = Cavg
Concentration of alcohol in water = 0% = C2

10/w2 = (0 - 5) / (5 - 20) = 1/3

w2 = 30 lts

Check out the weighted avg blog to understand this:
https://www.veritasprep.com/blog/2011/0 ... -averages/
https://www.veritasprep.com/blog/2011/0 ... -mixtures/
_________________
Karishma
Veritas Prep GMAT Instructor

Re: How much water should be added to 10 liters of a 20%-solution of alcoh   [#permalink] 18 Apr 2019, 20:30
Display posts from previous: Sort by