Eight litres are drawn off from a vessel full of water and s : GMAT Problem Solving (PS)
Check GMAT Club Decision Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

 It is currently 23 Jan 2017, 10:14

### 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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# Eight litres are drawn off from a vessel full of water and s

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

Manager
Joined: 07 Jun 2010
Posts: 50
Location: United States
Followers: 1

Kudos [?]: 38 [5] , given: 7

Eight litres are drawn off from a vessel full of water and s [#permalink]

### Show Tags

12 Jun 2010, 13:17
5
KUDOS
36
This post was
BOOKMARKED
00:00

Difficulty:

95% (hard)

Question Stats:

46% (03:50) correct 54% (02:56) wrong based on 568 sessions

### HideShow timer Statistics

Eight litres are drawn off from a vessel full of water and substituted by pure milk. Again eight litres of the mixture are drawn off and substituted by pure milk. If the vessel now contains water and milk in the ratio 9:40, find the capacity of the vessel.

A. 21 liters
B. 22 liters
C. 20 liters
D. 14 liters
E. 28 liters
[Reveal] Spoiler: OA
Manager
Joined: 24 Mar 2010
Posts: 104
Followers: 1

Kudos [?]: 30 [0], given: 12

Re: Eight litres are drawn off from a vessel full of water and s [#permalink]

### Show Tags

12 Jun 2010, 18:42
the equation you'd get once 8 lts are drawn the second time is: (w-16)/16 = 9/40 where w is the capacity of the vessel.
Solving for w, w = 19.6. So, its C
_________________

Please do consider giving kudos if you like my posts

Manager
Joined: 07 Jun 2010
Posts: 50
Location: United States
Followers: 1

Kudos [?]: 38 [0], given: 7

Re: Eight litres are drawn off from a vessel full of water and s [#permalink]

### Show Tags

12 Jun 2010, 21:37
iambroke wrote:
the equation you'd get once 8 lts are drawn the second time is: (w-16)/16 = 9/40 where w is the capacity of the vessel.
Solving for w, w = 19.6. So, its C

Ya but second time 8 liters are removed from the mixture of milk and water not only water.
Math Expert
Joined: 02 Sep 2009
Posts: 36618
Followers: 7099

Kudos [?]: 93534 [19] , given: 10578

Eight litres are drawn off from a vessel full of water and s [#permalink]

### Show Tags

13 Jun 2010, 04:49
19
KUDOS
Expert's post
22
This post was
BOOKMARKED
virupaksh2010 wrote:
Eight litres are drawn off from a vessel full of water and substituted by pure milk. Again eight litres of the mixture are drawn off and substituted by pure milk.If the vessel now contains water and milk in the ratio 9:40, find the capacity of the vessel.

A. 21 liters
B. 22 liters
C. 20 liters
D. 14 liters
E. 28 liters

Let the capacity of the vessel be $$x$$.

After the first removal there would be $$x-8$$ liters of water left in the vessel. Note that the share of the water would be $$\frac{x-8}{x}$$;

After the second removal, the removed mixture of 8 liters will contain $$8*\frac{x-8}{x}$$ liters of water, so there will be $$(x-8)-8*\frac{x-8}{x}=\frac{(x-8)^2}{x}$$ liters of water left.

As the ratio of water to milk after that is $$\frac{9}{40}$$, then the ratio of water to the capacity of the vessel would be $$\frac{9}{40+9}=\frac{9}{49}$$.

So $$\frac{\frac{(x-8)^2}{x}}{x}=\frac{9}{49}$$ --> $$\frac{(x-8)^2}{x^2}=\frac{9}{49}$$ --> $$\frac{x-8}{x}=\frac{3}{7}$$ --> $$x=14$$.

_________________
Manager
Joined: 24 Mar 2010
Posts: 104
Followers: 1

Kudos [?]: 30 [0], given: 12

Re: Eight litres are drawn off from a vessel full of water and s [#permalink]

### Show Tags

13 Jun 2010, 08:44
Oops, should've read the question better..sorry abt that....thanks Bunuel...
_________________

Please do consider giving kudos if you like my posts

Manager
Joined: 14 Apr 2010
Posts: 230
Followers: 2

Kudos [?]: 150 [0], given: 1

Re: Eight litres are drawn off from a vessel full of water and s [#permalink]

### Show Tags

13 Jun 2010, 21:39
After the second removal, the removed mixture of 8 liters will contain 8 * (x-8)/x liters of water, so there will be x-8-8 * (x-8)/8 = (x-8)^2/x liters of water left.

Please explain this part
Manager
Joined: 07 Jun 2010
Posts: 50
Location: United States
Followers: 1

Kudos [?]: 38 [1] , given: 7

Re: Eight litres are drawn off from a vessel full of water and s [#permalink]

### Show Tags

14 Jun 2010, 05:49
1
KUDOS
bibha wrote:
After the second removal, the removed mixture of 8 liters will contain 8 * (x-8)/x liters of water, so there will be x-8-8 * (x-8)/8 = (x-8)^2/x liters of water left.

Please explain this part

Step1 :-

Water in vessel = x

8 liters is removed and replaced with milk

so now,

Water = x-8
Milk = 8

Step 2 :-

Now again 8 liters of mixture is removes , so water in that mixture is w = (x-8/x) * 8

So Total water removed = x-8-w = x-8-(x-8/x)*8 = (x^2-8x-8x-64)/x = (x^2-16x-64)/x
Director
Joined: 23 Apr 2010
Posts: 584
Followers: 2

Kudos [?]: 78 [0], given: 7

Re: Eight litres are drawn off from a vessel full of water and s [#permalink]

### Show Tags

12 Jul 2010, 05:45
Is this a real GMAT question? Would be very tough to solve it in 3 minutes.
Manager
Joined: 12 Jun 2007
Posts: 128
Followers: 6

Kudos [?]: 71 [0], given: 2

Re: Eight litres are drawn off from a vessel full of water and s [#permalink]

### Show Tags

16 Jul 2010, 00:25
one more way:

Vessel capacity be 20litre:

8litre water removed and milk added: W=12litre, M=8litre

8litre mixture removed, (removed proportionately) : W= 12-4.8 = 7.2litre, M= 8-3.2 = 4.8 litre

8litre milk added ; W=7.2 litre, M=12.8 litre

Ratio will be 72/128 = 18/32 = 9/16

As we can see that milk is less so we have to select the ratio even less than 20,

Vessel capcity be 14 litre

8litre water removed and milk added: W=6 litre, M=8 litre

8litre mixture removed, (removed proportionately) : W= 6-3.4 = 2.6 litre, M= 8-4.6 = 3.4 litre

8litre milk added ; W=2.6 litre, M=11.4 litre

Ratio will be 26/114 = 8.66/38 (approx) very close to 9/40

So correct option is D
Manager
Status: one more time
Joined: 05 Jul 2010
Posts: 72
Location: United States
Concentration: Strategy, Entrepreneurship
GMAT 1: 700 Q49 V37
GMAT 2: 740 Q50 V40
GPA: 3.48
WE: Web Development (Computer Software)
Followers: 0

Kudos [?]: 10 [4] , given: 6

Re: Eight litres are drawn off from a vessel full of water and s [#permalink]

### Show Tags

16 Jul 2010, 22:47
4
KUDOS
I solved it 2:28 mins in reverse way.

First 8 l milks added.
Then another 8 litre milk added.
so total is milk < 16 (as some milk is removed)
since final ratio of water is 9:40

water shud be < 16*9/40 i.e < 3....
so total must be less than 19...

in the given options it is clear that 14 is the answer.
Manager
Status: Last few days....Have pressed the throttle
Joined: 20 Jun 2010
Posts: 70
WE 1: 6 years - Consulting
Followers: 3

Kudos [?]: 46 [2] , given: 27

Re: Eight litres are drawn off from a vessel full of water and s [#permalink]

### Show Tags

05 Sep 2010, 02:00
2
KUDOS
virupaksh2010 wrote:
Eight litres are drawn off from a vessel full of water and substituted by pure milk. Again eight litres of the mixture are drawn off and substituted by pure milk.If the vessel now contains water and milk in the ratio 9:40, find the capacity of the vessel.

A. 21 litrers

B. 22 litres

C. 20 litres

D. 14 litres

E. 28 litres

Using Wine formula:

{ (P-8) / P }^2 = 9/49

P solves to 14 - Ans - D
_________________

Consider giving Kudos if my post helps in some way

Director
Joined: 23 Apr 2010
Posts: 584
Followers: 2

Kudos [?]: 78 [0], given: 7

Re: Eight litres are drawn off from a vessel full of water and s [#permalink]

### Show Tags

13 Feb 2012, 12:23
Bunuel, could you please pin point to a mistake in my reasoning?

Let T = total capacity of vessel

1.) the concentration of milk after the first round is 8/T
2.) After the second round the concentration of milk is $$40/49$$

$$8/T$$ * (T-8) + 8 = $$40/49$$ T

Now, I can't solve this equation. And even substituting answer choices won't help.

Where's the mistake?

Thank you very much.
Math Expert
Joined: 02 Sep 2009
Posts: 36618
Followers: 7099

Kudos [?]: 93534 [1] , given: 10578

Re: Eight litres are drawn off from a vessel full of water and s [#permalink]

### Show Tags

13 Feb 2012, 13:12
1
KUDOS
Expert's post
nonameee wrote:
Bunuel, could you please pin point to a mistake in my reasoning?

Let T = total capacity of vessel

1.) the concentration of milk after the first round is 8/T
2.) After the second round the concentration of milk is $$40/49$$

$$8/T$$ * (T-8) + 8 = $$40/49$$ T

Now, I can't solve this equation. And even substituting answer choices won't help.

Where's the mistake?

Thank you very much.

Equation is correct.

$$\frac{8}{t}(t-8)+8=\frac{40}{49}t$$ --> $$\frac{t-8}{t}+1=\frac{5t}{49}$$. Now, if you substitute t=14 you'll see that it'll hold true.
_________________
Director
Joined: 23 Apr 2010
Posts: 584
Followers: 2

Kudos [?]: 78 [0], given: 7

Re: Eight litres are drawn off from a vessel full of water and s [#permalink]

### Show Tags

13 Feb 2012, 13:19
Bunuel, thanks a lot. I must have made some miscalculation.

Conceptually the question is interesting. However the numbers are quite "difficult" to work with. Do you think that a real GMAT question would have better numbers?
Math Expert
Joined: 02 Sep 2009
Posts: 36618
Followers: 7099

Kudos [?]: 93534 [0], given: 10578

Re: Eight litres are drawn off from a vessel full of water and s [#permalink]

### Show Tags

13 Feb 2012, 13:25
nonameee wrote:
Bunuel, thanks a lot. I must have made some miscalculation.

Conceptually the question is interesting. However the numbers are quite "difficult" to work with. Do you think that a real GMAT question would have better numbers?

If you and up with an equation shown in my post above then it won't be that difficult to solve it, for your equation it's better to plug numbers of course. So I think that the question, though tough, is still a GMAT type.
_________________
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7130
Location: Pune, India
Followers: 2140

Kudos [?]: 13706 [9] , given: 222

Re: Eight litres are drawn off from a vessel full of water and s [#permalink]

### Show Tags

15 Feb 2012, 00:58
9
KUDOS
Expert's post
4
This post was
BOOKMARKED
nonameee wrote:
Bunuel, thanks a lot. I must have made some miscalculation.

Conceptually the question is interesting. However the numbers are quite "difficult" to work with. Do you think that a real GMAT question would have better numbers?

Actually, the numbers are quite suitable for a very efficient, quick and oral solution. This is what I thought of when I came up with the answer in 20 secs. Mind you, you need to go through the link provided below to understand this theory. Else the 20 sec solution will probably not make sense to you.

We are substituting milk so we should work with water.

Final concentration of water = 9/49
There were two iterations. So, 9/49 = (100%)*(Vi/Vf)^2
Vi/Vf = 3/7
Since we are putting 8 liters of water but difference between Vi and Vf is 4, final volume (which is also equal to volume of the vessel) must be twice too i.e. 7*2 = 14 liters.

http://www.veritasprep.com/blog/2012/01 ... -mixtures/
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for \$199

Veritas Prep Reviews

Intern
Joined: 21 Mar 2009
Posts: 21
Followers: 0

Kudos [?]: 18 [0], given: 0

Re: Eight litres are drawn off from a vessel full of water and s [#permalink]

### Show Tags

31 Dec 2012, 11:01
1
This post was
BOOKMARKED
nonameee wrote:
Bunuel, thanks a lot. I must have made some miscalculation.

Conceptually the question is interesting. However the numbers are quite "difficult" to work with. Do you think that a real GMAT question would have better numbers?

This is not a GMAT like question. Answers in gmat are usually sorted. as for as calculation is concerned it is easy. See below

Following formulae works in such scenario. More about its derivation later: If out of x, y is taken repeatedly after nth trial amount left is x(1-y/x)^n

Here asuming x ltr for water water left after two attempts is : x(1-8/x)^2

=> (x(1-8/x)^2)/x = 9/(9+40) => 1-8/x = 3/7 => 8/x = 4/7 or x = (7/4)*8 = 14ltr
Manager
Joined: 14 Dec 2012
Posts: 82
Location: United States
Followers: 1

Kudos [?]: 16 [0], given: 186

Re: Eight litres are drawn off from a vessel full of water and s [#permalink]

### Show Tags

25 May 2013, 10:28
Bunuel wrote:
virupaksh2010 wrote:
Eight litres are drawn off from a vessel full of water and substituted by pure milk. Again eight litres of the mixture are drawn off and substituted by pure milk.If the vessel now contains water and milk in the ratio 9:40, find the capacity of the vessel.

A. 21 litrers

B. 22 litres

C. 20 litres

D. 14 litres

E. 28 litres

Let the capacity of the vessel be $$x$$.

After the first removal there would be $$x-8$$ liters of water left in the vessel. Note that the share of the water would be $$\frac{x-8}{x}$$;

After the second removal, the removed mixture of 8 liters will contain $$8*\frac{x-8}{x}$$ liters of water, so there will be $$x-8-8*\frac{x-8}{x}=\frac{(x-8)^2}{x}$$ liters of water left.

As the ratio of water to milk after that is $$\frac{9}{40}$$, then the ratio of water to the capacity of the vessel would be $$\frac{9}{40+9}=\frac{9}{49}$$.

So $$\frac{\frac{(x-8)^2}{x}}{x}=\frac{9}{49}$$ --> $$\frac{(x-8)^2}{x^2}=\frac{9}{49}$$ --> $$\frac{x-8}{x}=\frac{3}{7}$$ --> $$x=14$$.

if we are removing 8 litres of mixture,does that mean we are removing water share ?? because in mixture,how can we remove water now,as it contains milk too now. why do we use 8*water share??Pls clarify..
Math Expert
Joined: 02 Sep 2009
Posts: 36618
Followers: 7099

Kudos [?]: 93534 [0], given: 10578

Re: Eight litres are drawn off from a vessel full of water and s [#permalink]

### Show Tags

26 May 2013, 03:59
up4gmat wrote:
Bunuel wrote:
virupaksh2010 wrote:
Eight litres are drawn off from a vessel full of water and substituted by pure milk. Again eight litres of the mixture are drawn off and substituted by pure milk.If the vessel now contains water and milk in the ratio 9:40, find the capacity of the vessel.

A. 21 litrers

B. 22 litres

C. 20 litres

D. 14 litres

E. 28 litres

Let the capacity of the vessel be $$x$$.

After the first removal there would be $$x-8$$ liters of water left in the vessel. Note that the share of the water would be $$\frac{x-8}{x}$$;

After the second removal, the removed mixture of 8 liters will contain $$8*\frac{x-8}{x}$$ liters of water, so there will be $$x-8-8*\frac{x-8}{x}=\frac{(x-8)^2}{x}$$ liters of water left.

As the ratio of water to milk after that is $$\frac{9}{40}$$, then the ratio of water to the capacity of the vessel would be $$\frac{9}{40+9}=\frac{9}{49}$$.

So $$\frac{\frac{(x-8)^2}{x}}{x}=\frac{9}{49}$$ --> $$\frac{(x-8)^2}{x^2}=\frac{9}{49}$$ --> $$\frac{x-8}{x}=\frac{3}{7}$$ --> $$x=14$$.

if we are removing 8 litres of mixture,does that mean we are removing water share ?? because in mixture,how can we remove water now,as it contains milk too now. why do we use 8*water share??Pls clarify..

We are calculating how much water is left in the vessel after two removals.
_________________
Senior Manager
Joined: 10 Apr 2012
Posts: 276
Location: United States
Concentration: Technology, Other
GPA: 2.44
WE: Project Management (Telecommunications)
Followers: 5

Kudos [?]: 736 [0], given: 325

Re: Eight litres are drawn off from a vessel full of water and s [#permalink]

### Show Tags

03 Jun 2013, 12:24
VeritasPrepKarishma wrote:
nonameee wrote:
Bunuel, thanks a lot. I must have made some miscalculation.

Conceptually the question is interesting. However the numbers are quite "difficult" to work with. Do you think that a real GMAT question would have better numbers?

Actually, the numbers are quite suitable for a very efficient, quick and oral solution. This is what I thought of when I came up with the answer in 20 secs. Mind you, you need to go through the link provided below to understand this theory. Else the 20 sec solution will probably not make sense to you.

We are substituting milk so we should work with water.

Final concentration of water = 9/49
There were two iterations. So, 9/49 = (100%)*(Vi/Vf)^2
Vi/Vf = 3/7
Since we are putting 8 liters of water but difference between Vi and Vf is 4, final volume (which is also equal to volume of the vessel) must be twice too i.e. 7*2 = 14 liters.

http://www.veritasprep.com/blog/2012/01 ... -mixtures/

Hi Karishma , Could you please elaborate the highlighted portion ? I am unable to grasp the last part of the solution . Thanks in advance .
Re: Eight litres are drawn off from a vessel full of water and s   [#permalink] 03 Jun 2013, 12:24

Go to page    1   2   3    Next  [ 42 posts ]

Similar topics Replies Last post
Similar
Topics:
13 Pipe A and Pipe B fill water into a tank of capacity 1000 litres at 6 30 Aug 2014, 03:24
40 A 100-litre mixture of milk and water contains 36 litres of 18 26 Aug 2014, 23:28
1 A vessel of Capacity 2 litre has 25% of Alcohol 1 12 Oct 2013, 05:41
1 In a mixture of 45 litres the ratio of milk to water 1 21 Feb 2013, 07:00
8 A recipe for soda requires w litres of water for every litre 10 29 Apr 2008, 05:01
Display posts from previous: Sort by

# Eight litres are drawn off from a vessel full of water and s

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group and phpBB SEO Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.