Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 09 Feb 2016, 20:00

### 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

Author Message
TAGS:
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 6226
Location: Pune, India
Followers: 1676

Kudos [?]: 9609 [1] , given: 197

Re: Eight litres are drawn off from a vessel full of water and s [#permalink]  03 Jun 2013, 19:44
1
KUDOS
Expert's post
guerrero25 wrote:
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 .

This is the ratios concept in action here even though I haven't used ratio explicitly.
Vi is the volume after you remove 8 lts but before you put it back. Vf is the volume after you put the 8 lts back in.

But you get Vi/Vf = 3/7 i.e. their ratio is 3:7. But the actual difference in their volume is 8lts.
so 7x - 3x = 8 giving you x = 2
Vi = 6 lts, Vf = 14 lts

(All I did above was I saw that the difference between 3 and 7 is 4 (the ratio difference) but actual difference is 8 so the multiplier is 2. Hence the actual volume would be twice of the ratio too. Check out my ratio posts on my blog to understand the multiplier concept)
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews  Veritas Prep GMAT Discount Codes Knewton GMAT Discount Codes GMAT Pill GMAT Discount Codes Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 6226 Location: Pune, India Followers: 1676 Kudos [?]: 9609 [1] , given: 197 Re: Eight litres are drawn off from a vessel full of water and s [#permalink] 19 Jul 2013, 19:58 1 This post received KUDOS Expert's post 1 This post was BOOKMARKED Quote: 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 The way the equation is expressed, it seems to me that the number used for Vf should be the volume of the vessel (this is my understanding of what Vf is supposed to represent). However, that is obviously incorrect. Thus, I am having difficulty conceptualizing what Vf actually represents in the solution you have provided and, further, how you were able to intuitively determine that it should be doubled. I understand that Vi of 3 and Vf of 7 must be doubled in order to ensure that Vf-Vi=8. However, I do not understand why this is permissible within the construct of the concentration equation. Responding to a pm: You are correct. In this question Vf is the capacity of the vessel. What is Vf in replacement questions? Replacement consists of two steps: - 'withdraw from the vessel' and 'put back into the vessel'. When you withdraw from the vessel, the volume goes down - This is Vi for the next step. When you put back, the volume comes up again - this is Vf. In this step, since amount of water stays the same (you are putting in milk), CiVi = CfVf In this question, vessel is FULL of water and you are substituting part of it by milk. So it will be FULL when you put milk in it in step 2. So Vf is the capacity of the vessel. Also, we are using ratios here. Say, you know a/b = 1/2. If a = 10, what is b? It is 20, right? Similarly, you know a/b = 1/2. If b-a = 4, what is a? Note that on the ratio scale, the difference between b and a is 1 (2 - 1). But actually it is 4 so a must be 4 and b must be 8. Check out my posts on ratios: http://www.veritasprep.com/blog/2011/03 ... of-ratios/ Since Vi/Vf = 3/7 but Vf - Vi = 8 (twice of what it is on the ratio scale), Vi must be 6 and Vf must be 14. _________________ Karishma Veritas Prep | GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199

Veritas Prep Reviews

Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 6226
Location: Pune, India
Followers: 1676

Kudos [?]: 9609 [0], given: 197

Re: Eight litres are drawn off from a vessel full of water and s [#permalink]  13 Aug 2013, 21:39
Expert's post
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/

Responding to a pm:

Cf*Vf = Ci*Vi
Cf = Ci * (Vi/Vf)

When you add milk for the first time, concentration of water in initial solution is 100%

Cf = 100% (Vi/Vf)

Then you remove some solution which doesn't change its concentration which is 100% (Vi/Vf)
When you add milk again, initial concentration is 100% (Vi/Vf) and the final concentration is given by

Cf2 = 100% (Vi/Vf) * (Vi/Vf) = 100%(Vi/Vf)^2

We know that this Cf2 is given to be 9/49

So Vi/Vf = 3/7

So every time we take out some solution, the volume of the solution reduces to Vi and every time we add it back, it goes up to Vf.
7x - 3x = 8 lts
x = 2 lts

So Vi is 6 lts and Vf is 14 lts. The capacity of the vessel i.e. the volume when it is full (i.e. when we put back the 8 lts of milk) is 14 lts.
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Manager Joined: 30 May 2013 Posts: 190 Location: India Concentration: Entrepreneurship, General Management GPA: 3.82 Followers: 0 Kudos [?]: 46 [0], given: 72 Re: Eight litres are drawn off from a vessel full of water and s [#permalink] 14 Aug 2013, 06:07 oldstudent 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. Possible AnswersSelected Possible Answer 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 Hi, Will this formula holds good for all this types of questions? Regards, Rrsnathan. Senior Manager Joined: 10 Jul 2013 Posts: 335 Followers: 3 Kudos [?]: 228 [0], given: 102 Re: Eight litres are drawn off from a vessel full of water and s [#permalink] 14 Aug 2013, 13:20 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 Milk and water can change in amount but Total capacity will not. So stay with capacity. That's the theme should work on. REMEMBER, STICK WITH CAPACITY. Capacity = x 1st event: water : capacity = (x-8) : x 2nd event: 8 liters more solution replaced. but how much water it carried OUT with itself ? So, EARLIER x liters solution contained (x-8) liter water or, 1 liter ....................... = (x-8)/x liter water or, 8 liters ...................... = 8(x-8)/x liter So now we have water = x-8 - {8(x-8)/x} = (x-8)^2 / x liter GIVEN, water:milk = 9:40 , So total = 49 . Here, water : capacity = 9:49 Finally, water : capacity = {(x-8)^2/x} : x = 9:49 or, x = 14 (Answer) _________________ Asif vai..... Director Joined: 17 Apr 2013 Posts: 633 Concentration: Entrepreneurship, Leadership Schools: HBS '16 (II) GMAT 1: 710 Q50 V36 GMAT 2: 750 Q51 V41 GMAT 3: 790 Q51 V49 GPA: 3.3 Followers: 36 Kudos [?]: 237 [0], given: 287 Re: Eight litres are drawn off from a vessel full of water and s [#permalink] 15 Aug 2013, 10:24 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 I am also getting 19.6 _________________ Like my post Send me a Kudos It is a Good manner. My Debrief: how-to-score-750-and-750-i-moved-from-710-to-189016.html Director Joined: 17 Apr 2013 Posts: 633 Concentration: Entrepreneurship, Leadership Schools: HBS '16 (II) GMAT 1: 710 Q50 V36 GMAT 2: 750 Q51 V41 GMAT 3: 790 Q51 V49 GPA: 3.3 Followers: 36 Kudos [?]: 237 [0], given: 287 Re: Eight litres are drawn off from a vessel full of water and s [#permalink] 15 Aug 2013, 10:58 VeritasPrepKarishma wrote: Quote: 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 The way the equation is expressed, it seems to me that the number used for Vf should be the volume of the vessel (this is my understanding of what Vf is supposed to represent). However, that is obviously incorrect. Thus, I am having difficulty conceptualizing what Vf actually represents in the solution you have provided and, further, how you were able to intuitively determine that it should be doubled. I understand that Vi of 3 and Vf of 7 must be doubled in order to ensure that Vf-Vi=8. However, I do not understand why this is permissible within the construct of the concentration equation. Responding to a pm: You are correct. In this question Vf is the capacity of the vessel. What is Vf in replacement questions? Replacement consists of two steps: - 'withdraw from the vessel' and 'put back into the vessel'. When you withdraw from the vessel, the volume goes down - This is Vi for the next step. When you put back, the volume comes up again - this is Vf. In this step, since amount of water stays the same (you are putting in milk), CiVi = CfVf In this question, vessel is FULL of water and you are substituting part of it by milk. So it will be FULL when you put milk in it in step 2. So Vf is the capacity of the vessel. Also, we are using ratios here. Say, you know a/b = 1/2. If a = 10, what is b? It is 20, right? Similarly, you know a/b = 1/2. If b-a = 4, what is a? Note that on the ratio scale, the difference between b and a is 1 (2 - 1). But actually it is 4 so a must be 4 and b must be 8. Check out my posts on ratios: http://www.veritasprep.com/blog/2011/03 ... of-ratios/ Since Vi/Vf = 3/7 but Vf - Vi = 8 (twice of what it is on the ratio scale), Vi must be 6 and Vf must be 14. What is the wine Formula, your solutions are always amazing. _________________ Like my post Send me a Kudos It is a Good manner. My Debrief: how-to-score-750-and-750-i-moved-from-710-to-189016.html Director Joined: 17 Apr 2013 Posts: 633 Concentration: Entrepreneurship, Leadership Schools: HBS '16 (II) GMAT 1: 710 Q50 V36 GMAT 2: 750 Q51 V41 GMAT 3: 790 Q51 V49 GPA: 3.3 Followers: 36 Kudos [?]: 237 [0], given: 287 Re: Eight litres are drawn off from a vessel full of water and s [#permalink] 15 Aug 2013, 12:07 VeritasPrepKarishma wrote: 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/ Responding to a pm: Cf*Vf = Ci*Vi Cf = Ci * (Vi/Vf) When you add milk for the first time, concentration of water in initial solution is 100% Cf = 100% (Vi/Vf) Then you remove some solution which doesn't change its concentration which is 100% (Vi/Vf) When you add milk again, initial concentration is 100% (Vi/Vf) and the final concentration is given by Cf2 = 100% (Vi/Vf) * (Vi/Vf) = 100%(Vi/Vf)^2 We know that this Cf2 is given to be 9/49 So Vi/Vf = 3/7 So every time we take out some solution, the volume of the solution reduces to Vi and every time we add it back, it goes up to Vf. 7x - 3x = 8 lts x = 2 lts So Vi is 6 lts and Vf is 14 lts. The capacity of the vessel i.e. the volume when it is full (i.e. when we put back the 8 lts of milk) is 14 lts. What is Ci and Cf here. _________________ Like my post Send me a Kudos It is a Good manner. My Debrief: how-to-score-750-and-750-i-moved-from-710-to-189016.html Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 6226 Location: Pune, India Followers: 1676 Kudos [?]: 9609 [0], given: 197 Re: Eight litres are drawn off from a vessel full of water and s [#permalink] 16 Aug 2013, 02:41 Expert's post trafficspinners wrote: What is Ci and Cf here. I am not sure what you mean by "wine formula". Here is the link which discussed Ci and Cf i.e. the replacement concept: 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

Manager
Status: Persevering
Joined: 15 May 2013
Posts: 225
Location: India
GMAT Date: 08-02-2013
GPA: 3.7
WE: Consulting (Consulting)
Followers: 1

Kudos [?]: 72 [0], given: 34

Re: Eight litres are drawn off from a vessel full of water and s [#permalink]  18 Aug 2013, 04:20
Here is the general formula

water/capacity =(1-(quantity taken out/total volume))^n
_________________

--It's one thing to get defeated, but another to accept it.

Intern
Joined: 05 Jun 2013
Posts: 9
Location: United States
Concentration: Operations, Marketing
GMAT 1: 740 Q50 V41
WE: Supply Chain Management (Consulting)
Followers: 0

Kudos [?]: 6 [0], given: 1

Re: Eight litres are drawn off from a vessel full of water and s [#permalink]  16 Sep 2013, 03:00
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 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 $$\frac{\frac{(x-8)^2}{x}}{x}=\frac{9}{49}$$ --> $$\frac{(x-8)^2}{x^2}=\frac{9}{49}$$ --> $$\frac{x-8}{x}=\frac{3}{7}$$ --> $$x=14$$.

I tried it like this:

water remaining after 2 times = (x-8)^2 / x
Milk rem = 8x-64 / x

thus, (x-8)^2 / 8x-64 = 9/20
this gives the ans x = 11.6
can u tell me what I'm missing here?
Math Expert
Joined: 02 Sep 2009
Posts: 31288
Followers: 5353

Kudos [?]: 62285 [0], given: 9445

Re: Eight litres are drawn off from a vessel full of water and s [#permalink]  16 Sep 2013, 03:31
Expert's post
Cartman2013 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 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 $$\frac{\frac{(x-8)^2}{x}}{x}=\frac{9}{49}$$ --> $$\frac{(x-8)^2}{x^2}=\frac{9}{49}$$ --> $$\frac{x-8}{x}=\frac{3}{7}$$ --> $$x=14$$.

I tried it like this:

water remaining after 2 times = (x-8)^2 / x
Milk rem = 8x-64 / x

thus, (x-8)^2 / 8x-64 = 9/20
this gives the ans x = 11.6
can u tell me what I'm missing here?

Milk = x - (x-8)^2/x = 16(x-4)/x not 8x-64/x.

Also, the ratio is 9:40 not 9:20.

Hope it helps.
_________________
Intern
Joined: 05 Jun 2013
Posts: 9
Location: United States
Concentration: Operations, Marketing
GMAT 1: 740 Q50 V41
WE: Supply Chain Management (Consulting)
Followers: 0

Kudos [?]: 6 [0], given: 1

Re: Eight litres are drawn off from a vessel full of water and s [#permalink]  16 Sep 2013, 05:47
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 $$\frac{\frac{(x-8)^2}{x}}{x}=\frac{9}{49}$$ --> $$\frac{(x-8)^2}{x^2}=\frac{9}{49}$$ --> $$\frac{x-8}{x}=\frac{3}{7}$$ --> $$x=14$$.

I tried it like this:

water remaining after 2 times = (x-8)^2 / x
Milk rem = 8x-64 / x

thus, (x-8)^2 / 8x-64 = 9/20
this gives the ans x = 11.6
can u tell me what I'm missing here?[/quote]

Milk = x - (x-8)^2/x = 16(x-4)/x not 8x-64/x.

Also, the ratio is 9:40 not 9:20.

Hope it helps.[/quote]

Intern
Joined: 06 Aug 2012
Posts: 20
Followers: 0

Kudos [?]: 1 [0], given: 18

Re: Eight litres are drawn off from a vessel full of water and s [#permalink]  29 Nov 2013, 05:55
Dear Brunel ,

Can we use this formula?

(x-y/x)^n = Qualtity after n operations / Initial qty in vessel

(x-8/x)^2 = 9/49
Intern
Joined: 06 Aug 2012
Posts: 20
Followers: 0

Kudos [?]: 1 [0], given: 18

Re: Eight litres are drawn off from a vessel full of water and s [#permalink]  29 Nov 2013, 06:00
Brunel ,

Please explain this concept in little detail ...

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.
Intern
Joined: 28 Feb 2014
Posts: 10
GPA: 3.27
Followers: 0

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

Re: Eight litres are drawn off from a vessel full of water and s [#permalink]  30 Oct 2014, 09:56
when you state that (x-8)-8*[(x-8)/x] = (x-8)^2/x , what happens to the -8 since you have two? would that not then be (x-16)*[(x-8)/x]?
Math Expert
Joined: 02 Sep 2009
Posts: 31288
Followers: 5353

Kudos [?]: 62285 [0], given: 9445

Re: Eight litres are drawn off from a vessel full of water and s [#permalink]  31 Oct 2014, 05:51
Expert's post
mmcneilly wrote:
when you state that (x-8)-8*[(x-8)/x] = (x-8)^2/x , what happens to the -8 since you have two? would that not then be (x-16)*[(x-8)/x]?

$$(x-8)-\frac{8*(x-8)}{x} =\frac{x(x-8)-8*(x-8)}{x}=\frac{(x-8)(x-8)}{x}=\frac{(x-8)^2}{x}$$.

Hope it's clear.
_________________
Intern
Joined: 08 Mar 2015
Posts: 1
Followers: 0

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

Eight litres are drawn off from a vessel full of water and s [#permalink]  17 May 2015, 22:23
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

(1-8/x)^2=(3/7)^2 ( So square - square is out)
=x-8/x =3/7
=7x-56=3x
=7x-3x=56
x=56/4
=14
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 6226
Location: Pune, India
Followers: 1676

Kudos [?]: 9609 [1] , given: 197

Re: Eight litres are drawn off from a vessel full of water and s [#permalink]  18 May 2015, 05:10
1
KUDOS
Expert's post
guerrero25 wrote:
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 .

This is a ratios concept.
Vi = 3x, Vf = 7x
7x - 3x = 8 (because 8 lts of water was put)
x = 2

So Vi = 3*2 = 6
Vf = 7*2 = 14

You can do the same thing orally like this:
We get Vi : Vf = 3 : 7
The difference between Vi and Vf on the ratio scale is 4 (7 - 3) but actually it is 8. This means the multiplier is 2. So actual values of Vi and Vf must be 3*2 = 6 and 7*2 = 14.

Check this post for more on ratios: http://www.veritasprep.com/blog/2011/03 ... of-ratios/
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

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

Veritas Prep Reviews

Intern
Joined: 31 May 2015
Posts: 4
Followers: 0

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

Eight litres are drawn off from a vessel full of water and s [#permalink]  05 Jun 2015, 19:59
If we look at it logically.. its quite a simple problem.... Lets go step by step...
We know that 8 liters of milk was added twice and some Milk would have come out in the second take out.. So we know that
8 liters < Milk in the mixture < 16 liters
now we already know the final ratio.. lets apply that ..
8 * 49/40 liters < Total mixture < 16 * 49/40
9.8 liters < total mixture < 19.6 liters

Only solution in that range is 14.. hence our answer.. However if the answer choices had been close we might have issue.. but then we can reassuringly rely on GMAT to not require us to make all these calculations ..
Eight litres are drawn off from a vessel full of water and s   [#permalink] 05 Jun 2015, 19:59

Go to page   Previous    1   2   3    Next  [ 41 posts ]

Similar topics Replies Last post
Similar
Topics:
12 Pipe A and Pipe B fill water into a tank of capacity 1000 litres at 5 30 Aug 2014, 03:24
17 A 100-litre mixture of milk and water contains 36 litres of 14 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
5 A recipe for soda requires w litres of water for every litre 9 29 Apr 2008, 05:01
Display posts from previous: Sort by