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# PS- Lets see who cracks it.....

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Manager
Joined: 28 Jan 2004
Posts: 203
Location: India
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PS- Lets see who cracks it..... [#permalink]  05 Feb 2004, 03:12
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Please show me the right way to do this.

A container contained 80Kg of milk. from this container 8Kg of milk was taken and replaced by water. the process of taking out 8kg of liquid was repeated 2 times. How much milk is now there in the vessel.

A. 54
B. 56
C. 58.32
D. 53.18
E. I m not that smart.....
GMAT Instructor
Joined: 07 Jul 2003
Posts: 770
Location: New York NY 10024
Schools: Haas, MFE; Anderson, MBA; USC, MSEE
Followers: 13

Kudos [?]: 52 [0], given: 0

Re: PS- Lets see who cracks it..... [#permalink]  05 Feb 2004, 03:42
mdfrahim wrote:
Please show me the right way to do this.

A container contained 80Kg of milk. from this container 8Kg of milk was taken and replaced by water. the process of taking out 8kg of liquid was repeated 2 times. How much milk is now there in the vessel.

A. 54
B. 56
C. 58.32
D. 53.18
E. I m not that smart.....

The way to do this is
1) realize that you remove a "solution" and add "water" which creates a new solution of X% milk.
2) everytime you remove 8kg of the solution, keep track of how much of that solution is milk by multiplying 8kg x X%.
repeat.
3) The amount of milk left is 80kg less that amount you removed.

P.S. strickly speaking, we must assume milk and water have same density.
_________________

Best,

AkamaiBrah
Former Senior Instructor, Manhattan GMAT and VeritasPrep
Vice President, Midtown NYC Investment Bank, Structured Finance IT
MFE, Haas School of Business, UC Berkeley, Class of 2005
MBA, Anderson School of Management, UCLA, Class of 1993

Manager
Joined: 28 Jan 2004
Posts: 203
Location: India
Followers: 2

Kudos [?]: 14 [0], given: 4

Some one please do what Akamiah has suggested. I am not able to get anything..its going toooooo complex.
Intern
Joined: 29 May 2003
Posts: 13
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C is right (I think) [#permalink]  05 Feb 2004, 07:01
Actually there is no need to calculate it.

8*3 = 24kg milk, so if we pretend that we remove 8kg of milk only three times there will be 56kg milk left. But now we know that some of what we remove will be water so there has to be more than 56kg of milk left.

GMAT Club Legend
Joined: 15 Dec 2003
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First drain:
8kg of milk taken out. You are left with 72 kg of milk and 8kg of water

Second drain:
The liquid left is with a concentration of 90% (72kg) of milk
Then when you take 8kg out, you are taking 90% milk and 10% water
Therefore, the quantity of milk left will be 72kg * 0.9 = 64.8kg milk after the second drain

Third drain:
Same process. 64.8kg of milk * 0.9 = 58.32kg of milk left
_________________

Best Regards,

Paul

Director
Joined: 03 Jul 2003
Posts: 655
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Kudos [?]: 22 [0], given: 0

Re: PS- Lets see who cracks it..... [#permalink]  05 Feb 2004, 07:42
mdfrahim wrote:
Please show me the right way to do this.

A container contained 80Kg of milk. from this container 8Kg of milk was taken and replaced by water. the process of taking out 8kg of liquid was repeated 2 times. How much milk is now there in the vessel.

A. 54
B. 56
C. 58.32
D. 53.18
E. I m not that smart.....

Good Question. But, the Question should be reworded to
".... This process of taking out 8Kg of liquid was repeated 2 *MORE*
times....".

I interpreted the question as taking 8kg liquid only two times.
Did anyone else interpret in the same way?

Interesting question. Keep these kind of questions flooding the forum !
GMAT Club Legend
Joined: 15 Dec 2003
Posts: 4313
Followers: 27

Kudos [?]: 217 [0], given: 0

I agree with you kpadma. It got me confused too as to the number of times the process was repeated. I guess the answer choices gave me the hint.
_________________

Best Regards,

Paul

Senior Manager
Joined: 06 Dec 2003
Posts: 366
Location: India
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Ans is C: 58.32

milk left after 3rd operation=(1-8/80)^3 * 80

Cheers, Dharmin
Director
Joined: 28 Oct 2003
Posts: 503
Location: 55405
Followers: 1

Kudos [?]: 10 [0], given: 0

kpadma: I agree that the phrasing is suspect, but your correction isn't any better. To be "repeated 2 more times" it must have already been repeated. "Performed two more times" would be the clearest way to ask this.

I know this is PS, not SC, but these little differences are important.
Director
Joined: 03 Jul 2003
Posts: 655
Followers: 2

Kudos [?]: 22 [0], given: 0

stoolfi wrote:
kpadma: I agree that the phrasing is suspect, but your correction isn't any better. To be "repeated 2 more times" it must have already been repeated. "Performed two more times" would be the clearest way to ask this.

I know this is PS, not SC, but these little differences are important.

Stoolfi: You are most welcome to correct the mistakes!
How else are we going to learn?
SVP
Joined: 30 Oct 2003
Posts: 1797
Location: NewJersey USA
Followers: 5

Kudos [?]: 41 [0], given: 0

I agree with stoolfi about this question. It is not clear whether the diluation occured 2 times or 3 times.
if it occured 2 times then remaining milk is 0.9*0.9 * 80 = 64.8
if it occured 3 times then remaining milk is 0.9*0.9*0.9 * 80 = 58.32

( 8Kg is 10 percent of 80kg so 90% milk remains at each dilution )
Manager
Joined: 28 Jan 2004
Posts: 203
Location: India
Followers: 2

Kudos [?]: 14 [0], given: 4

Well...the correct answer is 58.32. Anand the dilution has occured 3 times.
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