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A 100-litre mixture of milk and water contains 36 litres of [#permalink]

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27 Aug 2014, 00:28

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Question Stats:

55% (03:47) correct
45% (02:44) wrong based on 257 sessions

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A 100-litre mixture of milk and water contains 36 litres of milk. 'x' litres of this mixture is removed and replaced with an equal quantum of water. If the process is repeated once, then the concentration of the milk stands reduced at 25%. What is the value of x?

A) 17.5 litres B) 16.67 litres C) 17.67 litres D) 16.5 litres E) 16 litres

Re: A 100-litre mixture of milk and water contains 36 litres of [#permalink]

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27 Aug 2014, 17:47

I was thinking this:

Current mixture: 36% or 36 liters of milk. Since my total liters don't change my new milk content is 25 liters. Thus 36-(36/100)=25. Not sure where I'm going wrong either.

A 100-litre mixture of milk and water contains 36 litres of [#permalink]

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27 Aug 2014, 22:56

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My guess is that the question is incorrect because if 16.67 L is the answer, then the amount of milk removed would be 36% of 16.67 L = 6 L. So milk percentage should be reduced to 30% and not 25%.

Please correct me if I am wrong.

Oh, I forgot to read that the process is repeated once.

The above approach involved wolfram alpha, so not useful on the gmat.

Simplest approach is:

To get from 36 to 25 in two independent iterations, we can spot that there is only one way by removing a constant 1/6th is removed at each stage: 6 + 5.

(1/6)*100 = 16.67 L Ans.

Last edited by bazc on 28 Aug 2014, 01:59, edited 3 times in total.

Re: A 100-litre mixture of milk and water contains 36 litres of [#permalink]

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28 Aug 2014, 01:11

alphonsa wrote:

A 100-litre mixture of milk and water contains 36 litres of milk. 'x' litres of this mixture is removed and replaced with an equal quantum of water. If the process is repeated once, then the concentration of the milk stands reduced at 25%. What is the value of x?

A) 17.5 litres B) 16.67 litres C) 17.67 litres D) 16.5 litres E) 16 litres

Source: 4Gmat

Milk ................ Water .................. Total

Re: A 100-litre mixture of milk and water contains 36 litres of [#permalink]

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28 Aug 2014, 04:56

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This post was BOOKMARKED

PareshGmat wrote:

alphonsa wrote:

A 100-litre mixture of milk and water contains 36 litres of milk. 'x' litres of this mixture is removed and replaced with an equal quantum of water. If the process is repeated once, then the concentration of the milk stands reduced at 25%. What is the value of x?

A) 17.5 litres B) 16.67 litres C) 17.67 litres D) 16.5 litres E) 16 litres

Source: 4Gmat

Milk ................ Water .................. Total

A 100-litre mixture of milk and water contains 36 litres of [#permalink]

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28 Aug 2014, 04:59

alphonsa wrote:

PareshGmat wrote:

alphonsa wrote:

A 100-litre mixture of milk and water contains 36 litres of milk. 'x' litres of this mixture is removed and replaced with an equal quantum of water. If the process is repeated once, then the concentration of the milk stands reduced at 25%. What is the value of x?

A) 17.5 litres B) 16.67 litres C) 17.67 litres D) 16.5 litres E) 16 litres

Source: 4Gmat

Milk ................ Water .................. Total

Re: A 100-litre mixture of milk and water contains 36 litres of [#permalink]

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28 Aug 2014, 06:44

For 100 lts of mixture, we have 36 lts of milk.(36%) after removing some amount of mixture and adding the same quantity of water the milk content is 25lts.(25%)

Difference in milk = 9lts

100 lts of mixture has 36 lts of milk, so how much mixture will have 9lts of milk 100 - 36 ? - 9

=>(9*100)/36 = 25

So 25 lts of mixture is replaced by 25lts of water.

Per my understanding there is something missing in the question???

Re: A 100-litre mixture of milk and water contains 36 litres of [#permalink]

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28 Aug 2014, 07:11

gayam wrote:

For 100 lts of mixture, we have 36 lts of milk.(36%) after removing some amount of mixture and adding the same quantity of water the milk content is 25lts.(25%)

Difference in milk = 9lts

100 lts of mixture has 36 lts of milk, so how much mixture will have 9lts of milk 100 - 36 ? - 9

=>(9*100)/36 = 25

So 25 lts of mixture is replaced by 25lts of water.

Per my understanding there is something missing in the question???

Re: A 100-litre mixture of milk and water contains 36 litres of [#permalink]

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28 Aug 2014, 21:42

gayam wrote:

For 100 lts of mixture, we have 36 lts of milk.(36%) after removing some amount of mixture and adding the same quantity of water the milk content is 25lts.(25%)

Difference in milk = 9lts

100 lts of mixture has 36 lts of milk, so how much mixture will have 9lts of milk 100 - 36 ? - 9

=>(9*100)/36 = 25

So 25 lts of mixture is replaced by 25lts of water.

Per my understanding there is something missing in the question???

OK, Thanks mate. I get it now. I think the question would be more clear if it problem states "the process is repeated once again".

Re: A 100-litre mixture of milk and water contains 36 litres of [#permalink]

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05 Mar 2016, 16:49

I believe I would not be the first person to say that this is a very BAD question for GMAT practice.

Water = 64/100 Milk = 36/100 so when we remove x, we remove 0.36x of milk, and we are left with 36-0.36x of milk. then we add x of water, and we have 64+0.36x water.

since we need to repeat this.. we need to find new ratio of milk and water: milk = (36-0.36x)/100 and we remove again (36-0.36x)x/100

we then are told that 36-0.36x - (36-0.36x)x/100 = 25 11=0.36x + (36-0.36x)x/100 multiply by 100 1100 = 36x+36x-0.36x^2 1100=72x-0.36x^2

to solve this..is a nightmare...to be honest..I spent almost 1 hour to try to figure out maybe there's a shortcut..but there is not

YOU WILL NEVER SEE SUCH A COMPLEX QUADRATIC EQUATION on GMAT!

Re: A 100-litre mixture of milk and water contains 36 litres of [#permalink]

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24 Apr 2016, 11:26

mvictor wrote:

I believe I would not be the first person to say that this is a very BAD question for GMAT practice.

Water = 64/100 Milk = 36/100 so when we remove x, we remove 0.36x of milk, and we are left with 36-0.36x of milk. then we add x of water, and we have 64+0.36x water.

since we need to repeat this.. we need to find new ratio of milk and water: milk = (36-0.36x)/100 and we remove again (36-0.36x)x/100

we then are told that 36-0.36x - (36-0.36x)x/100 = 25 11=0.36x + (36-0.36x)x/100 multiply by 100 1100 = 36x+36x-0.36x^2 1100=72x-0.36x^2

to solve this..is a nightmare...to be honest..I spent almost 1 hour to try to figure out maybe there's a shortcut..but there is not

YOU WILL NEVER SEE SUCH A COMPLEX QUADRATIC EQUATION on GMAT!

Working formula ... Initial Concentration*Initial Volume=Final Concentration*Final Volume. Let X is the part removed from 100 lts. 36%(1-X/100)^2 = 25% * 100% (1-x/100)^2=25/36------>(1-x/100)^2=(5/6)^2 100-X=500/6 x=100/6------>16.67... Ans B

A 100-litre mixture of milk and water contains 36 litres of [#permalink]

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10 Oct 2016, 09:17

Well This was my approach. In 100L mixture we have 36 L milk and 64 L water. Hence M and W are in the ratio of 9:16. x L of solution has been removed. Hence we have 36-9/25x of milk and 64- 16/25x of water. FOR CALCULATION SIMPLICITY multiply and divide 9/25x by 4 WE GET 36/100x Since this procedure is repeated 2 times. This was my equation 25=36*(36-36/100x)^2)/(36)^2

By solving it. We get x=100/6 OR 50/3 OR 16.67

FOCUS ON CONCEPT RATHER THAN MEMORISING THE FORMULAS

Re: A 100-litre mixture of milk and water contains 36 litres of [#permalink]

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11 Oct 2017, 11:28

After first removal, the mixture would be \(100-x\) and will contain \(36*\frac{(100-x)}{100}\) liter milk. After second removal, the mixture would be \(100-x\) and will contain \(36*\frac{(100-x)}{100}*\frac{(100-x)}{100}\)liter milk