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A 100litre mixture of milk and water contains 36 litres of [#permalink]
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27 Aug 2014, 00:28
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A 100litre 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
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Re: A 100litre mixture of milk and water contains 36 litres of [#permalink]
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27 Aug 2014, 06:58
can anyone explain me, I did
0.36(100x)+0x=0.27(100) 360.36x=27 x=25
and what is wrong?



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Re: A 100litre 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.



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A 100litre 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.
In which case,
36  25 = 36%x + (36  36%x)%x 11 = 36% (x + x  x^2/100) 110000/36 = x^2 + 200x x = 16.67
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.



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Re: A 100litre mixture of milk and water contains 36 litres of [#permalink]
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28 Aug 2014, 01:11
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alphonsa wrote: A 100litre 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 36 .................... 64 ......................... 100 X litres of mixture is removed; so water & milk gets removed proportionally \(36  \frac{36x}{100}\) ............. \(64  \frac{64x}{100}\) ............... 100  x Now x litres of water is added \(36  \frac{36x}{100}\) ............. \(64  \frac{64x}{100} + x\) ............... 100 Process is repeated; Again x litres of mixture is removed Now, milk in the new solution \(= (36\frac{9x}{25})%\) So, milk is x litres of mixture \(= (36\frac{9x}{25}) * \frac{x}{100}\) Milk content in new mixture\(= 36  \frac{36x}{100}  (36\frac{9x}{25}) * \frac{x}{100} = 25\) This is a complex quadratic equation..... this question is good indeed, seems some flaw in the numeric.... Bunuel, your kind comments please..........
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A 100litre mixture of milk and water contains 36 litres of [#permalink]
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28 Aug 2014, 01:16
Temurkhon wrote: can anyone explain me, I did
0.36(100x)+0x=0.27(100) 360.36x=27 x=25
and what is wrong? The iteration is twice, kindly refer my post above......
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Re: A 100litre mixture of milk and water contains 36 litres of [#permalink]
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28 Aug 2014, 04:56
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PareshGmat wrote: alphonsa wrote: A 100litre 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 36 .................... 64 ......................... 100 X litres of mixture is removed; so water & milk gets removed proportionally \(36  \frac{36x}{100}\) ............. \(64  \frac{64x}{100}\) ............... 100  x Now x litres of water is added \(36  \frac{36x}{100}\) ............. \(64  \frac{64x}{100} + x\) ............... 100 Process is repeated; Again x litres of mixture is removed Now, milk in the new solution \(= (36\frac{9x}{25})%\) So, milk is x litres of mixture \(= (36\frac{9x}{25}) * \frac{x}{100}\) Milk content in new mixture\(= 36  \frac{36x}{100}  (36\frac{9x}{25}) * \frac{x}{100} = 25\) This is a complex quadratic equation..... this question is good indeed, seems some flaw in the numeric.... Bunuel, your kind comments please.......... 36 36x/100 ... Why 36x/100



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A 100litre 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 100litre 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 36 .................... 64 ......................... 100 X litres of mixture is removed; so water & milk gets removed proportionally \(36  \frac{36x}{100}\) ............. \(64  \frac{64x}{100}\) ............... 100  x Now x litres of water is added \(36  \frac{36x}{100}\) ............. \(64  \frac{64x}{100} + x\) ............... 100 Process is repeated; Again x litres of mixture is removed Now, milk in the new solution \(= (36\frac{9x}{25})%\) So, milk is x litres of mixture \(= (36\frac{9x}{25}) * \frac{x}{100}\) Milk content in new mixture\(= 36  \frac{36x}{100}  (36\frac{9x}{25}) * \frac{x}{100} = 25\) This is a complex quadratic equation..... this question is good indeed, seems some flaw in the numeric.... Bunuel, your kind comments please.......... 36 36x/100 ... Why 36x/100 x% of 36 = 36% of x of milk is removed in the first iteration.



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Re: A 100litre 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???



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Re: A 100litre 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??? No, process is repeated, so twice totally. Please refer above post. Posted from my mobile device



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Re: A 100litre mixture of milk and water contains 36 litres of [#permalink]
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28 Aug 2014, 08:10
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36(1x)^2=25
Solve for x: 36x^272x+11=0 (66x6x)
Factors: x=1/6, x=11/6
1/6*100=16.67
11/6*100=183 (not possible)
Hence, x=16.67



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Re: A 100litre 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".



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A 100litre mixture of milk and water contains 36 litres of [#permalink]
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29 Aug 2014, 04:13
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I just found a direct way of doing this. For replacement problems C(Final)/C(Initial) = \((1x/y)^n\) Where C is the concentration x is the amount replaced y is the total amount and n is the number of replacement Therefore for the given problem (25/36) = \((1 x/100 )^2\) Take Square root on both sides 5/6 = (1 x/100) x= 16.67 litres



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Re: A 100litre mixture of milk and water contains 36 litres of [#permalink]
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29 Aug 2014, 05:39
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alphonsa wrote: :D I just found a direct way of doing this. For replacement problems C(Final)/C(Initial) = \((1x/y)^n\) Where C is the concentration x is the amount replaced y is the total amount and n is the number of replacement Therefore for the given problem (25/36) = \((1 x/100 )^2\) Take Square root on both sides 5/6 = (1 x/100) x= 16.67 litres That's fine as long as you get the logic behind it is similar to decline in population. Final = Original * ( 1  rate)^n



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Re: A 100litre 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 360.36x 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 = (360.36x)/100 and we remove again (360.36x)x/100
we then are told that 360.36x  (360.36x)x/100 = 25 11=0.36x + (360.36x)x/100 multiply by 100 1100 = 36x+36x0.36x^2 1100=72x0.36x^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!



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Re: A 100litre 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 360.36x 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 = (360.36x)/100 and we remove again (360.36x)x/100
we then are told that 360.36x  (360.36x)x/100 = 25 11=0.36x + (360.36x)x/100 multiply by 100 1100 = 36x+36x0.36x^2 1100=72x0.36x^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%(1X/100)^2 = 25% * 100% (1x/100)^2=25/36>(1x/100)^2=(5/6)^2 100X=500/6 x=100/6>16.67... Ans B



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A 100litre 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 369/25x 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*(3636/100x)^2)/(36)^2
By solving it. We get x=100/6 OR 50/3 OR 16.67
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Re: A 100litre mixture of milk and water contains 36 litres of [#permalink]
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24 Oct 2016, 08:03
its really not clear that there are two iterations!! if this process is repeated once suggests that there is only one. :S



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Re: A 100litre mixture of milk and water contains 36 litres of [#permalink]
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25 Apr 2017, 11:44
goforgmat wrote: its really not clear that there are two iterations!! if this process is repeated once suggests that there is only one. :S I agree with this... The question should say "the process is repeated AGAIN" .. once seems to suggest that the process happened once. This took me around 4 minutes to solve..



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Re: A 100litre mixture of milk and water contains 36 litres of [#permalink]
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After first removal, the mixture would be \(100x\) and will contain \(36*\frac{(100x)}{100}\) liter milk. After second removal, the mixture would be \(100x\) and will contain \(36*\frac{(100x)}{100}*\frac{(100x)}{100}\)liter milk ∴ \(36*\frac{(100x)}{100}*\frac{(100x)}{100}=25\) \(=>\)\((\frac{(100x)}{100})^2\)=\(\frac{25}{36}\) \(=>(\frac{(100x)}{100})\)=\(\frac{5}{6}\) \(=>6006x=500\) \(=> 6x=100\) \(=>x=16.67\)
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