GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 16 Nov 2019, 18:52 ### 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

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # A 100-litre mixture of milk and water contains 36 litres of

Author Message
TAGS:

### Hide Tags

Current Student B
Joined: 22 Jul 2014
Posts: 120
Concentration: General Management, Finance
GMAT 1: 670 Q48 V34 WE: Engineering (Energy and Utilities)
A 100-litre mixture of milk and water contains 36 litres of  [#permalink]

### Show Tags

5
1
63 00:00

Difficulty:   85% (hard)

Question Stats: 56% (02:40) correct 44% (03:11) wrong based on 293 sessions

### HideShow timer Statistics

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
Current Student B
Joined: 22 Jul 2014
Posts: 120
Concentration: General Management, Finance
GMAT 1: 670 Q48 V34 WE: Engineering (Energy and Utilities)
A 100-litre mixture of milk and water contains 36 litres of  [#permalink]

### Show Tags

16
18 I just found a direct way of doing this.

For replacement problems

C(Final)/C(Initial) = $$(1-x/y)^n$$

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 ##### General Discussion
Director  G
Joined: 23 Jan 2013
Posts: 523
Schools: Cambridge'16
Re: A 100-litre mixture of milk and water contains 36 litres of  [#permalink]

### Show Tags

1
can anyone explain me, I did

0.36(100-x)+0x=0.27(100)
36-0.36x=27
x=25

and what is wrong?
Manager  B
Joined: 27 May 2014
Posts: 76
Re: A 100-litre mixture of milk and water contains 36 litres of  [#permalink]

### Show Tags

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.
Intern  Joined: 27 Aug 2014
Posts: 27
GMAT Date: 09-27-2014
A 100-litre mixture of milk and water contains 36 litres of  [#permalink]

### Show Tags

4
2
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.

Originally posted by bazc on 27 Aug 2014, 22:56.
Last edited by bazc on 28 Aug 2014, 01:59, edited 3 times in total.
SVP  Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1729
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Re: A 100-litre mixture of milk and water contains 36 litres of  [#permalink]

### Show Tags

2
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

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.......... _________________
Kindly press "+1 Kudos" to appreciate SVP  Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1729
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
A 100-litre mixture of milk and water contains 36 litres of  [#permalink]

### Show Tags

Temurkhon wrote:
can anyone explain me, I did

0.36(100-x)+0x=0.27(100)
36-0.36x=27
x=25

and what is wrong?

The iteration is twice, kindly refer my post above......
_________________
Kindly press "+1 Kudos" to appreciate Current Student B
Joined: 22 Jul 2014
Posts: 120
Concentration: General Management, Finance
GMAT 1: 670 Q48 V34 WE: Engineering (Energy and Utilities)
Re: A 100-litre mixture of milk and water contains 36 litres of  [#permalink]

### Show Tags

1
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

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 Intern  Joined: 27 Aug 2014
Posts: 27
GMAT Date: 09-27-2014
A 100-litre mixture of milk and water contains 36 litres of  [#permalink]

### Show Tags

1
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

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.
Intern  Joined: 28 Jan 2013
Posts: 27
Re: A 100-litre mixture of milk and water contains 36 litres of  [#permalink]

### Show Tags

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???
Intern  Joined: 27 Aug 2014
Posts: 27
GMAT Date: 09-27-2014
Re: A 100-litre mixture of milk and water contains 36 litres of  [#permalink]

### Show Tags

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.

Posted from my mobile device
Intern  Joined: 08 Oct 2013
Posts: 1
Re: A 100-litre mixture of milk and water contains 36 litres of  [#permalink]

### Show Tags

4
1
36(1-x)^2=25

Solve for x: 36x^2-72x+11=0 (-66x-6x)

Factors: x=1/6, x=11/6

1/6*100=16.67

11/6*100=183 (not possible)

Hence, x=16.67
Intern  Joined: 28 Jan 2013
Posts: 27
Re: A 100-litre mixture of milk and water contains 36 litres of  [#permalink]

### Show Tags

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".
Intern  Joined: 27 Aug 2014
Posts: 27
GMAT Date: 09-27-2014
Re: A 100-litre mixture of milk and water contains 36 litres of  [#permalink]

### Show Tags

1
2
alphonsa wrote:
:-D I just found a direct way of doing this.

For replacement problems

C(Final)/C(Initial) = $$(1-x/y)^n$$

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
Board of Directors P
Joined: 17 Jul 2014
Posts: 2497
Location: United States (IL)
Concentration: Finance, Economics
GMAT 1: 650 Q49 V30 GPA: 3.92
WE: General Management (Transportation)
Re: A 100-litre mixture of milk and water contains 36 litres of  [#permalink]

### Show Tags

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!
Director  D
Joined: 05 Mar 2015
Posts: 986
Re: A 100-litre mixture of milk and water contains 36 litres of  [#permalink]

### Show Tags

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
Manager  B
Joined: 02 Jul 2016
Posts: 130
Location: India
GMAT 1: 650 Q49 V28 GPA: 4
A 100-litre mixture of milk and water contains 36 litres of  [#permalink]

### Show Tags

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
Senior Manager  G
Joined: 09 Feb 2015
Posts: 328
Location: India
Concentration: Social Entrepreneurship, General Management
GMAT 1: 690 Q49 V34 GMAT 2: 720 Q49 V39 GPA: 2.8
Re: A 100-litre mixture of milk and water contains 36 litres of  [#permalink]

### Show Tags

its really not clear that there are two iterations!!
if this process is repeated once suggests that there is only one. :S
Intern  B
Joined: 08 May 2011
Posts: 21
Re: A 100-litre mixture of milk and water contains 36 litres of  [#permalink]

### Show Tags

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..
Retired Moderator P
Status: The best is yet to come.....
Joined: 10 Mar 2013
Posts: 481
Re: A 100-litre mixture of milk and water contains 36 litres of  [#permalink]

### Show Tags

2
2
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

∴ $$36*\frac{(100-x)}{100}*\frac{(100-x)}{100}=25$$
$$=>$$$$(\frac{(100-x)}{100})^2$$=$$\frac{25}{36}$$
$$=>(\frac{(100-x)}{100})$$=$$\frac{5}{6}$$
$$=>600-6x=500$$
$$=> -6x=-100$$
$$=>x=16.67$$
_________________
Hasan Mahmud Re: A 100-litre mixture of milk and water contains 36 litres of   [#permalink] 11 Oct 2017, 11:28

Go to page    1   2    Next  [ 27 posts ]

Display posts from previous: Sort by

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