GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 07 Jul 2020, 20:45

### 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

# 3L of milk are drawn from a container containing 30L of milk. It is re

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 65062
3L of milk are drawn from a container containing 30L of milk. It is re  [#permalink]

### Show Tags

16 Apr 2020, 01:13
00:00

Difficulty:

65% (hard)

Question Stats:

55% (02:28) correct 45% (02:24) wrong based on 62 sessions

### HideShow timer Statistics

Competition Mode Question

3L of milk are drawn from a container containing 30L of milk. It is replaced by water and the process is repeated 2 times. What is the ratio of milk to water at the end?

A. $$\frac{729}{271}$$

B. $$\frac{743}{229}$$

C. $$\frac{81}{19}$$

D. $$\frac{2187}{100}$$

E. $$\frac{813}{19}$$

_________________
CR Forum Moderator
Joined: 18 May 2019
Posts: 811
Re: 3L of milk are drawn from a container containing 30L of milk. It is re  [#permalink]

### Show Tags

16 Apr 2020, 01:39
1
2
We are given that there was a 30L milk in a container. Out of this milk, 3 liters of milk was taken out and replaced with 3L of water. This process of drawing out 3L from the container was repeated twice.
After the first replacement, the amount of milk left$$= 30-3=27L$$ concentration of milk in container = $$0.9$$
After second replacement the amount of milk left$$= 27 - 3*0.9 = 27-2.7 = 24.3L.$$ Concentration is now $$\frac{243}{300} = 0.81$$
After third replacement the amount of milk left $$= 24.3 - 3*0.81 = 24.3-2.43 = 21.87L$$.
Concetration $$=\frac{21.87}{30}=\frac{729}{1000}$$
Hence for every $$729L$$ of milk there is $$(1000-729) = 271L$$ of water.
So ration of milk to water $$= \frac{729}{271}$$

DS Forum Moderator
Joined: 19 Oct 2018
Posts: 1994
Location: India
Re: 3L of milk are drawn from a container containing 30L of milk. It is re  [#permalink]

### Show Tags

16 Apr 2020, 02:04
1
1
Amount of Milk after 3 Replacements/ Total Volume of the mixture = $$(1-\frac{3}{30})^3$$

Amount of Milk after 3 Replacements/ Total Volume of the mixture = $$\frac{729}{1000}$$

ratio of milk to water at the end = 729 : (1000-729) = 729 : 271
Senior Manager
Joined: 24 Oct 2015
Posts: 496
Location: India
Schools: Sloan '22, ISB, IIM
GMAT 1: 650 Q48 V31
GPA: 4
Re: 3L of milk are drawn from a container containing 30L of milk. It is re  [#permalink]

### Show Tags

16 Apr 2020, 03:25
1
1
Formula in use: Final concentration = Initial concentration * $$(1- \frac{amount replaced}{total amount})^{n}$$

Final concentration of milk = $$100*(1-\frac{3}{30})^3$$ = $$100*(\frac{27}{30})^3$$ = 72.9%
concentration of water = 27.1%
milk:water = $$\frac{729}{271}$$
Ans: A
GMATWhiz Representative
Joined: 07 May 2019
Posts: 802
Location: India
Re: 3L of milk are drawn from a container containing 30L of milk. It is re  [#permalink]

### Show Tags

16 Apr 2020, 04:15
1

Solution:

• Initial amount of milk in container = 30 L
• Initial amount of water in container = 0 L
• 3 L of milk is removed and replaced with water
o Amount of milk in container = 30 – 3 = 27L
o Amount of water in the container = 3L
 Ratio of milk to water = $$\frac{27}{3} = \frac{9}{1}$$
• Now, again 3L solution is removed from the container.
o In this case only milk is not removed, water is also removed.
o Milk removed from the container = $$\frac{9}{10}*3 = 2.7$$ L
 Milk left in the container = $$27 – 2.7 = 24.3$$ L
o Water removed from the container = $$\frac{1}{10}*3 = 0.3$$
 Water left in the container = $$3 – 0.3 = 2.7$$ L
 Water in the container after the addition of 3 litre water = $$2.7+3 = 5.7$$ L
o Ratio of milk to water = $$\frac{24.3}{5.7}$$.
• Now, 3L solution is replaced with water one more time
o Milk removed = $$\frac{24.3}{30}*3 = 2.43$$
 Milk left in the solution = $$24.3 – 2.43 = 21.87$$ L
o Water removed =$$\frac{5.7}{30}*3=0.57L$$
 Water left = $$5.7 – 0.57 = 5.13$$ L
Water in container after the addition = $$5.13+3=8.13$$
• Ratio of milk to water = $$\frac{21.87}{8.13} = \frac{2187}{813}=\frac{729}{271}$$
Hence, the correct answer is Option A.
_________________

GMAT Prep truly Personalized using Technology

Prepare from an application driven course that serves real-time improvement modules along with a well-defined adaptive study plan. Start a free trial to experience it yourself and get access to 25 videos and 300 GMAT styled questions.

Score Improvement Strategy: How to score Q50+ on GMAT | 5 steps to Improve your Verbal score
Study Plan Articles: 3 mistakes to avoid while preparing | How to create a study plan? | The Right Order of Learning | Importance of Error Log
Helpful Quant Strategies: Filling Spaces Method | Avoid Double Counting in P&C | The Art of Not Assuming anything in DS | Number Line Method
Key Verbal Techniques: Plan-Goal Framework in CR | Quantifiers the tiny Game-changers | Countable vs Uncountable Nouns | Tackling Confusing Words in Main Point
Sloan MIT School Moderator
Joined: 07 Mar 2019
Posts: 1287
Location: India
GMAT 1: 580 Q43 V27
WE: Sales (Energy and Utilities)
Re: 3L of milk are drawn from a container containing 30L of milk. It is re  [#permalink]

### Show Tags

16 Apr 2020, 08:29
3L of milk are drawn from a container containing 30L of milk. It is replaced by water and the process is repeated 2 times. What is the ratio of milk to water at the end?

A. 729/271

B. 743/229

C. 81/19

D. 2187/100

E. 813/19

After removing 3L of milk 3L of water is added. So the mixture has Milk to Water ratio of 9:1. Milk is 27L and Water is 2.7L. Now the process is repeated again so 3L of the mixture is removed.
Removed mixture has water content of 0.3L and Milk content of 2.7L. Total milk content left = 24.3L. As 3L of water is added total water content is 2.7 + 3 = 5.7L
Ratio of Milk to Water = $$\frac{24.3}{5.7}$$ = $$\frac{81}{19}$$

_________________
Intern
Joined: 16 Apr 2020
Posts: 1
Re: 3L of milk are drawn from a container containing 30L of milk. It is re  [#permalink]

### Show Tags

16 Apr 2020, 09:24
Gotta add up to a whole number no math needed but each time factor out 10% off the next calculation.

Posted from my mobile device
SVP
Joined: 24 Nov 2016
Posts: 1663
Location: United States
Re: 3L of milk are drawn from a container containing 30L of milk. It is re  [#permalink]

### Show Tags

16 Apr 2020, 10:10
1
Quote:
3L of milk are drawn from a container containing 30L of milk. It is replaced by water and the process is repeated 2 times. What is the ratio of milk to water at the end?

con_final=con_initial(vol_intial-pure/vol_initial)^3
x=100%milk(30-3/30-3+3)^3
x=(27/30)^3=(3^3/3*10)^3=3^9/3^3*10^3
x=3^6/10^3=729/1000=milk/total
milk/water=729/(1000-729)=729/271

ans (A)
Senior Manager
Status: Student
Joined: 14 Jul 2019
Posts: 371
Location: United States
Concentration: Accounting, Finance
GPA: 3.9
WE: Education (Accounting)
Re: 3L of milk are drawn from a container containing 30L of milk. It is re  [#permalink]

### Show Tags

16 Apr 2020, 10:31
1
3L of milk are drawn from a container containing 30L of milk. It is replaced by water and the process is repeated 2 times. What is the ratio of milk to water at the end?
After 1st replacement : Milk 27 Water 3
After 2nd replacement, REDUCED milk = 3*27/30 = 2.7 .New ratio M:W = 24.3 : 5.7 = 8.1 : 1.9
After 3rd time, milk reduced = 3 * 81/100 = 2.43. New ratio M:W = (24.3 -2.43) 5.7 +2.43) =21.87 : 8.13 = 7.29 : 2.71
Director
Joined: 30 Sep 2017
Posts: 962
GMAT 1: 720 Q49 V40
GPA: 3.8
3L of milk are drawn from a container containing 30L of milk. It is re  [#permalink]

### Show Tags

16 Apr 2020, 14:50
Worthy question!

Although not necessary for this specific question, I will do generalization to such typical MIXTURE PROBLEM so that you can solve similar, but harder question (eg. repeated 10x etc.)

Process #1: (30-3) litre wine left = 30*(1-1/10) = 30*(9/10)^1 litre wine left, total 30L;

#2: {30*(9/10)^1} - {30*(9/10)^1}/30*3L= 30*(9/10)*(1-1/10) = 30*(9/10)^2 litre wine left, total 30L;

... etc

I clearly see now following patterns when process are repeated N times:
Wine left =30*(9/10)^N
Water content =30*{1-(9/10)^N}

N=2
Wine left =30*(9/10)^2 =30*(81/100)
Water content =30*{1-(9/10)^2} = 31*(19/100)
---> Wine to water ratio
= 30*(81/100) / {30*(19/100)}
= 81/19

Posted from my mobile device
Retired Moderator
Status: enjoying
Joined: 19 Feb 2007
Posts: 5566
Location: India
WE: Education (Education)
Re: 3L of milk are drawn from a container containing 30L of milk. It is re  [#permalink]

### Show Tags

16 Apr 2020, 17:07
Top Contributor
The ratio of milk: water after two repeats is 24L Milk and 6L water, 24/6 or four times. The closest answer is only C, which is 81/19. However, I am not clear why the option 24/6 is not given as an answer.
_________________
If as a non –native, you do not get an inkling of that algorithm for the correct answer in the first few moments, then you need help. You can kick start with my course material from foundation to zenith in a few steps. 919884544509 / newnaren@gmail.com
Director
Joined: 16 Jan 2019
Posts: 652
Location: India
Concentration: General Management
WE: Sales (Other)
Re: 3L of milk are drawn from a container containing 30L of milk. It is re  [#permalink]

### Show Tags

16 Apr 2020, 18:11
1
1
10% of a 100% solution of milk is replaced with water thrice

Final concentration of milk=100%*(9/10)*(9/10)*(9/10)=72.9%

Final concentration of water=100-72.9=27.1%

Ratio=729/271

Posted from my mobile device
Manager
Joined: 23 Jan 2020
Posts: 163
Re: 3L of milk are drawn from a container containing 30L of milk. It is re  [#permalink]

### Show Tags

16 Apr 2020, 18:43
Ans C
milk proportion intially = 1;
after adding water, mp reduces = 27/30=9/10
when it is done twice = 1*9/10*9/10=81/100
final mp is 81/100
so mp:wp = 81:19
Math Expert
Joined: 02 Aug 2009
Posts: 8753
Re: 3L of milk are drawn from a container containing 30L of milk. It is re  [#permalink]

### Show Tags

16 Apr 2020, 19:59
1
3L of milk are drawn from a container containing 30L of milk. It is replaced by water and the process is repeated 2 times. What is the ratio of milk to water at the end?

Formula for such questions is Ratio of mlk:total =n (1-replaced quantity/total quantity)^(number of times) = $$(1-\frac{3}{30})^3=(\frac{9}{10})^3=729/1000$$.
So water = 1000-729=271
Thus milk:water=$$\frac{729}{271}$$

A
_________________
PS Forum Moderator
Joined: 18 Jan 2020
Posts: 1080
Location: India
GPA: 4
Re: 3L of milk are drawn from a container containing 30L of milk. It is re  [#permalink]

### Show Tags

16 Apr 2020, 20:21
1
30 litre milk - 3litres of milk + 3 litres of water.
27:3= milk : water - litre mixture
27-2.7:3-0.3= 24.3:2.7
+ 3 litre water.
24.3:5.7
- 3 litre of mixture.
24.3-2.43 : 5.7-0.57
21.87 : 5.13
21.87:8.13
2187/813
729/271
OA is A

Posted from my mobile device
Director
Joined: 25 Jul 2018
Posts: 731
Re: 3L of milk are drawn from a container containing 30L of milk. It is re  [#permalink]

### Show Tags

16 Apr 2020, 23:22
1
After the first process,
—> $$27L$$ —milk
—> $$\frac{27}{30} = \frac{9}{10}= 0.9L$$ milk in 1L mixture

After 2nd process
—> $$27 —3*0.9= 27–2.7 = 24.3L$$ milk
—> $$\frac{24.3}{30}$$L milk in 1L mixture

After 3rd process,
—> $$24.3 —3*\frac{24.3}{30} = 24.3 —2.43 = 21.87L$$ milk
$$30 —21.87 = 8.13$$L water
—> $$\frac{milk}{water} = \frac{21.87}{8.13} = \frac{2187}{813} = \frac{729}{271}$$

Posted from my mobile device
Manager
Joined: 23 Jan 2020
Posts: 163
3L of milk are drawn from a container containing 30L of milk. It is re  [#permalink]

### Show Tags

17 Apr 2020, 00:44
I really cannot get this..the process is done only twice right, why are we doing it thrice?
Math Expert
Joined: 02 Sep 2009
Posts: 65062
Re: 3L of milk are drawn from a container containing 30L of milk. It is re  [#permalink]

### Show Tags

17 Apr 2020, 00:45
monikakumar wrote:
I really cannot get this..the process is done only twice right, why are we doing it thrice?

For me "...repeated 2 times" means that something was done once and then repeated 2 more times.
_________________
Manager
Joined: 23 Jan 2020
Posts: 163
Re: 3L of milk are drawn from a container containing 30L of milk. It is re  [#permalink]

### Show Tags

17 Apr 2020, 00:49
Bunuel wrote:
monikakumar wrote:
I really cannot get this..the process is done only twice right, why are we doing it thrice?

For me "...repeated 2 times" means that something was done once and then repeated 2 more times.

So this is how we have to view this question in GMAT also?..is this how GMAT also interpret?
Director
Joined: 30 Sep 2017
Posts: 962
GMAT 1: 720 Q49 V40
GPA: 3.8
3L of milk are drawn from a container containing 30L of milk. It is re  [#permalink]

### Show Tags

17 Apr 2020, 01:49
2
I will do generalization to this typical mixture problem so that we can solve similar, but harder question (eg. repeated 100x etc.)

Process #1: (30-3) litre milk left = 30*(1-1/10) = 30*(9/10)^1 litre milk left, total 30L;

#2: 30*(9/10) - 30*(9/10)*(3L/30) = 30*(9/10)*(9/10) = 30*(9/10)^2 litre milk left, total 30L;

...etc

Now, I clearly see patterns when process are repeated N times:
Milk left =30*(9/10)^N
Water content =30*{1-(9/10)^N}

When N=3,
Milk left =30*(9/10)^3 =30*(729/1000)
Water content =30*{1-(9/10)^3} = 31*(271/1000)
So, milk to water ratio
= 729/271

Posted from my mobile device
3L of milk are drawn from a container containing 30L of milk. It is re   [#permalink] 17 Apr 2020, 01:49