There are two identical containers A & B. The container A contains 1

Question

GMATBusters’ Quant Quiz Question -6 
There are two identical containers A & B. The container A contains 1 Litre pure water and container B contains B 1 litre of pure milk. Now 5 cups of water container A taken out and is mixed well in container B. Then, 5 cups of this mixture is taken out and mixed in the container A. If M denotes the proportion of milk in the container A and N denote the proportion of water in container B, then:
A. M<N
B. M>N
C. M=N
D. 2M= N
E. Info insufficient, can’t be determined.

pk123 · Answer

There are two identical containers A & B. The container A contains 1 Litre pure water and container B contains B 1 litre of pure milk. Now 5 cups of water container A taken out and is mixed well in container B. Then, 5 cups of this mixture is taken out and mixed in the container A. If M denotes the proportion of milk in the container A and N denote the proportion of water in container B, then:
Let a cup is equal to 100ml = 1/10 of the litre
hence A quantity after 5 cups of water is taken out = 1 - 5*100= 0.5 litre
B quantity after 5 cups of water is added = 1 + 0.5litre ( 1 litre milk & 0.5litre= water)
Now 5 cups of mixture is taken out from B, so B quantity becomes 1 litre but proportion of milk and water remains unchanged which is N= proportion of water = 0.5/(1.5)=1/3
A water quantity becomes = 0.5litre + 0.5/3 = 2/3 and milk quantity is 0.5*2/3 = 1/3
hence proportion of milk = (1/3)/1 = 1/3

hence M= if M denotes the proportion of milk in the container A = 1/3
hence M= N

lets say when 800ml = 0.8 litre is taken out so A quantity after 5 cups of water is taken out = 0.2
B quantity= 1.8 litre but proportion of water in mixture= 0.8/1.8= 4/9
N = proportion of water in container B= 4/9
A quantity after 0.8 litre is now taken from mixture B = 1 litre and proportion of milk = 0.8*5/9= 4/9
M= if M denotes the proportion of milk in the container A = 4/9

hence C is the answer

Raxit85 · Answer

Here the ratio of mixtures( i.e milk , water) doesnot matter. But the important point is that whether the total amount ( either pure or mixture ) being transferred is equal or not. Since the total amount ( i.e 5 cups) being transferred from each one to another , hence A =B.

So, C is the answer.

So, C is the answer.

shameekv1989 · Answer

There are two identical containers A & B. The container A contains 1 Litre pure water and container B contains B 1 litre of pure milk. Now 5 cups of water container A taken out and is mixed well in container B. Then, 5 cups of this mixture is taken out and mixed in the container A. If M denotes the proportion of milk in the container A and N denote the proportion of water in container B, then:
A. M<N
B. M>N
C. M=N
D. 2M= N
E. Info insufficient, can’t be determined.

Answer - C

We can have any proportion of 5 cups mixed in other container, the result will be container A having same % of milk as in container B having water

For eg. we take 500 ml (for 5 cups) of water mixed with milk -> Result will 1.5 ltrs having 0.5 ltr of water giving concentration of 0.5/1.5 => 1/3 => N = 33.33% of water

So 500 ml of this concentration will contain 2/3 of 500 ml of milk => 33.33% milk in 500 ml

When we add 500 ml of this concentration in 500 ml of water -> result will be 33.33% milk in 1 ltr of mixture => M

Therefore M = N

Similarly,

If we take 200 ml (for 5 cups) then 200 ml of water mixed in 1 ltr of milk -> 0.2 ltr water in 1.2 ltr of mixture -> 0.2/1.2 =1/6 concentration of water = N

When we mix 200 ml of this concentration => 5/6 of 200 ml added to 500 ml of water => 1000/6 in 1 ltr mixture => 1/6 of milk => M

Again M=N.

KhulanE · Answer

A 0% 1litre water
B 100% 1litre milk

if 5cups is equal to 0.9litre
proportion of milk in B is 100%*1+0%*0.9=x*1.9 x=52.6%, N=100%-52.6%=47.4%
proportion of milk in A is 0%*0.1+52.6%*0.9=M*1 M=47.4% N=M

if 5cups is equal to 0.1litre
proportion of milk in B is 100%*1+0%*0.1=x*1.1 x=90.9%, N=100%-90.9%=9.1%
proportion of milk in A is 0%*0.9+90.9%*0.1=M*1 M=9.1% N=M

in any measurement of 5cups M and N are equal so C is right

shridhar786 · Answer

container A (water) = 1000 ml
container B (milk) = 1000 ml

let the capacity of 1 cup = 100 ml

now 5 cups of water (that is 500 ml) is taken out from A and is mixed with B
the concentration of A and B after the process

container A = 500 ml
container B - milk = 1000 ml water = 500 ml---ratio of milk to water = 2:1

now 5 cups of mixture (that is 500 ml) is taken out and mixed with A 
milk and water taken out will be in ratio 2:1
let 2t of milk and t water is taken out from B

500 = 3t
t =  \frac{500}{3 } 
water taken out from B =  \frac{500}{3}  ml
milk taken out from B =  \frac{1000}{3}  ml

the concentration of A and B after the process

container A - milk =  \frac{1000}{3}  ml water =  \frac{2000}{3}  ml

ratio of milk : water = 1:2
proportion of milk in container A =  \frac{1}{3}  = M

container B - milk =  \frac{2000}{3}  ml water =  \frac{1000}{3}  ml

ratio of milk : water = 2:1
proportion of water in container B =  \frac{1}{3}  = N

from here we get M = N

C is the answer

aditibarjatya · Answer

Solution:

Question 6 :  There are two identical containers A & B. The container A contains 1 Litre pure water and container B contains B 1 litre of pure milk. Now 5 cups of water container A taken out and is mixed well in container B. Then, 5 cups of this mixture is taken out and mixed in the container A. If M denotes the proportion of milk in the container A and N denote the proportion of water in container B, then:

A. M<N 
 B. M>N 
 C. M=N 
 D. 2M= N 
 E. Info insufficient, can’t be determined.

In this question, we need to find out how the proportion of milk or N in A relates to the proportion of water in B after the transfer of mixture from B to A. .

Information given in the question: Water in A = Milk in B = 1 litre. 
 First transfer : First 5 cups of water from A to B makes remaining quantity in A = 1 litre - 5 cups of water
Let 1 cup measures x litres. Then, 5 cups = 5x litres. Thus, quantity in A =  1 - 5x  litres. 
Moreover, resulting mixture in B after the transfer = 1 litre milk + 5 cups of water (from A). Total quantity of mixture in B =  1 + 5x  litres.

Second transfer : 5 cups of mixture from B to A. Therefore, resulting quantity in B would be reduced to 1 litre again and quantity in A too would increase from  1 - 5x  to 1 litre. However, B is a mixture of water and milk before the second transfer. The mixture contains 1 litre milk and 5x litres water. Thus, if quantity of 5x is transferred from the mixture in B to A, then resulting ratios of milk to water can be calculated by:

Proportion of milk in B  =  \frac{1}{(1 + 5x)} .
 Proportion of water in B  =  \frac{5x}{(1 + 5x)} .
 Proportion of milk in B after transfer of 5x cups to A  =  1 - \frac{1*5x}{(1 + 5x)}  =  \frac{1}{(1 + 5x)} 
 Quantity of milk transferred  =  \frac{5x}{(1 + 5x)}

Proportion of water in B after transfer of 5x cups to A  =  N  =  5x - \frac{5x*5x}{(1 + 5x)}  = 5x/1 + 5x
 N  can be written as  \frac{5x}{1}  as the total quantity remaining in B after the transfer is 1 litres.

The proportion of milk in A after the transfer or  M  =  \frac{5x}{(1 - 5x + 5x)}  or  \frac{5x}{1 }  as the total quantity in A after the addition of 5x litres or 5 cups is  1 - 5x + 5x or 1  litres.

Thus,  M = N = \frac{5x}{1}  and  option C  is the right answer.

ajaymahadev · Answer

I had to think about this for some time.

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

There are two identical containers A & B. The container A contains 1

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

There are two identical containers A & B. The container A contains 1

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards