A vessel is full of milk. 1/3 of the solution is taken out

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shivanshchauhan94: Newbie | Next Rank: 10 Posts; Posts: 3; Joined: Sat Jul 29, 2017 11:28 pm

A vessel is full of milk. 1/3 of the solution is taken out

by shivanshchauhan94 » Sun Jul 28, 2019 2:49 am

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A vessel is full of milk. 1/3 of the solution is taken out and replaced with water. This process is repeated thrice. At the end of it, if 16 liters of milk remains, how much water will be present in the vessel?

A) 39 ltr
B)42 ltr
C)17 ltr
D)38 ltr
E) 40 ltr
[spoiler] (D)[/spoiler]

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Source: Beat The GMAT — Problem Solving | Sun Jul 28, 2019 2:49 am

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by GMATGuruNY » Sun Jul 28, 2019 3:08 am

The term thrice is archaic and will not appear on the GMAT.
The following reflects the intended meaning:

shivanshchauhan94 wrote:A vessel is full of milk. 1/3 of the solution is taken out and replaced with water. This process is performed a total of 3 times. At the end of it, if 16 liters of milk remains, how much water will be present in the vessel?

A) 39 ltr
B)42 ltr
C)17 ltr
D)38 ltr
E) 40 ltr

Let m = the original volume of milk,

Each time 1/3 of the volume is removed, 2/3 of the milk is left behind.
Since performing this process 3 times leaves behind 16 liters, we get:
(2/3)(2/3)(2/3)m = 16
m = (16*27)/8 = 54

Amount of water at the end of the 3 processes = (original volume of milk) - (remaining milk after 3 processes) = 54 - 16 = 38 liters.

The correct answer is D.

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by Scott@TargetTestPrep » Tue Aug 06, 2019 4:48 pm

shivanshchauhan94 wrote:A vessel is full of milk. 1/3 of the solution is taken out and replaced with water. This process is repeated thrice. At the end of it, if 16 liters of milk remains, how much water will be present in the vessel?

A) 39 ltr
B)42 ltr
C)17 ltr
D)38 ltr
E) 40 ltr
[spoiler] (D)[/spoiler]

We can let x = the amount of milk, in liters, originally in the vessel.

After the first action, we have 2/3x liters of milk in the vessel.

After the second action, we have 2/3(2/3x) liters of milk in the vessel.

After the third action, we have 2/3[2/3(2/3x)] liters of milk in the vessel.

We can create the equation:

2/3[2/3(2/3x)] = 16

(8/27)x = 16

x = 16 * 27/8 = 54

That is, the full capacity of the vessel is 54 liters. Since now the amount of milk left in the vessel is 16 liters, the rest, 38 liters, must be water.

Answer: D

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