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]

Solve 700-Level Algebra Qs In 90 Secs!

Master 700-level Inequalities and Absolute Value Questions

Attend this free GMAT Algebra Webinar and learn how to master the most challenging Inequalities and Absolute Value problems with ease.

**
**

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

Founder and CEO

[email protected]

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

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

##### This topic has expert replies

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

## Timer

00:00

## Your Answer

**A**

**B**

**C**

**D**

**E**

## Global Stats

- GMATGuruNY
- GMAT Instructor
**Posts:**15539**Joined:**Tue May 25, 2010 12:04 pm**Location:**New York, NY**Thanked**: 13060 times**Followed by:**1906 members**GMAT Score:**790

The term

The following reflects the intended meaning:

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.

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

Let m = the original volume of milk,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

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.

Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.

Followed here and elsewhere by over 1900 test-takers.

I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.

My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.

I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].

Student Review #1

Student Review #2

Student Review #3

Followed here and elsewhere by over 1900 test-takers.

I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.

My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.

I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].

Student Review #1

Student Review #2

Student Review #3

### GMAT/MBA Expert

- [email protected]
- GMAT Instructor
**Posts:**6896**Joined:**Sat Apr 25, 2015 10:56 am**Location:**Los Angeles, CA**Thanked**: 43 times**Followed by:**29 members

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

**Scott Woodbury-Stewart**

Founder and CEO

[email protected]

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews