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

 It is currently 18 Oct 2019, 21:50

### 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

# When 20% of a solution of milk and water is removed and replaced with

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

Senior Manager
Joined: 29 Nov 2018
Posts: 280
Concentration: Marketing, Strategy
When 20% of a solution of milk and water is removed and replaced with  [#permalink]

### Show Tags

14 Apr 2019, 10:33
4
00:00

Difficulty:

55% (hard)

Question Stats:

58% (02:18) correct 43% (02:27) wrong based on 40 sessions

### HideShow timer Statistics

When 20% of a solution of milk and water is removed and replaced with water, the ratio of milk and water becomes 2 : 3. Find the ratio of milk and water in the original solution.

(1) 1 : 1
(2) 1 : 2
(3) 2 : 1
(4) 1 : 3
(5) 3 : 2
VP
Joined: 07 Dec 2014
Posts: 1224
When 20% of a solution of milk and water is removed and replaced with  [#permalink]

### Show Tags

14 Apr 2019, 18:25
1
cfc198 wrote:
When 20% of a solution of milk and water is removed and replaced with water, the ratio of milk and water becomes 2 : 3. Find the ratio of milk and water in the original solution.

(1) 1 : 1
(2) 1 : 2
(3) 2 : 1
(4) 1 : 3
(5) 3 : 2

let m=volume of milk in original solution
w=volume of water in original solution
.8m/[.8w+.2(m+w)]=2/3→
.8m/(w+.2m)=2/3→
m=w
m:w=1:1
Manager
Joined: 28 Jan 2019
Posts: 97
Location: India
GMAT 1: 700 Q49 V36
GPA: 4
WE: Manufacturing and Production (Manufacturing)
Re: When 20% of a solution of milk and water is removed and replaced with  [#permalink]

### Show Tags

16 Apr 2019, 11:57
gracie wrote:
cfc198 wrote:
When 20% of a solution of milk and water is removed and replaced with water, the ratio of milk and water becomes 2 : 3. Find the ratio of milk and water in the original solution.

(1) 1 : 1
(2) 1 : 2
(3) 2 : 1
(4) 1 : 3
(5) 3 : 2

let m=volume of milk in original solution
w=volume of water in original solution
.8m/[.8w+.2(m+w)]=2/3→
.8m/(w+.2m)=2/3→
m=w
m:w=1:1

Hi Gracie,
Can you please elaborate the formulae and the approach that you've used here?
_________________
"Luck is when preparation meets opportunity!"
Manager
Joined: 07 Apr 2018
Posts: 101
Location: United States
Concentration: General Management, Marketing
GMAT 1: 600 Q45 V28
GPA: 3.8
Re: When 20% of a solution of milk and water is removed and replaced with  [#permalink]

### Show Tags

17 Apr 2019, 18:59
Total volume =100.
Milk Volume=X.
Water Volume=100-X.
After taking out 20% of volume out.
Milk volume= 0.8X
Water Volume =0.8(100-X)
When 20 l water is added to it
Total volume of water will be 0.8(100-X)+20
Hence ratio of milk to water will be
0.8x : 0.8(100-x)+20 =2:3
solving x=50
hence initial solution will have 1:1 ratio.
Manager
Joined: 14 Apr 2017
Posts: 66
Location: Hungary
GMAT 1: 760 Q50 V42
WE: Education (Education)
Re: When 20% of a solution of milk and water is removed and replaced with  [#permalink]

### Show Tags

18 Apr 2019, 02:51
cfc198 wrote:
When 20% of a solution of milk and water is removed and replaced with water, the ratio of milk and water becomes 2 : 3. Find the ratio of milk and water in the original solution.

(1) 1 : 1
(2) 1 : 2
(3) 2 : 1
(4) 1 : 3
(5) 3 : 2

This is a global ratio problem, which we can solve by using the weighted arithmetic average formula.

First, focus on the ratio of the volume of milk to the total volume, $$M:Total$$.

Let $$x$$ be the partial ratio for the original solution in the above context. The partial ratio for the water added is obviously 0.

The weights used in the formula will be the volumes of the remaining original solution and the water added, respectively. In this case, we don't know the weights in natural units, but fortunately only the relative size of the weights matter in weighted averages. If 20% of the original solution is replaced with water, then 80% of the new solution will be from the original one.

$$\frac{80x+20\cdot 0}{100}=\frac{2}{2+3}$$

$$\frac{4}{5}x=\frac{2}{5}$$

$$x=\frac{1}{2} \implies M:Total=1:2 \implies M:W:Total=1:1:2$$

If you would like to see more solutions using the concept of global and partial ratios/averages, then download my book below and search for the keyword partial.
_________________
My book with my solutions to all 230 PS questions in OG2018:
Zoltan's solutions to OG2018 PS
Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 8109
Location: United States (CA)
Re: When 20% of a solution of milk and water is removed and replaced with  [#permalink]

### Show Tags

18 Apr 2019, 19:10
cfc198 wrote:
When 20% of a solution of milk and water is removed and replaced with water, the ratio of milk and water becomes 2 : 3. Find the ratio of milk and water in the original solution.

(1) 1 : 1
(2) 1 : 2
(3) 2 : 1
(4) 1 : 3
(5) 3 : 2

Let m = the amount of milk originally in the solution and w = the amount of water originally in the solution, we can create the equation:

(m - 0.2m)/(m + w) = 2/5

0.8m/(m + w) = 2/5

4m = 2m + 2w

2m = 2w

m/w = 2/2 = 1/1

_________________

# Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9706
Location: Pune, India
Re: When 20% of a solution of milk and water is removed and replaced with  [#permalink]

### Show Tags

18 Apr 2019, 20:14
cfc198 wrote:
When 20% of a solution of milk and water is removed and replaced with water, the ratio of milk and water becomes 2 : 3. Find the ratio of milk and water in the original solution.

(1) 1 : 1
(2) 1 : 2
(3) 2 : 1
(4) 1 : 3
(5) 3 : 2

Using our weighted average formula:

Say concentration of milk in the original solution = C1
Concentration of milk in water = 0
Concentration of milk in the final solution = 2/5
Since 20% of the solution is removed and replaced, the new solution has 80% original solution and 20% water.

4/1 = (0 - 2/5) / (2/5 - C1)

4*(2/5 - C1) = - 2/5

C1 = 1/2

Hence, milk:water = 1:1
_________________
Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >
Re: When 20% of a solution of milk and water is removed and replaced with   [#permalink] 18 Apr 2019, 20:14
Display posts from previous: Sort by

# When 20% of a solution of milk and water is removed and replaced with

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne