It is currently 24 Nov 2017, 06:22

Close

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
Your Progress

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

A dishonest milkman sells a 40 liter mixture of milk and water that co

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

Hide Tags

Expert Post
1 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 42356

Kudos [?]: 133204 [1], given: 12439

A dishonest milkman sells a 40 liter mixture of milk and water that co [#permalink]

Show Tags

New post 28 Jan 2015, 07:53
1
This post received
KUDOS
Expert's post
6
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

84% (01:48) correct 16% (02:31) wrong based on 213 sessions

HideShow timer Statistics

A dishonest milkman sells a 40 liter mixture of milk and water that contains milk and water in the ratio of 3:2. He takes out 20 liters of the mixture and replaces it with an equal amount of milk. He then takes out 20 liters of this new mixture and replaces it with an equal amount of water to create his final mixture. What is the ratio of milk and water in the final mixture?

A. 2:5
B. 3:5
C. 2:3
D. 3:2
E. 5:3

Kudos for a correct solution.
[Reveal] Spoiler: OA

_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 133204 [1], given: 12439

Expert Post
1 KUDOS received
Math Expert
User avatar
P
Joined: 02 Aug 2009
Posts: 5234

Kudos [?]: 5894 [1], given: 118

Re: A dishonest milkman sells a 40 liter mixture of milk and water that co [#permalink]

Show Tags

New post 28 Jan 2015, 08:17
1
This post received
KUDOS
Expert's post
ans C 2:3...
initial 40 ltrs ... when 20 ltr left m:w=3:2=12:8..
when 20l milk added... m:w=32:8..
now 20l removed, means half of each left=16:4..
now add 20 l water m:w=16:24=2:3
_________________

Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

Kudos [?]: 5894 [1], given: 118

3 KUDOS received
Senior Manager
Senior Manager
avatar
Joined: 27 Oct 2013
Posts: 253

Kudos [?]: 130 [3], given: 79

Location: India
Concentration: General Management, Technology
GMAT Date: 03-02-2015
GPA: 3.88
Re: A dishonest milkman sells a 40 liter mixture of milk and water that co [#permalink]

Show Tags

New post 28 Jan 2015, 08:38
3
This post received
KUDOS
Here we go:

Quantity of mixture = 40

Lets divide the whole process into three steps.


Step 1:
Milk:Water = 3:2

Milk = 24
Water = 16


Step 2:
He takes out 20 liters of the mixture and replaces it with an equal amount of milk.

Quantity of milk = 20 + 3/5 * (20) = 32
Water = 40 - 32 = 8

New ratio

Milk:Water = 4:1

Step 3:
He then takes out 20 liters of this new mixture and replaces it with an equal amount of water to create his final mixture.

Quantity of water = 20 + 1/5 * (20) = 24
Milk = 40 - 24 = 16

Ration in the final mixture

Milk:Water = 16:24 = 2:3

Option C is correct

Kudos [?]: 130 [3], given: 79

Intern
Intern
User avatar
Joined: 23 Nov 2014
Posts: 23

Kudos [?]: 11 [0], given: 22

Location: China
Concentration: Entrepreneurship, General Management
GMAT 1: 550 Q41 V25
GMAT 2: 680 Q47 V35
WE: General Management (Hospitality and Tourism)
Re: A dishonest milkman sells a 40 liter mixture of milk and water that co [#permalink]

Show Tags

New post 28 Jan 2015, 22:34
Bunuel wrote:
A dishonest milkman sells a 40 liter mixture of milk and water that contains milk and water in the ratio of 3:2. He takes out 20 liters of the mixture and replaces it with an equal amount of milk. He then takes out 20 liters of this new mixture and replaces it with an equal amount of water to create his final mixture. What is the ratio of milk and water in the final mixture?

A. 2:5
B. 3:5
C. 2:3
D. 3:2
E. 5:3

Kudos for a correct solution.


C: 2:3

I took the long route.. i would like to solve this algebraically.. I am pondering over that now...

Kudos [?]: 11 [0], given: 22

Expert Post
4 KUDOS received
EMPOWERgmat Instructor
User avatar
P
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 10178

Kudos [?]: 3542 [4], given: 173

Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: 340 Q170 V170
Re: A dishonest milkman sells a 40 liter mixture of milk and water that co [#permalink]

Show Tags

New post 29 Jan 2015, 00:03
4
This post received
KUDOS
Expert's post
Hi maxk297,

While many ratio questions can be solved by setting up an algebraic equation, this really isn't one of those questions. It's pure Arithmetic - we're given the starting numbers, we're told what to add and subtract, and then we're asked for an end result. In that way, this is somewhat rare among the typical ratio questions that you'll see on Test Day. THOSE questions can normally be solved by doing Algebra, TESTing THE ANSWERS or by doing 'brute force' Arithmetic.

GMAT assassins aren't born, they're made,
Rich
_________________

760+: Learn What GMAT Assassins Do to Score at the Highest Levels
Contact Rich at: Rich.C@empowergmat.com

Rich Cohen

Co-Founder & GMAT Assassin

Special Offer: Save $75 + GMAT Club Tests Free
  Official GMAT Exam Packs + 70 Pt. Improvement Guarantee
www.empowergmat.com/

***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***********************

Kudos [?]: 3542 [4], given: 173

4 KUDOS received
SVP
SVP
User avatar
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1851

Kudos [?]: 2724 [4], given: 193

Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Re: A dishonest milkman sells a 40 liter mixture of milk and water that co [#permalink]

Show Tags

New post 29 Jan 2015, 00:38
4
This post received
KUDOS
Answer = C. 2:3

............................... Milk ............... Water ....................... Total

Initial ...................... 24 .................... 16 .............................. 40

20 Lts mix. taken out 24-12 ............... 16-8 ........................... 40-20

20 Lts milk added..... 12+20 ................ 8 .............................. 40

20 Lts mix. taken out 32-16 ............... 8-4 ........................... 40-20

20 Lts water added..... 16 ................ 4+20 .............................. 40

New ratio = 16:24 = 2:3
_________________

Kindly press "+1 Kudos" to appreciate :)

Kudos [?]: 2724 [4], given: 193

2 KUDOS received
SVP
SVP
User avatar
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1851

Kudos [?]: 2724 [2], given: 193

Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Re: A dishonest milkman sells a 40 liter mixture of milk and water that co [#permalink]

Show Tags

New post 29 Jan 2015, 00:53
2
This post received
KUDOS
maxk297 wrote:
Bunuel wrote:
A dishonest milkman sells a 40 liter mixture of milk and water that contains milk and water in the ratio of 3:2. He takes out 20 liters of the mixture and replaces it with an equal amount of milk. He then takes out 20 liters of this new mixture and replaces it with an equal amount of water to create his final mixture. What is the ratio of milk and water in the final mixture?

A. 2:5
B. 3:5
C. 2:3
D. 3:2
E. 5:3

Kudos for a correct solution.


C: 2:3

I took the long route.. i would like to solve this algebraically.. I am pondering over that now...



Actually, there is a formula for such replacement questions....

\(Final_Concentration = Initial_Concentration * (1 - \frac{Replace}{Total})^{Number_of_replacements}\)
_________________

Kindly press "+1 Kudos" to appreciate :)

Kudos [?]: 2724 [2], given: 193

Expert Post
Math Expert
User avatar
P
Joined: 02 Aug 2009
Posts: 5234

Kudos [?]: 5894 [0], given: 118

Re: A dishonest milkman sells a 40 liter mixture of milk and water that co [#permalink]

Show Tags

New post 29 Jan 2015, 01:05
PareshGmat wrote:
maxk297 wrote:
Bunuel wrote:
A dishonest milkman sells a 40 liter mixture of milk and water that contains milk and water in the ratio of 3:2. He takes out 20 liters of the mixture and replaces it with an equal amount of milk. He then takes out 20 liters of this new mixture and replaces it with an equal amount of water to create his final mixture. What is the ratio of milk and water in the final mixture?

A. 2:5
B. 3:5
C. 2:3
D. 3:2
E. 5:3

Kudos for a correct solution.


C: 2:3

I took the long route.. i would like to solve this algebraically.. I am pondering over that now...



Actually, there is a formula for such replacement questions....

\(Final_Concentration = Initial_Concentration * (1 - \frac{Replace}{Total})^{Number_of_replacements}\)


Although nopt tried the formula on this Q, I think the formulae will stand if same item is replaced or added.. here u have two different items being added on both occassions
_________________

Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

Kudos [?]: 5894 [0], given: 118

Expert Post
1 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 42356

Kudos [?]: 133204 [1], given: 12439

Re: A dishonest milkman sells a 40 liter mixture of milk and water that co [#permalink]

Show Tags

New post 02 Feb 2015, 03:29
1
This post received
KUDOS
Expert's post
1
This post was
BOOKMARKED
Bunuel wrote:
A dishonest milkman sells a 40 liter mixture of milk and water that contains milk and water in the ratio of 3:2. He takes out 20 liters of the mixture and replaces it with an equal amount of milk. He then takes out 20 liters of this new mixture and replaces it with an equal amount of water to create his final mixture. What is the ratio of milk and water in the final mixture?

A. 2:5
B. 3:5
C. 2:3
D. 3:2
E. 5:3

Kudos for a correct solution.


VERITAS PREP OFFICIAL SOLUTION:

In this word problem, the key to success is staying organized and following the changes in value. The mixture begins with a 3:2 ratio of milk to water, so out of 40 liters you have:

24 milk, 16 water

The first change is that the milkman removes half of that mixture, so cut those totals in half:

12 milk, 8 water

Then he adds 20 liters of milk, so add 20 to the milk total, making the running tally:

32 milk, 8 water

The next step is to take out half of that mixture, so you'll cut those totals in half:

16 milk, 4 water

And then add 20 liters of water to get the final mixture:

16 milk, 24 water

Since that's the final mixture, take that as a ratio. 16 and 24 are each multiples of 8, so you have (2 * 8) milk and (3 * 8) water, leading to a ratio of 2:3.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 133204 [1], given: 12439

Expert Post
Target Test Prep Representative
User avatar
S
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 1821

Kudos [?]: 945 [0], given: 3

Location: United States (CA)
Re: A dishonest milkman sells a 40 liter mixture of milk and water that co [#permalink]

Show Tags

New post 04 Oct 2017, 16:39
Bunuel wrote:
A dishonest milkman sells a 40 liter mixture of milk and water that contains milk and water in the ratio of 3:2. He takes out 20 liters of the mixture and replaces it with an equal amount of milk. He then takes out 20 liters of this new mixture and replaces it with an equal amount of water to create his final mixture. What is the ratio of milk and water in the final mixture?

A. 2:5
B. 3:5
C. 2:3
D. 3:2
E. 5:3


The original mixture has a ratio of milk to water = 3x : 2x, and thus:

40 = 5x

x = 8

So, originally there were 3(8) = 24 liters of milk and 2(8) = 16 liters of water.

Since 20 liters of the mixture (i.e., half of the mixture) are removed, half of the milk (12 liters) and half of the water (8 liters) are removed. Thus, after 20 liters are removed, there are:

12 liters of milk and 8 liters of water in the mixture.

Since 20 liters of milk are added back in, we now have:

32 liters of milk and 8 liters of water in the mixture.

Since another 20 liters of the mixture (i.e., half of the mixture) are removed, half of the milk (16 liters) and half of the water (4 liters) are removed. Thus, after 20 liters are removed, there are:

16 liters of milk and 4 liters of water in the mixture.

Since 20 liters of water are added back in, we now have:

16 liters of milk and 24 liters of water in the mixture.

Thus, the final ratio of milk to water is 16/24 = 2/3.

Answer: C
_________________

Scott Woodbury-Stewart
Founder and CEO

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Kudos [?]: 945 [0], given: 3

Re: A dishonest milkman sells a 40 liter mixture of milk and water that co   [#permalink] 04 Oct 2017, 16:39
Display posts from previous: Sort by

A dishonest milkman sells a 40 liter mixture of milk and water that co

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


GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

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

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.