Mixture with Alligation

BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

This topic has expert replies

Post new topic Post Reply

Previous Topic Next Topic

nadib002: Senior | Next Rank: 100 Posts; Posts: 41; Joined: Mon Mar 02, 2009 6:27 pm

Mixture with Alligation

by nadib002 » Thu Apr 28, 2011 9:06 pm

A vessel contains 5 parts of milk and 1 part water. how much of the mixture is to be removed and replaced by water to make the resulting mixture 1/2 water and 1/2 milk ?

The answer is 2 2/5.

I used the alligation method wherein I took the ratio of water and solved for it. I got 2/5 ( the amount of water that needs to be removed). But i do-not seem to understand why we add 2 for the milk.

There is a post on the forum on the same question but i would like to know a way to solve using "Alligation" method

Could you please help

Quote

Source: Beat The GMAT — Problem Solving | Thu Apr 28, 2011 9:06 pm

Stuart@KaplanGMAT: GMAT Instructor; Posts: 3225; Joined: Tue Jan 08, 2008 2:40 pm; Location: Toronto; Thanked: 1710 times; Followed by:614 members; GMAT Score:800

by Stuart@KaplanGMAT » Fri Apr 29, 2011 12:10 am

Hi!

I've never heard of the "alligation" method - does it involve feeding part of the mixture to alligators? Sounds dangerous!

As an aside, this question is seriously flawed and impossible to answer in its current form, since you can't answer a "how much" question unless you have an actual quantity. If all we know is the ratio of water to milk, then all we can answer is "what percent of the mixture" must be replaced by water, not "how much of the mixture".

nadib002 wrote:A vessel contains 5 parts of milk and 1 part water. how much of the mixture is to be removed and replaced by water to make the resulting mixture 1/2 water and 1/2 milk ?

The answer is 2 2/5.

I used the alligation method wherein I took the ratio of water and solved for it. I got 2/5 ( the amount of water that needs to be removed). But i do-not seem to understand why we add 2 for the milk.

There is a post on the forum on the same question but i would like to know a way to solve using "Alligation" method

Could you please help

Stuart Kovinsky | Kaplan GMAT Faculty | Toronto

Kaplan Exclusive: The Official Test Day Experience | Ready to Take a Free Practice Test? | Kaplan/Beat the GMAT Member Discount
BTG100 for $100 off a full course

Quote

nadib002: Senior | Next Rank: 100 Posts; Posts: 41; Joined: Mon Mar 02, 2009 6:27 pm

by nadib002 » Fri Apr 29, 2011 6:16 am

@Stuart

Thank you for the post.

Here's the alligation method.

When combining a lower percentage (L) with a higher percentage (H) to achieve a goal percentage (G):

The proportion needed of L = H-G (the positive difference between the higher percentage and the goal percentage)
The proportion needed of H = G-L (the positive difference between the lower percentage and the goal percentage)

[Courtesy GMATGuruNY]

I used the above method to solve the problem wherein I took

Initial percentage of water = (5/6)*100

Goal percentage of water = (1/2)%100

Amount removed = 100% water

Am I missing something here?

Here's the link to the original post:
https://www.beatthegmat.com/please-can-s ... 12244.html

Please help

Thank you

Quote

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

by GMATGuruNY » Fri Apr 29, 2011 6:42 am

nadib002 wrote:A vessel contains 5 parts of milk and 1 part water. how much of the mixture is to be removed and replaced by water to make the resulting mixture 1/2 water and 1/2 milk ?

The answer is 2 2/5.

I used the alligation method wherein I took the ratio of water and solved for it. I got 2/5 ( the amount of water that needs to be removed). But i do-not seem to understand why we add 2 for the milk.

There is a post on the forum on the same question but i would like to know a way to solve using "Alligation" method

Could you please help

As Stuart noted, the problem should give a volume.
Let's assume that the total volume is 5 liters milk + 1 liter water = 6 liters.

Using alligation:

Fraction of water in the original solution = 1/6
Fraction of water in the water to be added = 1
Desired fraction of water in the final mixture = 1/2

Proportion needed of the original solution = 1 - 1/2 = 1/2.
Proportion needed of the water to be added = 1/2 - 1/6 = 2/6.

Required ratio of solution to water = (1/2) : (2/6) = (3/6) : (2/6) = 3:2.

The sum of the elements in the ratio is 3+2 = 5.
The part of the ratio attributed to the added water = 2.
Thus, the added water = part/whole = 2/5 of the 6 liters.
(2/5) * 6 = 12/5.

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