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

Redeem

Mixture problem : with allegation method

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Senior | Next Rank: 100 Posts
Posts: 31
Joined: Sat Feb 23, 2013 12:12 pm
Thanked: 5 times

Mixture problem : with allegation method

by gmatquant25 » Wed Mar 13, 2013 10:33 am
One-fourth of a solution that was 10% by weight was replaced by a second solution resulting in a solution that was 16% sugar by weight. The second solution was what percent sugar by weight.

34%
24%
22%
18%
8.5%


I am trying to solve it using Allegation method , but not quit sure how to get the end result , Please help . Also, elaborate the steps so that I can understand the approach .
many thanks !

[spoiler]I started with 10% and x% in the first row

16% in the second row

and x-16% and 6% in the last one

this gives me x-16/6= ? "stuck here "
[/spoiler]
Top
Source: — Problem Solving |

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 511
Joined: Wed Aug 11, 2010 9:47 am
Location: Delhi, India
Thanked: 344 times
Followed by:86 members

by Anju@Gurome » Wed Mar 13, 2013 10:39 am
gmatquant25 wrote:One-fourth of a solution that was 10% by weight was replaced by a second solution resulting in a solution that was 16% sugar by weight. The second solution was what percent sugar by weight.
If we view this as an weighted average problem then weighted average of 10 and x is 16, where weight of 10 is 3/4 and weight of is 1/4.

Hence, (3/4)*10 + (1/4)*x = 16
-----> 30 + x = 4*16 = 64
-----> x = (64 - 30) = 34

The correct answer is A.
Anju Agarwal
Quant Expert, Gurome

Backup Methods : General guide on plugging, estimation etc.
Wavy Curve Method : Solving complex inequalities in a matter of seconds.

§ GMAT with Gurome § Admissions with Gurome § Career Advising with Gurome §
Top
Senior | Next Rank: 100 Posts
Posts: 31
Joined: Sat Feb 23, 2013 12:12 pm
Thanked: 5 times

by gmatquant25 » Wed Mar 13, 2013 11:06 am
thanks - I could solve this problem in every other way. I want to do it using allegation rule , It helps me solve such problems in no time .
Last edited by gmatquant25 on Wed Mar 13, 2013 11:51 am, edited 1 time in total.
Top
User avatar
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 » Wed Mar 13, 2013 1:09 pm
gmatquant25 wrote:One-fourth of a solution that was 10% by weight was replaced by a second solution resulting in a solution that was 16% sugar by weight. The second solution was what percent sugar by weight.

34%
24%
22%
18%
8.5%
Here's how to solve with alligation.
Let O = the original solution, R = the replacement solution, and M = the mixture.

Step 1: Plot the percentages on a number line, with the two ingredients on the ends and the mixture in the middle.
O 10%----------M=16%----------R

Step 2: Plot the distances between the percentages.
(distance between O and M) : (distance between M and R) is equal to the RECIPROCAL of the ratio of O to R in the mixture.
Since R = 1/4 of the mixture, O:R = 3:1.
Plotting the reciprocal of this ratio on the number line, we get:
O 10%----x-----M=16%----3x----R

Since x is the distance between O and M:
x = 16-10 = 6.
Since 3x is the distance between M and R:
R = 16 + 3x = 16 + 3*6 = 34.

The correct answer is A.
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
Top
User avatar
Master | Next Rank: 500 Posts
Posts: 131
Joined: Tue Aug 30, 2011 4:50 am
Location: India
Thanked: 28 times
Followed by:6 members

by vishugogo » Thu Mar 14, 2013 7:05 am
GMATGuruNY wrote: how is R = 1/4 of the mixture
Top
User avatar
Master | Next Rank: 500 Posts
Posts: 131
Joined: Tue Aug 30, 2011 4:50 am
Location: India
Thanked: 28 times
Followed by:6 members

by vishugogo » Thu Mar 14, 2013 7:08 am
Anju@Gurome wrote:[

how is weight of 10 is 3/4 and weight of x is 1/4
Top
User avatar
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 » Thu Mar 14, 2013 7:48 am
vishugogo wrote: how is R = 1/4 of the mixture
From the problem: ONE-FOURTH of a solution...WAS REPLACED by a second solution.
Thus, the replacement solution -- the value of R -- is equal to 1/4 of the resulting mixture.
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
Top
Post new topic Post Reply
• Page 1 of 1