• Kaplan Test Prep
    Free Practice Test & Review
    How would you score if you took the GMAT

    Available with Beat the GMAT members only code

    MORE DETAILS
    Kaplan Test Prep
  • Varsity Tutors
    Award-winning private GMAT tutoring
    Register now and save up to $200

    Available with Beat the GMAT members only code

    MORE DETAILS
    Varsity Tutors
  • EMPOWERgmat Slider
    1 Hour Free
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    EMPOWERgmat Slider
  • Veritas Prep
    Free Veritas GMAT Class
    Experience Lesson 1 Live Free

    Available with Beat the GMAT members only code

    MORE DETAILS
    Veritas Prep
  • e-gmat Exclusive Offer
    Get 300+ Practice Questions
    25 Video lessons and 6 Webinars for FREE

    Available with Beat the GMAT members only code

    MORE DETAILS
    e-gmat Exclusive Offer
  • Economist Test Prep
    Free Trial & Practice Exam
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    Economist Test Prep
  • PrepScholar GMAT
    5 Day FREE Trial
    Study Smarter, Not Harder

    Available with Beat the GMAT members only code

    MORE DETAILS
    PrepScholar GMAT
  • Magoosh
    Magoosh
    Study with Magoosh GMAT prep

    Available with Beat the GMAT members only code

    MORE DETAILS
    Magoosh
  • Target Test Prep
    5-Day Free Trial
    5-day free, full-access trial TTP Quant

    Available with Beat the GMAT members only code

    MORE DETAILS
    Target Test Prep

Mixture problem : with allegation method

This topic has 3 expert replies and 3 member replies
gmatquant25 Senior | Next Rank: 100 Posts Default Avatar
Joined
23 Feb 2013
Posted:
31 messages
Thanked:
5 times

Mixture problem : with allegation method

Post Wed Mar 13, 2013 10:33 am
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    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 !

    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 "

    Need free GMAT or MBA advice from an expert? Register for Beat The GMAT now and post your question in these forums!

    GMAT/MBA Expert

    Anju@Gurome GMAT Instructor
    Joined
    11 Aug 2010
    Posted:
    511 messages
    Followed by:
    86 members
    Thanked:
    344 times
    Post 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 §

    Thanked by: gmatquant25
    gmatquant25 Senior | Next Rank: 100 Posts Default Avatar
    Joined
    23 Feb 2013
    Posted:
    31 messages
    Thanked:
    5 times
    Post 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

    Post 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.

    _________________
    Mitch Hunt
    GMAT Private Tutor
    GMATGuruNY@gmail.com
    If you find one of my posts helpful, please take a moment to click on the "Thank" icon.
    Available for tutoring in NYC and long-distance.
    For more information, please email me at GMATGuruNY@gmail.com.

    Free GMAT Practice Test How can you improve your test score if you don't know your baseline score? Take a free online practice exam. Get started on achieving your dream score today! Sign up now.
    vishugogo Master | Next Rank: 500 Posts
    Joined
    30 Aug 2011
    Posted:
    131 messages
    Followed by:
    6 members
    Thanked:
    28 times
    Target GMAT Score:
    780
    Post Thu Mar 14, 2013 7:05 am
    [quote="GMATGuruNY"]how is R = 1/4 of the mixture

    vishugogo Master | Next Rank: 500 Posts
    Joined
    30 Aug 2011
    Posted:
    131 messages
    Followed by:
    6 members
    Thanked:
    28 times
    Target GMAT Score:
    780
    Post Thu Mar 14, 2013 7:08 am
    [quote="Anju@Gurome"][

    how is weight of 10 is 3/4 and weight of x is 1/4

    Post 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.

    _________________
    Mitch Hunt
    GMAT Private Tutor
    GMATGuruNY@gmail.com
    If you find one of my posts helpful, please take a moment to click on the "Thank" icon.
    Available for tutoring in NYC and long-distance.
    For more information, please email me at GMATGuruNY@gmail.com.

    Free GMAT Practice Test How can you improve your test score if you don't know your baseline score? Take a free online practice exam. Get started on achieving your dream score today! Sign up now.

    Best Conversation Starters

    1 LUANDATO 153 topics
    2 lheiannie07 87 topics
    3 Roland2rule 75 topics
    4 AAPL 62 topics
    5 ardz24 60 topics
    See More Top Beat The GMAT Members...

    Most Active Experts

    1 image description EconomistGMATTutor

    The Economist GMAT Tutor

    166 posts
    2 image description GMATGuruNY

    The Princeton Review Teacher

    130 posts
    3 image description Jay@ManhattanReview

    Manhattan Review

    128 posts
    4 image description Rich.C@EMPOWERgma...

    EMPOWERgmat

    121 posts
    5 image description Brent@GMATPrepNow

    GMAT Prep Now Teacher

    99 posts
    See More Top Beat The GMAT Experts