• 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
  • EMPOWERgmat Slider
    1 Hour Free
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

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

    Available with Beat the GMAT members only code

    MORE DETAILS
    Veritas Prep
  • 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
  • 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

Weighted Average problem

This topic has 3 expert replies and 1 member reply

Weighted Average problem

Post Sat Jul 22, 2017 1:46 am
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    A charitable association sold an average of 66 raffle tickets per member. Among the female members, the average was 70 raffle tickets. The male to female ratio of the association is 1:2. What was the average number of tickets sold by the male members of the association

    A. 50
    B. 56
    C. 58
    D. 62
    E. 66

    The women's differential multiplied by 2 will cancel with the men's differential multiplied by 1. If the men's differential is m, then:

    1*m + 2*(+4) = 0
    m + 8 = 0
    m = - 8

    The men sold an average of 8 fewer tickets than the total average: 66 - 8 = 58.

    Hello,

    Could you please further explain why the 1*m+2*4 must offset so that we can find m = -8?

    Many thanks

    Regards

    Anna

    Need free GMAT or MBA advice from an expert? Register for Beat The GMAT now and post your question in these forums!
    Post Sat Jul 22, 2017 9:35 am
    Hi Anna,

    When you're dealing with any type of 'average formula' question, the numbers above the average will always 'cancel out' the numbers below the average - because that's how averages 'work.'

    For example, if you have the numbers 1 and 3, then the average is (1+3)/2 = 4/2 = 2.
    The larger number (3) is '1 greater' than the average.
    The smaller number (1) is '1 less' than the average.
    Those differences 'cancel out' and you have the average.

    With a 'weighted average', the concept is exactly the same, but you have to account for a different number of terms above the average and below the average.

    For example, the average of 1, 1 and 4 is (1+1+4)/3 = 2.
    The larger number (4) is '2 greater' than the average.
    Each of the two smaller numbers (1 and 1) is '1 less' than the average.
    "2 greater' + '1 less' + '1 less' cancels out and you have the average.

    That same idea applies to this prompt. We know that the average is 66 and that there are two larger numbers (two 70s) for each smaller number (X).
    The two larger numbers (70) are each '4 greater' than the average.
    '4 greater' + '4 greater' = '8 greater'
    So the smaller number (X) has to be '8 less' than the average to cancel out the two larger numbers.
    X = 66 - 8 = 58

    Final Answer: C

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

    _________________
    Contact Rich at Rich.C@empowergmat.com

    GMAT/MBA Expert

    Post Sun Jul 23, 2017 2:35 pm
    Another way to think of this: since there are twice as many women as men, the average should be twice as close to the female average as it is to the male average.

    With that in mind, if the difference between the female average and the overall average is 4 (or 70 - 66), the difference between the male average and the overall average should be 8, since 4 is twice as close to the average as 8 is.

    From there, the male average is just 66 - 8, or 58, and we're done!

    Enroll in a Veritas Prep GMAT class completely for FREE. Wondering if a GMAT course is right for you? Attend the first class session of an actual GMAT course, either in-person or live online, and see for yourself why so many students choose to work with Veritas Prep. Find a class now!

    GMAT/MBA Expert

    Post Sun Aug 06, 2017 10:49 pm
    We could do it algebraically too, though I like the conceptual approach better.

    Let's call m the male average and f the female average. We know that the total number of tickets can be represented in two ways:

    (Average) * (# of People)

    OR

    (Female Average) * (# of Women) + (Male Average) * (# of Men)

    Since these represent the same number, they must be equal:

    66 * (m + w) = x * m + 70 * w

    We know that w = 2m, so we can replace w with 2m:

    66 * (m + 2m) = x * m + 70 * 2m

    198m = xm + 140m

    58m = xm

    58 = x

    and we're done! Smile

    Enroll in a Veritas Prep GMAT class completely for FREE. Wondering if a GMAT course is right for you? Attend the first class session of an actual GMAT course, either in-person or live online, and see for yourself why so many students choose to work with Veritas Prep. Find a class now!
    agrineer Newbie | Next Rank: 10 Posts Default Avatar
    Joined
    20 Oct 2009
    Posted:
    1 messages
    Post Sun Aug 20, 2017 9:23 am
    male to female is 1:2
    1*m+2*f
    1*m+2*70=198~~66is avg for 1, so 3*66=198
    m=198-140
    m=58

    Best Conversation Starters

    1 Vincen 180 topics
    2 lheiannie07 65 topics
    3 Roland2rule 49 topics
    4 ardz24 44 topics
    5 LUANDATO 23 topics
    See More Top Beat The GMAT Members...

    Most Active Experts

    1 image description Brent@GMATPrepNow

    GMAT Prep Now Teacher

    147 posts
    2 image description Rich.C@EMPOWERgma...

    EMPOWERgmat

    103 posts
    3 image description GMATGuruNY

    The Princeton Review Teacher

    102 posts
    4 image description EconomistGMATTutor

    The Economist GMAT Tutor

    94 posts
    5 image description DavidG@VeritasPrep

    Veritas Prep

    76 posts
    See More Top Beat The GMAT Experts