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OG 13-PS 16

This topic has 3 expert replies and 2 member replies
didieravoaka Master | Next Rank: 500 Posts Default Avatar
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OG 13-PS 16

Post Wed Oct 14, 2015 3:58 pm
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    On Monday, a person mailed 8 packages weighing an average (arithmetic mean) of 1238 pounds, and on Tuesday, 4 packages weighing an average of 1514 pounds. What was the average weight, in pounds, of all the packages the person mailed on both days?

    (A) 13 1/3

    (B) 13 13/16

    (C) 15 1/2

    (D) 15 15/16

    (E) 16 1/2

    OA- A

    I understand why the answer is A, but don't understand why in the process 8(12 3/8) becomes 8(99/8) instead of becoming 8(99).

    Please explain.

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    Post Wed Oct 14, 2015 4:01 pm
    didieravoaka wrote:
    On Monday, a person mailed 8 packages weighing an average (arithmetic mean) of 1238 pounds, and on Tuesday, 4 packages weighing an average of 1514 pounds. What was the average weight, in pounds, of all the packages the person mailed on both days?

    (A) 13 1/3

    (B) 13 13/16

    (C) 15 1/2

    (D) 15 15/16

    (E) 16 1/2

    OA- A

    I understand why the answer is A, but don't understand why in the process 8(12 3/8) becomes 8(99/8) instead of becoming 8(99).

    Please explain.
    You might want to review that question. I'm assuming there a fractions there.

    Cheers,
    Brent

    _________________
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    Post Wed Oct 14, 2015 4:07 pm
    Here's how the question should read:
    didieravoaka wrote:
    On Monday, a person mailed 8 packages weighing an average (arithmetic mean) of 12 3/8 pounds, and on Tuesday, 4 packages weighing an average of 15 1/4 pounds. What was the average weight, in pounds, of all the packages the person mailed on both days?

    (A) 13 1/3

    (B) 13 13/16

    (C) 15 1/2

    (D) 15 15/16

    (E) 16 1/2

    Weighted average of groups combined = (group A proportion)(group A average) + (group B proportion)(group B average) + (group C proportion)(group C average) + ...

    There are 12 packages in total. So, the proportions are 8/12 and 4/12 respectively.
    Plug in the values to get:
    Weighted average of all packages = (8/12)(12 3/8) + (4/12)(15 1/4)
    = (8/12)(99/8) + (4/12)(61/4)
    = 99/12 + 61/12
    = 160/12
    = 40/3
    = 13 1/3
    = A

    ------------------------
    For more information on weighted averages, you can watch this free GMAT Prep Now video: http://www.gmatprepnow.com/module/gmat-statistics?id=805

    Here are some additional practice questions related to weighted averages:
    - http://www.beatthegmat.com/weighted-averages-t117237.html
    - http://www.beatthegmat.com/weighted-average-t114506.html
    - http://www.beatthegmat.com/average-weight-of-men-and-women-t57853.html
    - http://www.beatthegmat.com/averages-question-t87118.html

    Cheers,
    Brent

    _________________
    Brent Hanneson – Founder of GMATPrepNow.com
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    Thanked by: didieravoaka
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    didieravoaka Master | Next Rank: 500 Posts Default Avatar
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    Post Wed Oct 14, 2015 4:29 pm
    Sorry Brent, I missed the fractions in the question.

    Here is the part I don't get...
    Weighted average of all packages = (8/12)(12 3/8) + (4/12)(15 1/4)
    = (8/12)(99/8) + (4/12)(61/4)

    Why we don't have instead,
    Weighted average of all packages = (8/12)(12 3/8) + (4/12)(15 1/4)
    = (8/12)(99) + (4/12)(61)

    Thanks,
    Marc

    Post Wed Oct 14, 2015 4:44 pm
    didieravoaka wrote:
    Sorry Brent, I missed the fractions in the question.

    Here is the part I don't get...
    Weighted average of all packages = (8/12)(12 3/8) + (4/12)(15 1/4)
    = (8/12)(99/8) + (4/12)(61/4)

    Why we don't have instead,
    Weighted average of all packages = (8/12)(12 3/8) + (4/12)(15 1/4)
    = (8/12)(99) + (4/12)(61)

    Thanks,
    Marc
    We want to convert MIXED fractions (12 3/8 and 15 1/4) into ENTIRE fractions.
    This is the same as rewriting 3 1/2 as 7/2
    Notice that 3 1/2 = 3 + 1/2 = 6/2 + 1/2 = 7/2

    Likewise, 12 3/9 = 12 + 3/8 = 96/8 + 3/8 = 99/8

    Here's a free video on converting fractions: http://www.gmatprepnow.com/module/gmat-arithmetic/video/1065
    The part you want starts at 5:40

    Cheers,
    Brent

    _________________
    Brent Hanneson – Founder of GMATPrepNow.com
    Use our video course along with Beat The GMAT's free 60-Day Study Guide

    Check out the online reviews of our course

    Thanked by: didieravoaka
    GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMAT’s FREE 60-Day Study Guide and reach your target score in 2 months!
    didieravoaka Master | Next Rank: 500 Posts Default Avatar
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    Post Wed Oct 14, 2015 5:00 pm
    I got it!

    Thanks,

    Marc.

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