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Math Help - Quantitative reasoning

  1. #1
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    Quantitative reasoning

    Hey guys,

    Im preparing for the GRE Exam and I am finding these quantitative reasoning problems quite difficult...I am so awful at Math. I am not sure this is the right thread for this question, please forgive me if it isn't..

    So this is the problem:

    The total number of recording titles distributed by music distributors L and M is 9,300. The number of recording titles distributed by L is 7,100 and the number of recording titles distributed by M is 5,200. Which of the following statements MUST be true?

    a. More than half the titles distributed by L are also distributed by M
    b. More than half the titles distributed by M are also distributed by L
    c. No titles are distributed by both L and M

    Is this a probability problem? Any tips would be appreciated...
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  2. #2
    MHF Contributor

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    Re: Quantitative reasoning

    no, it's an exercise in "inclusion/exclusion".

    our "universe" (of recording titles that exist to be distributed) has 9,300 things in it (you can think of this as the "master list" of all recordings currently sold).

    L handles 7,100 of these recordings, meaning there is 2,200 L doesn't carry.

    M handles 5,200 of these recordings, so even if 2,200 of those are the ones L doesn't handle, that makes for a 3,000 overlap (titles they both distribute). so obviously, (c) isn't true.

    (you could approach this "the other way": there are 4,100 titles M doesn't distribute. since L distributes 7,100, even if 4,100 of them were the ones L doesn't distribute, we still have a 3,000 overlap<---same figure for "shared distributed titles").

    now we just have to decide between (a) and (b). is 3,000 more than 1/2 of what L carries? if so, pick (a).

    is 3,000 more than 1/2 of what M carries? if so, pick (b).

    ********

    our universe breaks down like so:

    total number of titles = 9,300
    titles only L carries = A
    titles only M carries = B
    tiles both L and M carry = C.

    the problem tells us:

    A + C = 7,100
    B + C = 5,200

    A+B+C = 9,300

    the "object" is to find C, which the above shows is 3,000. you can do it algebraically like this:

    B = (A+B+C) - (A+C)
    C = (B+C) - B

    or:

    A = (A+B+C) - (B+C)
    C = (A+C) - A

    we know A+B+C and A+C from the beginning: A+B+C = 9,300, and A+C = 7,100, so B = 2,200, thus C = 5,200 - 2,200 = 3,000 (first method)

    or A = 9,300 - 5,200 = 4,100, so C = 7,100 - 4,100 = 3,000 (second method).
    Last edited by Deveno; January 5th 2013 at 05:39 AM.
    Thanks from MarkFL
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  3. #3
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    Re: Quantitative reasoning

    Hello, fsiwaju!

    The total number of recording titles distributed by music distributors L and M is 9,300.
    The number of recording titles distributed by L is 7,100
    and the number of recording titles distributed by M is 5,200.
    Which of the following statements MUST be true?

    a. More than half the titles distributed by L are also distributed by M
    b. More than half the titles distributed by M are also distributed by L
    c. No titles are distributed by both L and M

    L distributed 7,100 titles.
    M distributed 5,200 titles.
    . . This is a total of 12,300 titles.

    But we are told that the total number of titles is 9,300.
    . . Hence, there is an "overlap" of: 12,300 - 9,300 = 3,000 titles.

    The Venn diagram looks like this:
    Code:
                  * * *       * * *
              *           *           *
            *     L     *   *     M     *
           *           *     *           *
    
          *           *       *           *
          *   4,100   * 3,000 *   2,200   *
          *           *       *           *
    
           *           *     *           *
            *           *   *           *
              *           *           *
                  * * *       * * *
    Can you answer the question now?
    Thanks from MarkFL and fsiwaju
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