Fractions

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abhirup1711 Rising GMAT Star Default Avatar
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Fractions Post Thu Jun 13, 2013 5:55 am
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  • Lap #[LAPCOUNT] ([LAPTIME])
    3/20 members of a social club are retirees who are bridge players, 7/20 members are retirees, and one half of the members are bridge players. If 120 of the members are neither retirees nor bridge players,what is the total number of members in the social club?

    240
    300
    360
    400
    480

    Please help

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    Post Thu Jun 13, 2013 7:46 am
    abhirup1711 wrote:
    3/20 members of a social club are retirees who are bridge players, 7/20 members are retirees, and one half of the members are bridge players. If 120 of the members are neither retirees nor bridge players,what is the total number of members in the social club?

    240
    300
    360
    400
    480

    Please help
    This is an EITHER/OR problem.
    Every member EITHER plays bridge OR doesn't.
    Every member EITHER is a retiree or OR isn't.

    Since the fractions in the problem are 3/20 and 7/20, let the total number of members = 20x.
    To organize the data, draw a GROUP GRID:

    In the grid above, B = bridge, NB = no bridge, R = retiree, NR = not a retiree.

    3/20 members are retirees who are bridge players:
    RB = (3/20)20x = 3x.
    7/20 of the members are retirees:
    R = (7/20)20x = 7x.
    One half of the members are bridge players:
    B = (1/2)(20x) = 10x.
    Enter these values into the grid:


    Complete the grid:


    The grid indicates that the number of members who are neither retirees nor bridge players is equal to 6x.
    Since 120 members are neither retirees nor bridge players, we get:
    6x = 120
    x = 20.

    Thus:
    Total members = 20x = 20*20 = 400.

    The correct answer is D.

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    Post Fri Jun 14, 2013 5:12 am
    Total = Retirees + Players - Both + None

    Say, total = N
    So, retirees = 7N/20, players = N/2 = 10N/20, and both = 3N/20

    So, None = total - (retirees + players - both)
    So, None = N - (7N/20 + 10N/20 - 3N/20) = N - 14N/20 = 6N/20 = 3N/10

    So, 3N/10 = 120
    So, N = 120*10/3 = 400

    Answer : D

    Post Fri Jun 14, 2013 5:21 am
    I thought I'd point out that Mitch's "group grid" approach is also known as the Double Matrix Method. This technique can be used for most questions featuring a population in which each member has two characteristics associated with it.
    Here, we have a population of social club members, and the two characteristics are:
    - retirees or not retirees
    - bridge players or not bridge players

    To learn more about this technique, watch our free video: http://www.gmatprepnow.com/module/gmat-word-problems?id=919

    Then try these additional practice questions that can be solved using the Double Matrix Method:
    - http://www.beatthegmat.com/mba/2011/05/05/random-double-matrix-question-1
    - http://www.beatthegmat.com/mba/2011/05/09/random-double-matrix-question-2
    - http://www.beatthegmat.com/mba/2011/05/16/random-double-matrix-question-3
    - http://www.beatthegmat.com/ds-quest-t187706.html
    - http://www.beatthegmat.com/overlapping-sets-questions-t183320.html
    - http://www.beatthegmat.com/finance-majors-non-finance-majors-overlapping-set-question-t167425.html
    - http://www.beatthegmat.com/ds-french-japanese-t222297.html

    Cheers,
    Brent

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    Post Sun Feb 07, 2016 9:02 am
    Quote:
    Since the fractions in the problem are 3/20 and 7/20, let the total number of members = 20x.
    To organize the data, draw a GROUP GRID:

    In the grid above, B = bridge, NB = no bridge, R = retiree, NR = not a retiree.

    3/20 members are retirees who are bridge players:
    RB = (3/20)20x = 3x.
    7/20 of the members are retirees:
    R = (7/20)20x = 7x.
    One half of the members are bridge players:
    B = (1/2)(20x) = 10x.
    Hi Mitch ,

    One question.

    R= (7/20)20x = 7x understood

    It is given that 3/20 members of a social club are retirees who are bridge players , so now we have a R , which is 7x right.

    So why not RB = (3/20)7x ?

    Please explain and correct me.

    Many thanks in advance.

    SJ

    Post Sun Feb 07, 2016 9:51 am
    Hi SJ,

    When dealing with Overlapping Sets questions, you have to pay careful attention to language (so that you're putting the proper 'data' in the proper 'spot').

    Here, we're told that 3/20 OF MEMBERS in a club are retirees AND bridge players, so that would be (3/20)(20X).

    IF.... the prompt had stated 3/20 OF RETIREES are bridge players, then the calculation would be (3/20)(7X).

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