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Problem Solving on Set Theory

This topic has 2 expert replies and 1 member reply
mohaprasad Newbie | Next Rank: 10 Posts Default Avatar
Joined
02 Feb 2014
Posted:
2 messages

Problem Solving on Set Theory

Post Wed Feb 19, 2014 4:53 pm
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    Hello,

    Could you please assist me with the below question.
    The below question is from OG13 diagnostic test Q14.

    Of the 84 parents who attended a meeting at a school,
    35 volunteered to supervise children during the school picnic and
    11 volunteered both to supervise children during the picnic and
    to bring refreshments to the picnic.If the number of parents who
    volunteered to bring refreshments was 1.5 times the number of parents
    who neither volunteered to supervise children during picnic nor
    volunteered to bring refreshments,how many of the parents volunteered
    to bring refreshments?

    A.25
    B.36
    C.38
    D.42
    E.45

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    tomada Master | Next Rank: 500 Posts
    Joined
    25 Jan 2010
    Posted:
    406 messages
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    4 members
    Thanked:
    23 times
    Test Date:
    March 14, 2014
    GMAT Score:
    740
    Post Wed Feb 19, 2014 6:13 pm
    mohaprasad wrote:
    Hello,

    Could you please assist me with the below question.
    The below question is from OG13 diagnostic test Q14.

    Of the 84 parents who attended a meeting at a school,
    35 volunteered to supervise children during the school picnic and
    11 volunteered both to supervise children during the picnic and
    to bring refreshments to the picnic.If the number of parents who
    volunteered to bring refreshments was 1.5 times the number of parents
    who neither volunteered to supervise children during picnic nor
    volunteered to bring refreshments,how many of the parents volunteered
    to bring refreshments?

    A.25
    B.36
    C.38
    D.42
    E.45
    Looks like this question has been floating around the internet for a while. The following page contains a good explanation for how to solve this problem.

    http://gmatclub.com/forum/of-the-84-parents-who-attended-a-meeting-at-a-school-35-volunteered-111450.html

    _________________
    I'm really old, but I'll never be too old to become more educated.

    Thanked by: mohaprasad

    GMAT/MBA Expert

    Post Thu Feb 20, 2014 12:51 am
    This is a great question; the full solution below is taken from the GMATFix App (QID 8412).

    ttp://www.youtube.com/watch?v=7Ps18_HLT0E" target="_blank">

    -Patrick

    _________________


      Ask me about tutoring.

    Thanked by: mohaprasad
    Post Thu Feb 20, 2014 3:55 am
    mohaprasad wrote:
    Hello,

    Could you please assist me with the below question.
    The below question is from OG13 diagnostic test Q14.

    Of the 84 parents who attended a meeting at a school,
    35 volunteered to supervise children during the school picnic and
    11 volunteered both to supervise children during the picnic and
    to bring refreshments to the picnic.If the number of parents who
    volunteered to bring refreshments was 1.5 times the number of parents
    who neither volunteered to supervise children during picnic nor
    volunteered to bring refreshments,how many of the parents volunteered
    to bring refreshments?

    A.25
    B.36
    C.38
    D.42
    E.45
    Total = Group 1 + Group 2 - Both + Neither.

    The big idea with overlapping groups is the SUBTRACT THE OVERLAP.
    When we count everyone in Group 1 (those who volunteer to supervise) and everyone in Group 2 (those who volunteer to bring refreshments), those in BOTH groups (those who volunteer to do both) are counted TWICE.
    Thus, we SUBTRACT THE OVERLAP -- the number in both groups -- so that these people are not double-counted.

    In the problem above:
    Total = 84.
    Group 1 = Supervise = 35.
    Both = 11.
    Neither = x.
    Since the number of parents who volunteered to bring refreshments was 1.5 times the number of parents who neither volunteered to supervise during the picnic nor volunteered to bring refreshments:
    Group 2 = Refreshments = 1.5x.

    Plugging these values into the formula, we get:

    84 = 35 + 1.5x - 11 + x
    84 = 24 + 2.5x
    x = 60/(2.5) = 600/25 = 24.

    Thus:
    Refreshments = (1.5)x = (1.5)(24) = 36.

    The correct answer is B.

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    GMATGuruNY@gmail.com
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    Available for tutoring in NYC and long-distance.
    For more information, please email me at GMATGuruNY@gmail.com.

    Thanked by: mohaprasad
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