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Math Help - [SOLVED] Venn Diagram & Logic: Help

  1. #1
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    [SOLVED] Venn Diagram & Logic: Help

    A local television sends out questionnaires to determine if viewers would rather see a documentary, an interview show, or reruns of a game show. There were 300 responses with following results:

    90 were interested in an interview show and a documentary but not reruns.
    12 were interested in an interview show and reruns but not a documentary.
    42 were interested in reruns but not an interview show.
    72 were interested in an interview show but not a documentary.
    30 were interested in a documentary and reruns
    18 were interested in an interview show and reruns.
    24 were interested in none of the three.

    How many are interested in exactly one kind of show?

    I thought 42+72=114 would be the answer because it's one kind of show, and I tried the Venn Diagram but it won't make any sense because of the crazy data.

    Thanks for your help in advance.

    PS: Would absolutely love an explained answer.

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  2. #2
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    Venn diagram

    Hello hellotarina

    Welcome to Math Help Forum!
    Quote Originally Posted by hellotarina View Post
    A local television sends out questionnaires to determine if viewers would rather see a documentary, an interview show, or reruns of a game show. There were 300 responses with following results:

    A 90 were interested in an interview show and a documentary but not reruns.
    B 12 were interested in an interview show and reruns but not a documentary.
    C 42 were interested in reruns but not an interview show.
    D 72 were interested in an interview show but not a documentary.
    E 30 were interested in a documentary and reruns
    F 18 were interested in an interview show and reruns.
    G 24 were interested in none of the three.

    How many are interested in exactly one kind of show?

    I thought 42+72=114 would be the answer because it's one kind of show, and I tried the Venn Diagram but it won't make any sense because of the crazy data.

    Thanks for your help in advance.

    PS: Would absolutely love an explained answer.

    As you'll see I've labelled each of the statements A ... G. Have a look at the Venn diagram I've drawn. I put the numbers in using the statements in this order:

    • A:90
    • B:12
    • G:24
    • F:18 - 12 = 6
    • E:30 - 6 = 24
    • C:42 - 24 = 18
    • D:72 - 12 = 60
    • Finally 300 - sum of these = 66.

    So the number interested in exactly one kind of show = 66 + 60 + 18 = 144.

    Grandad
    Attached Thumbnails Attached Thumbnails [SOLVED] Venn Diagram & Logic: Help-untitled.jpg  
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  3. #3
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    Wink Thank you so much!!!

    You're awesome!
    Thanks Grandad!!!
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