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Math Help - Another Venn Diagram Problem :(

  1. #1
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    Another Venn Diagram Problem :(

    I'm sorry but I have another problem!

    In a city there are three major newspapers (A, B, C) of which at least two are read by 35% of the population. It is known that newspaper C is read by 45% of the population. A and B are read by 15% and all the three papers are read by 10%. What percent of the population read newspaper C only?
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  2. #2
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    There are only 7 regions. Name them and label them.

    A - A alone
    B - B alone
    C - C alone
    AB - A&B but not C
    AC - A&C but not B
    BC - B&C but not A
    ABC - All Three

    at least two are read by 35% of the population
    AB+AC+BC+ABC = 35

    newspaper C is read by 45% of the population.
    C + AC + BC + ABC = 45

    all the three papers are read by 10%
    ABC = 10

    A and B are read by 15%
    This is where I get lost. I do not know what this means.

    It might be: AB = 15

    If so, a little substitution and subtraction solve the problem.

    AB = 15
    ABC = 10
    AC+BC = 10
    C = 25
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  3. #3
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    Firstly, thanks so much!

    Quote Originally Posted by TKHunny View Post
    This is where I get lost. I do not know what this means.

    It might be: AB = 15

    If so, a little substitution and subtraction solve the problem.

    AB = 15
    ABC = 10
    AC+BC = 10
    C = 25
    Could it be that it means AB+ABC=15? That would make AB=5 and therefore C would be 15. Hmm...
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  4. #4
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    ...or maybe all EXCEPT C?

    I think you see my point. That hint is a little ambiguous. Absent clarification, on any exam or assignment, I would challenge it.
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  5. #5
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    solution

    Quote Originally Posted by merenwen View Post
    I'm sorry but I have another problem!

    In a city there are three major newspapers (A, B, C) of which at least two are read by 35% of the population. It is known that newspaper C is read by 45% of the population. A and B are read by 15% and all the three papers are read by 10%. What percent of the population read newspaper C only?
    let the total population be 100
    step: ABC is 10 ie;10 people read all the news paper
    step2: therefore AB is 5 ie; 10+5 =15 people read two news paper
    step3: given atleast 35% people read two news paper ie; AB+BC+CA+ABC=35
    AB=5
    ABC=10
    BC=X
    CA= X
    therefore 2X=35-15
    X=10
    and paper read by C= 45-10-10-10
    =15
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