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Math Help - venn diagram

  1. #1
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    venn diagram

    In a college, 60% of all sophomores have liberal studies as their major subject, 24% of all sophomores have social history as their major and the rest have other subjects or have not yet chosen a major. If 55% of all sophomores have chosen psychology as a course, then what is the minimum percent of all sophomores who have chosen psychology as a course and who also have liberal studies as their major subject?


    my answer is 15 is it correct
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  2. #2
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    Quote Originally Posted by arunachalam.s View Post
    In a college, 60% of all sophomores have liberal studies as their major subject, 24% of all sophomores have social history as their major and the rest have other subjects or have not yet chosen a major. If 55% of all sophomores have chosen psychology as a course, then what is the minimum percent of all sophomores who have chosen psychology as a course and who also have liberal studies as their major subject?


    my answer is 15 is it correct
    I prefer using a Karnaugh table:

    \begin{tabular}{l | c | c | c | c} & Liberal & Social history & Other & \\ \hline Psychology & x & a & b & 0.55\\ \hline Not Psychology & c & d & e & 0.45 \\ \hline & 0.6 & 0.24 & 0.16 & 1 \\ \end{tabular}<br />

    Your task is to find the smallest possible value of x. You have the following equations:

    x + a + b = 0.55 .... (1)

    x + c = 0.6 .... (2)

    c + d + e = 0.45 .... (3)

    b + e = 0.16 .... (4)

    a + d = 0.24 .... (5)

    and you want the smallest value of x for which these equations will be consistent.

    So I get x = 0.15 which is equivalent to 15% so yes you're correct.

    (No doubt someone will give a simple two line confirmation of this).
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  3. #3
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    what is the relevance of the 24 % figure ... probably u r missing some info
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  4. #4
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    Quote Originally Posted by nirax View Post
    what is the relevance of the 24 % figure ... probably u r missing some info
    The question is fine as it is. That should be clear from what I posted ealier. A minimum possible value of x is required, not the value.
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  5. #5
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    if all you are concerned with is liberal studies and psychology then social history is an irrelevant info ... even if that figure were 100%, your desired answer would not change.

    thats what led me to suspect that you r missing something
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