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Among 80 people attending a seminar consisting of a morning and and an evening sessions, 61 participated in the morning session and 43 in the afternoon session. Find:

(A) the greatest possible number of people who participated in one session only [I've got 43 buts the answer is 56]

(B) the least possible number of people who participated in one session only. [I've got 0 but answer is 18]

It is very confusing. Please if you can tell me also how the venn diagram would look like, i will be very grateful to you.

Please help me.

Thanks

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    You've got a universe of $80$ people, and (possibly) overlapping circles. In one circle are $61$ people representing the morning session and in the other circle there are $43$ people representing the afternoon session. You don't know how many people are in the overlap between the two circles or outside both circles. – 2017-02-25

1 Answers 1

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Assuming that all participants at least did one session, I get that everything is determined uniquely:

$|A \cup B| = |A| + |B| - |A \cap B|$, where $A$ are the morning session participants, $B$ the afternoon ones. The union is 80. And we know |A| = 61, |B| =43, so $80 = 104 - |A \cap B|$, so 24 people did both sessions.

Now $A \setminus B = 61 - 24 = 37$ and $B \setminus A = 43 - 24 = 19$. So 37 only attended the morning sessions, and 19 only the afternoon ones.

I'm not sure how to arrive at your target answers, or your own. Could you expand on that?

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    `not sure how to arrive at your target answers` FWIW $\,37+19=56$ happens to match the target number for (A), though not the question as literally worded. And $\,37-19=18$ but I can't fathom what question *that* would answer. – 2017-02-25
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    The question says the maximum and the minimum values. – 2017-03-02