Question 1122887: There are three student organizations ( A, B and C) in a school. 50 students were asked if they belong to any organizations and the following data were gathered from the survey.
7 belong to B only
20 belong to C
23 belong to A
5 belong to A and B but not C
8 belong to A and C but not B
14 belong to C but not B
15 belong to A but not B
Draw a venn diagram to determine how many of the student surveyed
(a) belong only to C
(b) do not belong to C
(c) belong to B and C but not A
(d) belong to exactly one organization
(e) do not belong to any organization
Answer by greenestamps(13200)   (Show Source):
You can put this solution on YOUR website!
(1) Draw the diagram with the three intersecting circles.
(2) 7 belong to B only. It should be easy to see where that "7" goes in the diagram.
(3) 20 belong to C. We can't do anything with that yet. Make a note somewhere that the total in C is 20.
(4) 23 belong to A. Likewise we can't do anything with that yet. Make another note.
(5) 5 belong to A and B but not C. It should be easy to see where that "5" goes in the diagram.
(6) 8 belong to A and C but not B. Likewise....
(7) 14 belong to C but not B. Together with (6), this tells us the number that are in C only. (It is far easier to see this in the diagram than in the statement of the problem.)
(8) 15 belong to A but not B. Similarly, this, together with (5), tells us the number that are in A only.
(9) That's the end of the given information. So go back to (3) and (4), which we didn't use yet, to see what they now tell us. The diagram (if you have put the right numbers in the right place), along with (4), tells us the number that are in all three of A, B, and C.
(10) Then (3) will tell us the number that are in B and C but not A.
(11) Then finally all the numbers in the three circles are known; from those you can determine the number that are in none of the three.
My answers (if I have drawn the diagram correctly!)...
(a) 6
(b) 50-6=44
(c) 6
(d) 10+7+6 = 23
(e) 6
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