Question

In a survey of 63 people, 23 people subscribe to magazine A, 21people subscribed to magazine B,and 17 people subscribed to magazine C. For any two of the magazines,4 people subscribed to both magazines but not to the third magazine. If 5 people in the survey did not subscibe to any of the three magazines,how many people subscribed to all three magazines?

My sister told me the answer is 9 but I still don't know how to do it. Thanks

Answer 1

BTW, the choices are

a)9
b)7
c)5
d)2
e)It cannot be determined from the info given.

Answer 2

best done with Venn diagram

draw 3 intersecting circles, place x in the intersection of all three since we are not given that number

look at the intersection of any two circles.
We already have x in the middle, so place 4 in each of the remaining region of the pairs

now go to each of the whole circles
in A we already have accounted for 8+x, so the open part of A is 23-8-x or 15-x
in the same way the open part of B is 13-x
and the open part of C is 9-x

now add them all up
15-x + 13-x + 9-x + 12 + x + 5 = 63
-2x = -9
x = 4.5

not possible, unless I made an arithmetic error,
there is something wrong with your data

Answer 3

What do you mean by the open part. Thanks

Answer 4

the part of the circle not covered by any part of the other two.

Answer 5

And shouldn't the answer be x=-4.5; I think you had make a mistake, but thanks

Answer 6

it should be 36 people in the survey not 63. I believe there was a typing error on this question.