Statistics problem dealing with attendance

[jaymode]

One hundred students attended at least one of three concerts: Pep Band, Country Sizzle, and Blue Mood. 48 heard the Pep Band concert. 36 heard the Country Sizzle concert. 60 heard the Blue Mood concert. 12 heard the Pep Band and Country Sizzle concerts. 20 heard the Country Sizzle and Blue Mood concerts. 16 heard the Pep Band and Blue Mood concerts. How many attended all three concerts?

Ok So I broke it down. The max number of people that could attend all three would be 12 since that is how many attened the Pep Band and Country Sizzle which is the least number. I do not really know how to proceed on this problem. If I had to guess my answer would be 4 attended all 3 because there is a difference of 4 between 12, 16, and 20. Also when adding those together you get 48. Then adding the others together and subtracting 100 you get 44, once again a difference of 4. But I am faily certain that is not the correct way to approach the problem.

 

[0rthodontist]

Well, I have no idea what your reasoning is but 4 is the correct answer. Draw a Venn diagram to help you visualize it, and add and subtract to find the intersection of the 3 concerts.