Expert: Steve Holleran - 9/10/2008

Question
A group of 85 people were asked whether they liked comedies, dramas, or
science fiction movies.  These were their responses: 18 people liked only
dramas.  34 people liked science fiction movies.  22 people liked comedies
and science fiction movies.  17 people liked comedies and dramas.  26 people
liked dramas but not comedies.  7 people liked all three.  Two people did not
like any of the three.

1. How many people liked dramas?
Answers:  26, 43, 25, 33 or none of these.

2. Also, how many people liked science fiction movies, but not comedies?
Answers: 8, 4, 19, 12, or none of these

3. How many people liked science fiction movies or dramas, but not
comedies?
Answers: 8, 22, 30, 32, or none of these

4. How many people liked exactly one of these types of movies?
Answers: 130, 33, 9, 43, or none of these

Answer
Hi Rich,

These types of questions are easily solved using a Venn Diagram.

I can't draw one here, so I tried to attach one that I found on the web.
It's tough to explain also, but I'll try.

If you print it out or bring it up alongside this, here's how it goes:

Start in the center overlapping region.  This represents those who like all three types, so 7 goes there.  Since 17 liked comedys and dramas, a 10 goes in the space overlapping C and D, but apart from the 7 (so 7 + 10 = 17).  Similarly, if 22 liked C and S, 22 - 7 from the center gives 15 in the overlap of C and S, but not in the center.

If you continue , I think you'll see how the rest go.  The two people who don't like any of them are outside all the circles.

So, the answers to the questions would be:

1.  10 + 7 + 8 + 18 = 43

2.  8 + 4 = 12

3.  4 + 8 + 18 = 30

4.  21 + 4 + 18 = 43


Hope the attachment comes through, and I hope you can follow it.
If it doesn't, let me know and I'll see if I can send it to you via regular email, because this site only accepts certain types of files.

Steve