# Thread: [SOLVED] Venn Diagram &amp; Logic: Help

1. ## [SOLVED] Venn Diagram &amp; Logic: Help

A local television sends out questionnaires to determine if viewers would rather see a documentary, an interview show, or reruns of a game show. There were 300 responses with following results:

90 were interested in an interview show and a documentary but not reruns.
12 were interested in an interview show and reruns but not a documentary.
42 were interested in reruns but not an interview show.
72 were interested in an interview show but not a documentary.
30 were interested in a documentary and reruns
18 were interested in an interview show and reruns.
24 were interested in none of the three.

How many are interested in exactly one kind of show?

I thought 42+72=114 would be the answer because it's one kind of show, and I tried the Venn Diagram but it won't make any sense because of the crazy data.

PS: Would absolutely love an explained answer.

2. ## Venn diagram

Hello hellotarina

Welcome to Math Help Forum!
Originally Posted by hellotarina
A local television sends out questionnaires to determine if viewers would rather see a documentary, an interview show, or reruns of a game show. There were 300 responses with following results:

A 90 were interested in an interview show and a documentary but not reruns.
B 12 were interested in an interview show and reruns but not a documentary.
C 42 were interested in reruns but not an interview show.
D 72 were interested in an interview show but not a documentary.
E 30 were interested in a documentary and reruns
F 18 were interested in an interview show and reruns.
G 24 were interested in none of the three.

How many are interested in exactly one kind of show?

I thought 42+72=114 would be the answer because it's one kind of show, and I tried the Venn Diagram but it won't make any sense because of the crazy data.

PS: Would absolutely love an explained answer.

As you'll see I've labelled each of the statements A ... G. Have a look at the Venn diagram I've drawn. I put the numbers in using the statements in this order:

• A:90
• B:12
• G:24
• F:18 - 12 = 6
• E:30 - 6 = 24
• C:42 - 24 = 18
• D:72 - 12 = 60
• Finally 300 - sum of these = 66.

So the number interested in exactly one kind of show = 66 + 60 + 18 = 144.