Question 1161156: A local television station sends out questionnaires to determine if viewers would rather see a documentary, an interview show, or reruns of a game show. There were 200 responses with the following results:
1. 60 were interested in an interview and a documentary, but not reruns
2. 8 were interested in an interview show and reruns, but not a documentary
3. 28 were interested in reruns but not in an interview show
4. 48 were interested in an interview show but not a documentary
5. 20 were interested in a documentary and in reruns
6. 12 were interested in an interview show and in reruns
7. 16 were interested in none of the three
How many are interested in exactly one kind of show?
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!
Fill-in directly (Black numbers)
I & D Only: 60, Clue 1. Region IV
I & R Only: 8, Clue 2. Region V
None: 16, Clue 7. Region VIII
Calculated (Magenta Numbers)
I but not D is any regions with and I but not a D. So the total of regions I and V is 48 by clue 4. However, we have region V as 8, so region I must be 48 minus 8, or 40.
I and R is any region with an I and an R regardless of the presence of a D, so by clue 6, the sum of regions V and VII must be 12, so VII must be 4 because V is 8.
From clue 5, the sum of VI and VII is 20, so knowing VII is 4, gives VI = 16.
Clue 3 says region III and VI must add up to 28; hence region III must be 8.
Since this is an analysis of 200 responses, the sum of all the regions on the graph must be 200. Since we have all but one of the regions filled in, the remaining region, namely II, is 200 minus the sum of all the others.
Then the answer to the question posed is the sum of regions I, II, and III.
You can do the rest of the arithmetic yourself.
John
My calculator said it, I believe it, that settles it
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