Question 1192679: A local television stations sends out questionnaires to determine if viewers would rather see a documentary, an interview show, or reruns of a game show. There were 250 responses with the following results.
75 were interested in an interview show and a documentary, but not reruns
10 were interested in an interview show and reruns, but not a documentary
35 were interested in reruns but not documentaries or interviews
60 were interested in an interview show but not a documentary
25 were interested in a documentary and reruns
15 were interested in an interview show and reruns
20 were interested in none of the three.
How many are interested in exactly one kind of show?
Answer by greenestamps(13203)   (Show Source):
You can put this solution on YOUR website!
Label the given pieces of information:
A. 75 were interested in an interview show and a documentary, but not reruns
B. 10 were interested in an interview show and reruns, but not a documentary
C. 35 were interested in reruns but not documentaries or interviews
D. 60 were interested in an interview show but not a documentary
E. 25 were interested in a documentary and reruns
F. 15 were interested in an interview show and reruns
G. 20 were interested in none of the three.
Draw a Venn diagram; items A, B, C, and G can be labeled directly.
B and F together tell us that 5 were interested in all three; B and D tell us that 50 were interested in only interview shows.
Then B and F, plus E, tell us that 20 were interested in documentaries and reruns but not interview shows...
... and lastly the total of 250 respondents, along with the other numbers we have determined, tell us that 35 like documentaries only.
And from the final diagram, we have....
ANSWER: The number of respondents interested in only one kind of show was 35+35+50=120
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