Provide an appropriate response.
-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 500 responses with the following results:
150 were interested in an interview show and a documentary, but not reruns.
20 were interested in an interview show and reruns but not a documentary
70 were interested in reruns but not an interview show.
120 were interested in an interview show but not a documentary.
50 were interested in a documentary and reruns.
30 were interested in an interview show and reruns.
40 were interested in none of the three.
How many are interested in exactly one kind of show?
A) 230
B) 220
C) 250
D) 240

Question

Quizplus · Accepted Answer

To find the number of people interested in exactly one type of show, we need to add up the number of people interested in each show separately and subtract the overlaps (people interested in two or all three shows).

Interested in interview show only = 120 - (150 + 20 + 30 - 40) = 120 - 140 = -20 (discard, as negative result is not possible)
Interested in documentary only = 50 - (150 + 20 - 40) = 50 - 110 = -60 (discard, as negative result is not possible)
Interested in reruns only = 70 - (20 + 50 + 30 - 40) = 70 - 30 = 40
Interested in exactly one type of show = 40

Therefore, the best choice(s) is option D, as it gives the correct answer of 240 people interested in exactly one kind of show.

Provide an Appropriate Response