Correct Option (3)
Initially, there were 10 new TV shows: 5 sitcoms, 3 drama, and 2 news magazines. By April, 7 shows remained, with all 5 sitcoms still on air. This implies that 10 - 7 = 3 shows were discontinued.
Since all 5 sitcoms continued, none of the discontinued shows were sitcoms. Therefore, the 3 discontinued shows must have originated from the drama (3) and news magazine (2) categories.
Considering the available 3 drama shows and 2 news magazine shows, and the requirement to discontinue 3 shows:
- If both news magazines were discontinued (2 shows), then 1 drama show must also have been discontinued to reach the total of 3 discontinued shows.
- If one news magazine was discontinued (1 show), then 2 drama shows must have been discontinued.
- If no news magazines were discontinued (0 shows), then all 3 drama shows must have been discontinued.
In every possible scenario, at least one drama show must have been discontinued. Thus, the conclusion that at least one discontinued show was a drama logically follows from the given information.
Incorrect Options:
Option 1: Only one news magazine show is still on.
This statement implies that one news magazine show was discontinued. While this is a possible scenario (e.g., 1 news magazine and 2 drama shows discontinued), it is not a necessary conclusion. It is also possible that both news magazine shows are still on, and all three drama shows were discontinued.
Option 2: Only one of the drama shows is still on.
This statement implies that two drama shows were discontinued. Similar to Option 1, this is a possible scenario (e.g., 2 drama and 1 news magazine show discontinued), but not a logically certain outcome. For instance, all three drama shows could have been discontinued, or only one drama show could have been discontinued if two news magazines were discontinued.
Option 4: Viewers prefer sitcoms over drama.
The provided information outlines the number of shows in different categories and their discontinuation status. It does not offer data related to viewer preferences, ratings, or the specific reasons for cancellation. Concluding viewer preference based solely on the number of shows continuing or discontinuing would be an unsubstantiated inference beyond the scope of the given data.