GATE EE 2023 Set 1 — Question 4
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Question
A recent survey shows that 65% of tobacco users were advised to stop consuming tobacco. The survey also shows that 3 out of 10 tobacco users attempted to stop using tobacco. Based only on the information in the above passage, which one of the following options can be logically inferred with certainty?
Correct answer
(B) A majority of tobacco users who were advised to stop consuming tobacco did not attempt to do so.
Solution
Let the total number of tobacco users be 100.
Number of users advised to stop = 65% of 100 = 65.
Number of users who attempted to stop = 3 out of 10 = 30% of 100 = 30.To find the number of advised users who did not attempt to stop, we consider the maximum possible overlap between those advised and those who attempted.
Maximum number of advised users who attempted to stop = 30 (if all who attempted were from the advised group).
Minimum number of advised users who did NOT attempt to stop = .In the group of advised users (total 65), the number who did not attempt is at least 35.
Since (i.e., ), the majority of advised users did not attempt to stop. This is true regardless of the actual overlap, as the number of non-attempters in the advised group will always be at least 35.
Number of users advised to stop = 65% of 100 = 65.
Number of users who attempted to stop = 3 out of 10 = 30% of 100 = 30.To find the number of advised users who did not attempt to stop, we consider the maximum possible overlap between those advised and those who attempted.
Maximum number of advised users who attempted to stop = 30 (if all who attempted were from the advised group).
Minimum number of advised users who did NOT attempt to stop = .In the group of advised users (total 65), the number who did not attempt is at least 35.
Since (i.e., ), the majority of advised users did not attempt to stop. This is true regardless of the actual overlap, as the number of non-attempters in the advised group will always be at least 35.
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