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GATE 2023 EE GA Q.4: solution and answer

GATE 2023 · EEGA Q.4 · 1 mark · MCQ

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?

  1. (A)

    A majority of tobacco users who were advised to stop consuming tobacco made an attempt to do so.

  2. (B)

    A majority of tobacco users who were advised to stop consuming tobacco did not attempt to do so.

  3. (C)

    Approximately 30% of tobacco users successfully stopped consuming tobacco.

  4. (D)

    Approximately 65% of tobacco users successfully stopped consuming tobacco.

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Answer and solution

ANSWER

(B) A majority of tobacco users who were advised to stop consuming tobacco did not attempt to do so.

Official answer: BSource: Official answer key, GATE 2023 EE (IIT Kanpur)

  1. Take the total number of tobacco users as 100. From the passage, 65 were advised to stop, and 3 out of 10, that is 30, attempted to stop.

  2. Take the best case for option (A): every one of the 30 who attempted was among the 65 who were advised. No arrangement puts more attempters inside the advised group.

  3. Even in this best case, the share of advised users who attempted is , which is below . So at least of the 65 advised users, , did not attempt.

  4. In every other case some of the 30 attempters were never advised, so the advised group holds even fewer of them and the share that did not attempt is even larger. Whatever the overlap, a majority of advised users did not attempt. So (B) is certain and (A) is impossible.

  5. Options (C) and (D) are about users who successfully stopped. The passage mentions only being advised and attempting, and says nothing about success, so neither can be inferred.

  6. Only (B) follows with certainty.

KEY IDEA

Test a "certainty" claim with the extreme case. Even if all 30% of attempters were among the 65% who were advised, they would make up only of that group. So more than half of the advised users must not have attempted, however the two groups overlap.

WATCH OUT FOR

One mistake is to treat "attempted to stop" as "successfully stopped" and pick (C), which just repeats the 30% figure. Another is to assume advice leads to attempts and pick (A) without checking that 30 attempters cannot be a majority of 65 advised users.

From the GATE 2023 EE paper. Every question of this paper · Download the full paper · All 18 Reading questions, with notes

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