GATE Electrical 2023 | GA | Question: 4

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? 

• A. A majority of tobacco users who were advised to stop consuming tobacco made an attempt to do so. 
• B. A majority of tobacco users who were advised to stop consuming tobacco did not attempt to do so.
• C.  Approximately $30 \%$ of tobacco users successfully stopped consuming tobacco.
• D. Approximately $65 \%$ of tobacco users successfully stopped consuming tobacco. 

Answer 1

The passage provides two pieces of information:

• $65\%$ of tobacco users were advised to stop consuming tobacco.
• $3$ out of $10$ tobacco users attempted to stop using tobacco.

Now, let's consider these percentages in the context of the question:

If $65\%$ of tobacco users were advised to stop, it means that $35\%$ were not advised to stop because the total percentage adds up to $100\%.$

If $3$ out of $10$ tobacco users attempted to stop, it means $7$ out of $10\;(\text{or}\; 70\%)$ did not attempt to stop.

Given this information, we can make the following logical inference:

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

This is because $70\%$ (the percentage who did not attempt to stop) is greater than $50\%$ which means that the majority did not make an attempt to stop.

Correct Answer: B

Comments

3 out of 10 users attempted to stop tobacco.
How can we infer that the 3 out of 10 was from the advised group?I think it should be from the the whole tobacco users.

in my intuition the answer would be b, because 65% were advised but half of 65% would be 32.5%.
30% is still less than the number(it also includes the people who were not advised still tried to stop).

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@nintendoit Exactly, this is the correct reasoning, even in the best case, assuming all users who attempted to stop were from those who were advised to (which might not be the case, because 3 out of 10 includes even those who were not advised to stop), it is still less than the majority of them (the 65%), which is why option B is correct.

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Question says "attempted to stop" but options says "successfully stoped" , so option C and D automatically get rejected.

No calculation required :)

Answer 2

The number of people try to stop consuming tobacco = 0.65*0.30*100 = 19.5%.

These numbers of the people are not in majority that's why the majority of the consuming population are not tried to do so.

Comments

Incorrect reasoning, check accepted answer