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GATE 2023 EE GA Q.6: solution and answer

GATE 2023 · EEGA Q.6 · 2 marks · MCQ

Students of all the departments of a college who have successfully completed the registration process are eligible to vote in the upcoming college elections. However, by the time the due date for registration was over, it was found that suprisingly none of the students from the Department of Human Sciences had completed the registration process.

Based only on the information provided above, which one of the following sets of statement(s) can be logically inferred with certainty?

(i) All those students who would not be eligible to vote in the college elections would certainly belong to the Department of Human Sciences.

(ii) None of the students from departments other than Human Sciences failed to complete the registration process within the due time.

(iii) All the eligible voters would certainly be students who are not from the Department of Human Sciences.

  1. (A)

    (i) and (ii)

  2. (B)

    (i) and (iii)

  3. (C)

    only (i)

  4. (D)

    only (iii)

See the question in the paper
GATE 2023 EE GA question 6Tap to open full size

Answer and solution

ANSWER

Only statement (iii) can be inferred with certainty, so the answer is (D) only (iii).

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

  1. Write the facts as rules. Rule 1: a student of any department who completed the registration process is eligible to vote. Registration is the only condition for eligibility that the passage gives, so read it as the rule for who may vote: eligible means registered. Fact 2: by the due date, no student from the Department of Human Sciences (HS) had completed registration.

  2. Combine them. No HS student meets the only eligibility condition, so no HS student is eligible to vote.

  3. Test (iii): every eligible voter completed registration, and no HS student did. So every eligible voter is a student from outside HS. (iii) follows with certainty.

  4. Test (i): it says every ineligible student is from HS. The passage says nothing about whether students of other departments also missed the deadline. Any such student would be ineligible without being in HS, so (i) cannot be inferred. It turns 'no HS student is eligible' around into 'every ineligible student is from HS', and that does not follow.

  5. Test (ii): it says every student outside HS registered on time. The passage talks only about HS students and says nothing about the rest, so (ii) cannot be inferred either.

  6. Only (iii) can be inferred with certainty, which is option (D).

KEY IDEA

Registration is the only route to eligibility, and no HS student registered, so no HS student is eligible. That is all the passage tells us. It supports 'every eligible voter is from outside HS' and says nothing about how students of other departments did.

WATCH OUT FOR

Many candidates turn 'no HS student is eligible' around into 'every ineligible student is from HS' and choose (B). Others assume every other department registered because the passage calls the HS result surprising, and choose (A). The passage is silent about the other departments, so neither (i) nor (ii) is certain.

From the GATE 2023 EE paper. Every question of this paper · Download the full paper · All 41 Reasoning questions, with notes

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