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GATE 2026 XH2 (English) – Question 16

Reasoning and Comprehension · Logical and analytical reasoning · 1 mark · Multiple select

Six statements, S1 to S6, are given.

S1: All GATE candidates are engineers.

S2: Some GATE candidates are CAT candidates.

S3: All GRE candidates are GATE candidates.

S4: All engineers are GRE candidates.

S5: Some CAT candidates are GRE candidates.

S6: Some CAT candidates are engineers.

Based on S1-S6, following options provide a set of three statements, followed by a fourth statement. Identify the option(s) where the fourth statement can be necessarily inferred from the set of three statements.

  1. {S1, S2, S3} => S5
  2. {S4, S1, S2} => S5
  3. {S6, S1, S3} => S5
  4. {S4, S3, S1} => S6

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Show answer and explanation

Correct answer: (B) {S4, S1, S2} => S5

Explanation

In (B), some GATE candidates are CAT candidates (S2), all GATE candidates are engineers (S1), and all engineers are GRE candidates (S4). So those CAT candidates are engineers and so GRE candidates, which gives S5. In (A), the GATE candidates who are CAT candidates need not be GRE candidates, since S3 only says every GRE candidate is a GATE candidate. In (C) nothing links the CAT candidates to the GRE candidates. In (D) there is no information about any CAT candidate, so S6 cannot be inferred.