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GATE 2026 EC – Question 5

General Aptitude · Analytical Aptitude: Logical Reasoning and Deduction · 1 mark · Multiple choice

The following observation is made about the scores obtained by 100 students in an exam: ‘For each student, there exists another student in the class such that their scores are at most ten marks away.’ If the above statement is false, which one of the following statements is necessarily true?

  1. For each student, the scores of all the other students are more than 10 marks away.
  2. There exists at least one student in the class for whom the scores of all the other students are more than 10 marks away.
  3. There is exactly one student in the class for whom the scores of some students are more than 10 marks away.
  4. For each student, the score of exactly one other student is more than 10 marks away.

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Show answer and explanation

Correct answer: (B) There exists at least one student in the class for whom the scores of all the other students are more than 10 marks away.

Explanation

The negation of ‘for all students there exists another within 10’ is ‘there exists a student for whom no other student is within 10’, i.e. all others are more than 10 away.