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GATE 2026 CH – Question 3

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

A school has 100 students distributed among 1st to 10th standards.
Based on this, which one of the following statements is always correct?

  1. There are at least 10 students who belong to the same standard.
  2. There is at least one student in each standard.
  3. There are at most 10 students in 10th standard.
  4. The total number of students from 1st to 5th standards is at least 50.

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Show answer and explanation

Correct answer: (A) There are at least 10 students who belong to the same standard.

Explanation

By the pigeonhole principle, if every standard had at most 9 students, the total would be at most 90, which is less than 100. So some standard has at least 10 students. The other statements can fail, for example when one standard has no student, or when 10th standard has 20 students.