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GATE 2026 XH2 (English) – 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

This is the pigeonhole principle. If every standard had at most 9 students, the school would have at most 90 students, but it has 100. So some standard must have at least 10. The other statements can fail: a standard may be empty, the 10th standard may have more than 10 students, and the first five standards may hold fewer than 50.