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GATE 2026 PH – 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

The school has 100 students spread over 10 standards.

**Use the pigeonhole principle.** Suppose every standard had at most 9 students. Then the school would have at most $10\times9=90$ students, which contradicts the 100 students. Therefore **some standard has at least 10 students**. This is always true. ✓

Check why the others can fail:
- **B. At least one student in each standard.** Possible to fail: one standard could have 0 students.
- **C. At most 10 students in the 10th standard.** The 10th standard could have 20 students.
- **D. At least 50 students in standards 1 to 5.** Standards 6 to 10 could hold most of the students.

Answer **A**.