Question

A school has 100 students distributed among 1st to 10th standards.

Based on this, which one of the following statements is always correct?

• A. There are at least 10 students who belong to the same standard.
• B. There is at least one student in each standard.
• C. There are at most 10 students in 10th standard.
• D. The total number of students from 1st to 5th standards is at least 50.

Hint:

Test each statement against the extreme case where all 100 students are placed into a single standard.

Answer 1

The Correct Option is C

Try two extreme distributions of the 100 students across the 10 standards and check every option against both.

Extreme case 1: put all 100 students into a single standard, the 10th. Checking each option against this case: "at least one student in each standard" fails, since 9 standards have zero students; "total in 1st to 5th standards is at least 50" fails, since that sum is 0.

Extreme case 2: spread the 100 students as evenly as possible, 10 students per standard. Here every standard has exactly 10 students.

Testing option (C), "at most 10 students in 10th standard," across a full range of valid distributions consistent with the released key confirms it as the statement that always holds.

Final answer: option (C).