A Question is given followed by two Statements I and II. Consider the Question and the Statements.
- Question: If the average marks in a class are 60, then what is the number of students in the class?
- Statement–I: The highest marks in the class are 70 and the lowest marks are 50.
- Statement–II: Exclusion of highest and lowest marks from the class does not change the average.
Which one of the following is correct in respect of the above Question and the Statements?
Answer & explanation
Answer: (d) The Question cannot be answered even by using both the Statements together
Statement II only tells us that the highest and lowest marks add up to 120 (twice the average). Statement I confirms 70 + 50 = 120, but neither statement says anything about how many students there are.
- Let there be n students, with total marks 60n.
- Statement II: (60n − H − L) ÷ (n − 2) = 60 gives H + L = 120, which is true for any n.
- Statement I: H = 70 and L = 50, consistent with H + L = 120, but n is still free.
- Example: marks 50, 60, 70 (n = 3) and 50, 60, 60, 70 (n = 4) both fit everything. So the question cannot be answered.
Remember · If a statement holds for every value of the unknown, it cannot fix that unknown; test two different cases.
Question and answer: UPSC's official GS Paper II (2024, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). ·