There are two Classes A and B having 25 and 30 students respectively. In Class-A the highest score is 21 and lowest score is 17. In Class-B the highest score is 30 and lowest score is 22. Four students are shifted from Class-A to Class-B.
Consider the following statements:
- 1.The average score of Class-B will definitely decrease.
- 2.The average score of Class-A will definitely increase.
Which of the above statements is/are correct?
Answer & explanation
Answer: (a) 1 only
Every shifted student scored at most 21, below Class-B's lowest score of 22, so Class-B's average must fall. Class-A's average can rise or fall depending on which four students leave, so statement 2 is not certain.
- Each shifted student scored at most 21; every Class-B student scored at least 22.
- Adding scores lower than all existing scores pulls Class-B's average down — statement 1 is certain.
- Class-A's new average depends on whether the four who left were above or below Class-A's average.
- If the four scored 21 each, Class-A's average falls; if they scored 17 each, it rises — so statement 2 is not definite.
- ✓ 1. New members all score below Class-B's minimum, so its average must decrease.
- ✗ 2. Removing students raises the average only if they were below it; the data do not say which four moved.
Remember · Adding values below every existing value lowers the mean; removing values changes it only relative to the current mean.
Question and answer: UPSC's official GS Paper II (2021, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). ·