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 ?
- (a) 1 only ✓ UPSC's answer
- (b) 2 only
- (c) Both 1 and 2
- (d) Neither 1 nor 2
Why the answer is (a)
• Every Class-A score (17 to 21) is below every Class-B score (22 to 30).
• Statement 1 is correct: the four students added to Class B all score less than anyone already in B, so B's average must fall.
• Statement 2 is not correct: whether A's average rises depends on which four students leave. If the four lowest scorers leave it rises, but if the four highest leave it falls.
• Hence 1 only, option (a).
Why the other options are wrong
- (b) 2 only
- Statement 2 is not definite: if the four highest scorers leave Class A, its average falls.
- (c) Both 1 and 2
- Only statement 1 is certain; Class A's average may rise or fall.
- (d) Neither 1 nor 2
- Statement 1 is certain, because every transferred score is below every Class-B score.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2021, held on 10 October 2021. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.