Q. 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
(b) 2 only
(c) Both 1 and 2
(d) Neither 1 nor 2
Correct Answer: (a) 1 only
Question from UPSC Prelims 2021 CSAT Paper
Explanation :
There are two classes a and b
Class A (Initial):
– Total students: 25
– Highest score: 21
– Lowest score: 17
– Four students will be shifted out
Class B (Initial):
– Total students: 30
– Highest score: 30
– Lowest score: 22
– Will receive four students from Class A
Analysis:
1. Effect on Class B’s Average:
– Initial students: 30
– New total: 34 students
– All incoming students have scores ≤ 21
– All original students have scores ≥ 22
– Therefore, adding any four students from Class A will definitely lower Class B’s average
2. Effect on Class A’s Average:
– Initial students: 25
– New total: 21 students
– Cannot determine if average will increase because:
- If highest scoring students (around 21) are shifted out → average will decrease
- If lowest scoring students (around 17) are shifted out → average will increase
- Without knowing which students are shifted, change in average is uncertain
Conclusion:
– Class B’s average will definitely decrease
– Class A’s average could increase or decrease depending on which students are shifted
