In a class, there are three groups A, B and C. If one student from group A and two students from group B are shifted to group C, then what happens to the average weight of the students of the class?
- (a) It increases.
- (b) It decreases.
- (c) It remains the same. ✓ UPSC's answer
- (d) No conclusion can be drawn due to insufficient data.
Why the answer is (c)
• Shifting one student from group A and two students from group B to group C changes only group membership, not the class total.
• The total number of students in the class remains the same because no student enters or leaves the class.
• The total weight of the class remains the same because the same students are still present.
• Class average weight = total weight of all students / total number of students.
• Since both numerator and denominator are unchanged, the class average weight remains the same, so option (c) follows.
Why the other options are wrong
- (a) It increases.
- It increases is wrong because no new weight is added to the class, only redistribution among groups occurs.
- (b) It decreases.
- It decreases is wrong because no student leaves the class and the total weight remains unchanged.
- (d) No conclusion can be drawn due to insufficient data.
- No conclusion can be drawn is wrong because the class average depends only on total weight and total number, both of which are unchanged.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2020, held on 4 October 2020. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.