UPSC Prelims 2021 · CSAT
Question 37: Basic Numeracy
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 ?
AnswerUPSC’s answer is (a).
Class A scores lie between 17 and 21, and Class B scores between 22 and 30. Any student moved from A scores at most 21, below every B score and so below B's average, so adding four such students must pull B's average down: statement 1 is certain. Statement 2 depends on who moves: if the four lowest scorers go, A's average rises, but if the highest go, it falls, so it is not certain. Remember: a value joining a group lowers its average whenever it is below that average; the effect of a value leaving depends on which one leaves.
- 1. Every student from A scored at most 21, below B's lowest score of 22, so B's average must fall.
- 2. A's average rises only if the students moved are below A's average; the highest scorers leaving would lower it.
How you could have got this
- If you were sure statement 1 is correct, (b) and (d) go: each of them leaves 1 out.
What you needed to know: Every student from A scored at most 21, below B's lowest score of 22, so B's average must fall.
- Then, if you were sure statement 2 is not correct, (c) goes: it includes 2.
What you needed to know: A's average rises only if the students moved are below A's average; the highest scorers leaving would lower it.
Only (a) is left. This one needs every statement.
Which options go is worked out from UPSC’s key and the options, not by a model.
Why each option is right or wrong
- (a) Right: only statement 1 is certain, because each moved score is below Class B's lowest score.
- (b) A's average rises only if students scoring below A's average move; that is not guaranteed.
- (c) Statement 2 is not certain, so both cannot be correct.
- (d) Statement 1 is definitely true, so this fails.
Answer: UPSC’s key. Explanation: written by UPSC Grade, not by UPSC.
Source: UPSC, Civil Services (Preliminary) Examination 2021, General Studies Paper II (CSAT), Series A. The paper on upsc.gov.in.