UPSC Prelims 2024 · CSAT

Question 66: Data Interpretation

A Question is given followed by two Statements I and II. Consider the Question and the Statements.

QuestionIf the average marks in a class are 60, then what is the number of students in the class?
Statement–IThe highest marks in the class are 70 and the lowest marks are 50.
Statement–IIExclusion of highest and lowest marks from the class does not change the average.

Which one of the following is correct in respect of the above Question and the Statements?

aThe Question can be answered by using one of the Statements alone, but cannot be answered using the other Statement alone

bThe Question can be answered by using either Statement alone

cThe Question can be answered by using both the Statements together, but cannot be answered using either Statement alone

dThe Question cannot be answered even by using both the Statements together

AnswerUPSC’s answer is (d).

Statement I gives the highest and lowest marks, and statement II says dropping them leaves the average unchanged, which means those two together average 60 too. Neither tells how many students there are: classes of different sizes can satisfy both conditions with an average of 60, for example marks 50, 60, 70, or 50, 60, 60, 60, 70.

Why each option is right or wrong

(a) Wrong. Neither statement alone gives the number.
(b) Wrong. Neither statement alone gives the number either.
(c) Wrong. Even together, the number of students stays open.
(d) Right. Both together still fit classes of many sizes.

Answer: UPSC’s key. Explanation: written by UPSC Grade, not by UPSC.

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Source: UPSC, Civil Services (Preliminary) Examination 2024, General Studies Paper II (CSAT), Series A. The paper on upsc.gov.in.