UPSC CSE 2024 · PYQ · Data Sufficiency / Averages · medium
A Question is given followed by two Statements I and II. Consider the Question and the Statements. Question: If the average marks in a class are 60, then what is the number of students in the class? Statement-I: The highest marks in the class are 70 and the lowest marks are 50. Statement-II: Exclusion 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?
A.The Question can be answered by using one of the Statements alone, but cannot be answered using the other Statement alone
B.The Question can be answered by using either Statement alone
C.The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone
D.The Question cannot be answered even by using both the Statements together✓ Correct
Explanation
Statement I gives only the highest and lowest marks (70 and 50) but does not tell us the number of students. Statement II says excluding the highest and lowest doesn't change the average — this gives information about the sum but not the count. Combining: if the average is 60 with n students, total sum = 60n. Excluding highest (70) and lowest (50): new sum = 60n − 120, with (n−2) students, average = (60n − 120)/(n − 2) = 60. This simplifies to 60n − 120 = 60n − 120, which is always true regardless of n. So we still cannot determine n uniquely. Both statements together are insufficient. The answer is (d).
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