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 ✓ UPSC's answer

Why the answer is (d)

• Statement I gives only the highest (70) and lowest (50) marks; the number of students cannot be found.

• Statement II: removing 70 and 50 leaves the average at 60. Since 70 + 50 = 120 = 2 × 60, this is true for any class size — it gives no equation for n.

• Even together, a class of 3, 10 or 50 students fits both statements.

• The question cannot be answered — option (d).

Why the other options are wrong

(a) The Question can be answered by using one of the Statements alone, but cannot be answered…: Neither statement alone fixes the number of students.
(b) The Question can be answered by using either Statement alone: Neither statement alone fixes the number of students.
(c) The Question can be answered by using both the Statements together, but cannot be…: Even together they do not help: removing 70 and 50 keeps the average at 60 for any class size, because 70 + 50 = 2 × 60.

Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2024, held on 16 June 2024. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.