CSAT Solved Papers/ 2024/Q66

2024 CSAT — Q66

Quant Data sufficiency 2.5 marks 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 Answer

Worked rationale

We need the count of students. Test whether the statements pin a count.

Statement-I alone (highest $70$ , lowest $50$ , average $60$ ): the class could have $2$ students ( $50, 70$ ), or $3$ ( $50, 60, 70$ ), or many — the average $60$ is consistent with countless sizes. Count not determined.

Statement-II alone (removing the max and min leaves the average unchanged): this only tells us the removed pair averages $60$ , i.e. $\text{max} + \text{min} = 120$ . It says nothing about how many students remain. Count not determined.

Both together. Statement I gives $\text{max}+\text{min} = 120$ (consistent with II) and average $60$ , but the number of students is still free — $2, 3, 5, 50$ students can all satisfy both. No count emerges.

Answer: (d) The Question cannot be answered even by using both the Statements together.

Why the other options miss

A

thought a statement was enough when it wasn’t: assumes “average $60$ , max $70$ , min $50$ ” forces a specific small class, ignoring that any size fits.
B

thought either statement was enough when neither is: the same error symmetrically; neither statement encodes a headcount.
C

assumed marks-facts must pin the headcount: the engineered trap — feels that “two facts about the marks” must determine the class, but both constrain the values, not the number of students.

Specialist insight

The question asks for a count, yet every datum given is about the marks (averages, extremes). An average plus extreme values constrains the distribution but never the population size — you can always add or remove students at the mean without violating any condition. The DS discipline: identify what the question actually asks for (here, $n$ ), then check whether any combination of statements pins that quantity. Both statements are about marks; neither touches $n$ , so even together they fail — a clean (d).

The trap, in one line

The statements constrain the marks (max $+$ min $=120$ , average $60$ ) but never the headcount — any class size fits, so even together they can't give $n$ : $(d)$ .

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