Q. 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 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 answer: d) The Question cannot be answered even by using both the Statements together
Question from UPSC Prelims 2024 CSAT Paper
Explanation:
Statement I: The highest marks in the class are 70 and the lowest marks are 50.
– This statement only gives us the range of marks but doesn’t provide any information about the number of students or the distribution of marks.
Statement II: Exclusion of highest and lowest marks from the class does not change the average.
– This statement tells us that removing the highest and lowest scores doesn’t affect the average, but it doesn’t give us specific information about the number of students.
Now, let’s consider if we can answer the question using these statements:
1. Using Statement I alone:
We can’t determine the number of students from just the highest and lowest marks.
2. Using Statement II alone:
We still can’t determine the number of students, as this statement only tells us about the impact of removing extreme scores on the average.
3. Using both statements together:
Even with both statements, we don’t have enough information to calculate the exact number of students. We know the average (60), the range of marks (50 to 70), and that removing the extremes doesn’t change the average. However, there could be multiple distributions of marks that satisfy these conditions with different numbers of students.
Therefore, the correct answer is indeed: d) The Question cannot be answered even by using both the Statements together