The teacher of a class took an MCQ test of Economic Awareness of 594 students in which the maximum marks were 65. Each question carried one mark and there was no negative marking. What can be the minimum possible number of students that have secured the same marks
To find the minimum possible number of students who have secured the same marks in the MCQ test, we need to consider the scenario where each student has obtained a different score.
Since there are a total of 594 students and the maximum marks in the test are 65, it implies that there are 65 different possible scores ranging from 0 to 65 (inclusive).
Assuming each student has a different score, we can start with the highest score (65) obtained by one student. The number of students having this score would be 1.
Now, for the next score (64), we can assign it to another student. Again, the number of students having this score would be 1.
We can continue this process until we reach a score of 1. At this point, all the remaining students would have a score of 1.
So, the minimum possible number of students securing the same marks would be the sum of the first 65 natural numbers since each number represents the number of students having the corresponding score.
Let's calculate that using the formula for the sum of the first n natural numbers:
Sum = (n/2) * (first number + last number)
Here, n = 65, first number = 1, and last number = 65.
Sum = (65/2) * (1 + 65)
Sum = 32.5 * 66
Sum = 2145
Therefore, the minimum possible number of students securing the same marks in the MCQ test is 2145.