The maximum mark in an examination is 100 and the minimum is 0. The av

The average mark of seven students such that no two of them have scored the same marks is 88.
This means: (the sum of all seven scores)/7 = 88
Multiply both sides by 7 to get: the sum of all seven scores = 616

The median score is 92
So if we write all seven scores in ascending order, the middlemost score will be 92 as follows: _, _, _, 92, _, _, _

What is the maximum possible difference between the highest and the least mark obtained by these seven students?
In order to maximize the range, we must maximize the biggest number and minimize the smallest number.

Let's start by maximizing the biggest number.
Since the maximum score is 100, our resulting set looks like this: _, _, _, 92, _, _, 100

At this point we want to minimize the smallest value.
Since the sum of all seven scores = 616, we want to maximize the value of every score except the smallest score.
When we do this we get: _, 90, 91, 92, 98, 99, 100

The sum of the 6 biggest numbers = 90 + 91 + 92 + 98 + 99 + 100 = 570
So, the last remaining number (the smallest number) = 616 - 570 = 46
So the seven scores are as follows: 46, 90, 91, 92, 98, 99, 100

Range = biggest - smallest = 100 - 46 = 54

Answer: D