I understand till the part where 9, out of 20, students can get a total of 85. I do not understand how do we get to the answer after that

85 is to be distributed among 9 people and the marks that each person can score is between 0 and 10 inclusive.

Let us say someone among the 9 people scores 0. Then we have 8 people remaining and yet we have 85 marks to be distributed among those 8. 85/8 = 10.625 this is more than 10 hence the least repeating number is not 0. Only when the least repeating number is 5. 8 people can score 10 to fulfill the possible integer value and also add the value of 9 people to equal 85

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Im sorry but I still don't get this

See there are 9 more people remaining and 85 is the score that needs to be divided. The score cannot be more than 10 as it is the whole number between 0-10.

Let us assume that the score is 10 for a person, then 75/9 = is not an integer
Let us assume that the score is 9 for a person, then 76/9 = is not an integer
Let us assume that the score is 8 for a person, then 77/9 = is not an integer
Let us assume that the score is 7 for a person, then 78/9 = is not an integer
Let us assume that the score is 6 for a person, then 79/9 = is not an integer
Let us assume that the score is 5 for a person, then 80/9 = is an integer -> That's it!

following

Total students : 20
Avg Score: 7
Since, Sum/total = avg we get sum=140
This means that 20 students scored a total of 140.

Now, the question mentions "atleast 1 student got every possible score".
So, 11 students scored {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
0 + 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 = 55

We have 20 - 11 = 9 students left and 140 - 55 = 85 total score to be distributed among the 9 students.
Now, we have to find ways to distribute the remaing 85 points.
There are many ways to do this among 9 students
For example:
1) 7 students score 10, 1 student scores 9, and 1 student scores 6 = 70 + 9 + 6 = 85
2) 8 students score 10, 1 student scores 5 = 80 + 5 = 85 etc

But the problem is that we need to find the lowest score possible for one of the 9 students, this forces us to allocate the maximum score for the remaining 8 students.
So the maximum value we can give the remaining 8 students is 10, this would force us to choose 5 as the lowest for the other student, so that the total adds up to 85
Therefore, example 2) 8 students score 10, 1 student scores 5 = 80 + 5 = 85 works! It's the only answer because if we reduce the score of any one of the 8 students then we would have to choose a score more than 5 for the 9th student to add up to 85. It will not give us the lowest score.
example 1) 7 students score 10, 1 student scores 9, and 1 student scores 6 = 70 + 9 + 6 = 85 does not work because 6 is not the lowest score possible.

Answer is (A) 5 > 4

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