Here is my solution why C is always correct -
From S1, we have 5 different integers
From S2, m is an integer but different from the above 5 integers
Now we have to say Yes or No for D>2. This is equivalent to saying that the Numerator should be greater than 20 in expression of D.
(Since sqrt (20/5) = sqrt (4) = 2)
Therefore, we want sum of 5 separate squares to be equal to 20.
Since all are integers, squares of the differences will be integers. Also, since m is different, 0 as a difference is ruled out. So at minimum, we have
2*1^2 + 2*2^2 +1*3^2 = 19 [Expression 1]
However, since m is an integer, a+b+c+d+e = 5n (n is any integer)
Subtracting this value from 5m; 5m - (a+b+c+d+e) = 5m - 5n
Therefore, (m-a) + (m-b) + (m-c) + (m-d) + (m-e) = 5(m-n)
For values to satisfy Expression 1 ; 1+1+2+2+3 = 5(m-n)
Therefore, 9 = 5(m-n) which is false since m and n are integers.
Hence, D has to be greater than 2, since Expression 1 always will be greater than 20, to satisfy S1 and S2.
And since there is at least 1 example (1,2,3,6,8) proves that C is the correct answer