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Thanks!

Mode = x

To find: Median - Mode

Statement 1:
Difference is less than "3"
Sets can be
x,x,x,x,x+1,x+1,x+1 ==> (x) - (x) = 0
Or,
x,x,x,x+1,x+1,x+2,x+2 ==> (x+1) - (x) = 1
INSUFFICIENT

Statement 2:
Average = x
x-1, x,x,x,x, x+1 ==> (x) - (x) = 0
x-4,x-3,x-2,x-1,x,x,x+10 ==> (x-1) - x = -1
INSUFFICIENT


Combining...

- - - - x - - - - -
The Left and Right side of "x" will have difference of max 2 and the average must be "x" .. that means LHS & RHS will be equal as "x" is integer.

So,
x-1,x,x,x,x+1 ==> (X) - (X) = 0

Answer {C}