Data Sufficiency

The mode of a set of integers is x. What is the difference between the median of this set of integers and x?
1. The difference between any two integers in the set is less than 3
2. The average of the set of integers is x

OA is C

Mode = x

To find: Median - Mode

Statement 1:
Difference is less than "3"
Set 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 [spoiler]{C}[/spoiler]