Second attempt:
Question Is 2y = z + x or equidistant
(1) :
As rightly shown in the above post, simplifies to : 12 > x+y+z
This can be multiple scenarios for sets, therefore statement is Insufficient.
(2) : median of the set {x, y, z, 4}
The problem here is that we don't know the relation of 4 with respect to the other numbers, therefore the median can be any of the following cases :
Case 1 : {4, x, y, z} --> (x+y)/2 y > x which is already specified.
Case 2 : {x, 4, y, z} --> (4+y)/2 y > 4
Case 3 : {x, y, 4, z} --> --> y > 4 which is contradictory (see case 2).
Case 4 : {x, y, z, 4} --> (y+z)/2 y > z which is contradictory to given
The only two valid cases are Case 1 and 2.
Hence, Insufficient.
(1) and (2) together :
From statement we know 12> x+y+z:
Case 1 : {4, x, y, z} --> y > 4
Case 2 : {x, 4, y, z} --> y > 4
The only set of values for integers y & z are y >= 5; z >= 6 ---- meaning the set order is (x, 4, y, z) = not equidistant
Sufficient, therefore C
Made some errors when posting the first answer but definitely takes more than 2 mins.