Data Sufficiency

Let's call the numbers a, b, and c, with a > b > c. We want to know if b = (a + b + c)/3, or if 2b = a + c.

S1:

a - c = 2*(a - b)

a - c = 2a - 2b

2b = a + c

Sufficient!

S2:

Suppose that (a + b + c) = 3a. Then b + c = 2a, but this is impossible! a > b and a > c.

Similarly, suppose that (a + b + c) = 3c. Then a + b = 2c, but this is impossible! a > c and b > c.

That leaves only one possibility: (a + b + c) = 3b, or a + c = 2b. Sufficient!