Statement (1) is insufficient. It doesn't give us any pertinent information; since we don't know anything about b or c, their relationship to a doesn't tell us anything useful about a.

Statement (2) can be translated into algebra:
(a + b + c)/3 < 10
a + b + c < 30

This, on its own, is insufficient. It's possible that a = 15 if, for instance, b = 7 and c = 7; it's also possible for a to be any number of other values.

Taken together, the statements are sufficient. Since all three variables are positive integers and a + b = c, c must be bigger than a. If a is 15, then c must be at least 16; since b is positive, a + b + c must be at least 32. (2) tells us that isn't possible. Thus, it's impossible for a to be 15. The answer is "no," and (C) is the correct choice.