Bunuel wrote:

If a, b and c are positive integers and c is odd, are both a and b divisible by c ?

(1) a + b is divisible by c. If a = b = c = 1, then the answer is YES but if a = 1, b = 2 and c = 3, then the answer is NO. Not sufficient.

(2) a - b is divisible by c. If a = b = c = 1, then the answer is YES but if a = b = 1, and c = 3, then the answer is NO. Not sufficient.

(1)+(2) From (1) a + b = cx and from (2) a - b = cy. Sum these two: 2a = c(x + y). This means that either c is a factor of a, or c is an odd factor of 2, so 1 (remember that we are told that c is odd). So, in either case a is divisible by c. Now, if a is divisible by c and a + b is divisible by c, then b must also be divisible by c. Sufficient.

Answer: C.

Can you please highlight more about it? How 'c is an odd factor of 2'?

It is really unclear