question: x=2?

(1) x is evenly divisible by exactly two positive integers.

this is true for any prime numbers
ex. x=3 - its divisible by 1,3

hence insufficient.

(2) The sum of any two distinct positive factors of x is odd.

the keyword here is "any".
lets say x=2, factors are 2,1 and their sum is odd.

for any other x, then sum of ANY 2 will not always be odd.
for example, x=3 > 3,1 the sum is even.
if x=4 > factors are 2,2,1,4 --> 4+2 = even, 2+1 = odd.

the trick in this question is the keyword "any".

Hence (B) is sufficient!