[spoiler]Solution: A

Explanation: While this question can be answered with conceptual thinking and/or number picking, it is tedious and error prone. The best approach is with algebra:
In the question stem you learn that ac + b is odd, and in statement 1 you learn that ac + ab is even. If you add the two expressions together you know that the result will be odd (odd + even = odd) and the combined expressions will be: ac + b + ac + ab = 2ac + ab + b or 2ac + b(a+1) As a result you know that 2ac + b(a+1) is odd and because 2ac is always even then b(a+1) must be odd. When a product is odd, both components must be odd so b is odd and statement 1 is sufficient. If you do the same with the second statement (combine it with the expression from the question stem) know that ac + b + b + c must be even (odd + odd = even). Simplifying this means that 2b + c(a+1) is even. This leaves the possibility that b is either odd or even as either 2b must be even but b could be odd or even. Answer is A. The biggest takeaway from this problem is to not forget algebraic manipulation, as people tend to gravitate toward number picking on these types of problems.[/spoiler]