Even or not

If c and d are integers, is c even?
1/ c(d+1) is even
2/ (c+2)(d+4) is even


OK, here's my crack at the problem.

but first ground rules:

odd x odd = odd
odd x even = even
even x even = even

Let's look at stem 1.

c(d+1) is even: it's telling us that when c is even d+1 is either even or odd. OR if c is odd, d+1 is even. Hence, c can be either even or odd. NOT SUFFICIENT.

Stem 2. Similar to stem 1, c+2 or d+4 can be either even or odd to make the statement work. hence, it's NOT SUFFICIENT.

Combined: Stem 1 & 2 tell us that c and c+2 are the same but d+1 and d+4 are different, meaning it's either even or odd. Since stem 1 & 2 results are even, C would have to be EVEN to satisfy stem 1 & 2.

The answer: C

@kshin78,

Thanks for your post.I understand up until that statement 1 alone is sufficient, neither is statement B alone; however, I still don't understand why combined, they are sufficient.

From my solving, both c and d can each be either even or odd, then? Thank you