Statement 1 tells us c * (d+1) is even. So either c is even, d+1 is even, or both are even. The +1 changes d from even to odd or vice versa.
Statement 2 tells us that (c+2) is even, (d+2) is even, or both are even. In this problem, whatever c and d are (even or odd) the +2 doesn't change that.
Neither is sufficient.
Now looking at them together... either d+1 or d+2 is odd. That means that c or c+2 has to be even in the statement where d+x is odd. Since c and c+2 both need to be either even or odd, you know that c is even.
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