is an integer n even?

[VJesus12]

If n is an integer, then is n even?

1) n(n+2)=even
2) n(n+3)=even

The OA is the option A.

Why is not sufficient the statement (2)? Experts, can you help me? Please.

[GMATGuruNY]

If n is an integer, then is n even?

1) n(n+2)=even
2) n(n+3)=even

Statement 1:
Case 1: n=1, with the result that n(n+2) = 1*3 = 3
Since the value in red is not even, Case 1 is not viable.
Case 2: n=3, with the result that n(n+2) = 3*5 = 15
Since the value in red is not even, Case 2 is not viable.
Case 3: n=5, with the result that n(n+2) = 5*7 = 35
Since the value in red is not even, Case 3 is not viable.
The cases above illustrate that NO ODD VALUE will satisfy Statement 1.
Thus, n must be EVEN, and the answer to the question stem is YES.
SUFFICIENT.

Statement 2:
Case 1: n=1, with the result that n(n+3) = 1*4 = 4
In this case, n is ODD, so the answer to the question stem is NO.
Case 1: n=2, with the result that n(n+3) = 2*5 = 10
In this case, n is EVEN, so the answer to the question stem is YES.
Since the answer is NO in Case 1 but YES in Case 2, INSUFFICIENT.

The correct answer is A.