Data Sufficiency

If n is an integer, is n - 1 even?

(1) n - 2 is odd

(2) n + 1 is even

[spoiler]OA=D[/spoiler]

Why is sufficient the first statement? May anyone help me? Thanks in advanced.

Gmat_mission wrote:If n is an integer, is n - 1 even?

(1) n - 2 is odd

(2) n + 1 is even

If n-1 is even, we get the following options for n-1:
n-1 = 0, 2, 4, 6, 8, 10, 12...
Adding 1 to every value in the list above, we get the following options for n:
n = 1, 3, 5, 7, 9, 11, 13....
The resulting list indicates that n-1 will be even if N IS ODD.
Question stem, rephrased:
Is n odd?

Statement 1:
Since n-2 is odd, we get the following options for n-2:
n-2 = 1, 3, 5, 7, 9, 11, 13....
Adding 2 to every value in the list above, we get the following options for n:
n = 3, 5, 7, 9, 11, 13, 15....
Every value in the resulting list in blue is ODD.
Thus, the answer to the rephrased question stem is YES.
SUFFICIENT.

Statement 2:
Since n+1 is even, we get the following options for n+1:
n+1 = 0, 2, 4, 6, 8, 10, 12...
Subtracting 1 from every value in the list above, we get the following options for n:
n = -1, 1, 3, 5, 7, 9, 11....
Every value in the resulting list in blue is ODD.
Thus, the answer to the rephrased question stem is YES.
SUFFICIENT.

The correct answer is D.