If x, y are integers, is x+y an odd number?

1) y=3x+5
When x is odd; ==> y = 3(odd) + 5 --------- (odd x odd = odd)
y = odd + 5 = odd + odd = even
Therefore y would be even. == > x + y = odd + even = odd.

When x is even; ==> y = 3 (even) + 5 ----------- (odd x even = even)
y = even + 5 = even + odd = odd
Therefore y would be odd. ==> x + y = even + odd = odd.

When x is 0. ==> y = 3(0) + 5 = 5. Y would be odd. x + y = 0 + odd = Odd. ---------- (1) is Sufficient.

2) y=2x-3
When x is odd; ==> y = 2(odd) - 3 --------- (even x odd = even)
y = even - 3 = even - odd = odd
Therefore y would be odd. ==> x + y = odd + odd = even. ---------- (2) is Insufficient.

When x is even; ==> y = 2 (even) - 3 ----------- (even x odd = even)
y = even - 3 = even - odd = odd
Therefore y would be odd. ==> x + y = even + odd = odd.

When x is 0; ==> y = 2(0) - 3 ==> y = -3. Y would be odd. x + y = 0 + odd = odd.
In (2) there are more than one possibilities. Hence (2) is Insufficient.
Only (1) alone is Sufficient. Answer A...