If x and y are positive integers, is x an even integer?

[BTGmoderatorLU]

Source: GMAT Prep

If x and y are positive integers, is x an even integer?

1) x(y+5) is an even integer.
2) 6y^2 + 41y + 25 is an even integer.

The OA is E

[GMATGuruNY]

Source: GMAT Prep

If x and y are positive integers, is x an even integer?

1) x(y+5) is an even integer.
2) 6y^2 + 41y + 25 is an even integer.

Statements combined:
Case 1: x=1 and y=1, with the result that x(y+5) = 6 and 6y²+41y+25 = 72
In this case, x is ODD, so the answer to the question stem is NO.

Case 2: x=2 and y=1, with the result that x(y+5) = 12 and 6y²+41y+25 = 72
In this case, x is EVEN, so the answer to the question stem is YES.

Since the answer is NO in Case 1 but YES in Case 2, the two statements combined are INSUFFICIENT.

The correct answer is E.