Yup, it's E.
Statement 1 doesn't help us. If y is odd, then y+5 is even. Therefore, no matter what x is, x(y+5) is going to be even (an even times any integer is even). So x could be odd (for a no answer) or even (for a yes). Insufficient.
Statement 2 says nothing about x, so it's automatically insufficent.
Putting them together proves that y is odd. Since we add 25 (odd) at the end, we need (6y^2 + 41y) to be odd (an odd + an odd is even). Since 6y^2 will always be even (again, an even times any integer is even) we have to add it to an odd to get an odd. 41 times an odd is the only way to get that number to be odd.
But, as we already said in statement 1, if y is odd then x can be either odd or even. So insufficent together, choice e.
An easy way not to get turned around in evens and odds is just to mark below the figures the actual words "odd" or "even" on your scrap paper. That way you don't have to keep it all in your head. For example, we automatically know that 6y^2 is even. So just write "even" below it and don't worry what actual number it is.
Cheers,
Steve
