I got this wrong this the first time around when pressed for time but it's pretty clear where I went wrong.
1) and 2) were easy to rule out as insufficient on their own.
x could be even or odd from the situation given in 1). 2) doesn't give us any information at all about x.
The answer must be C or E.
When looking at 1) + 2) I got confused how to pry information for 2). I kept seeing a quadratic equation, although factoring it would obviously do no good in this case.
When reviewing and having more time, I saw that:
6y^2 + 41y + 25 = even
6y^2 + 41y + odd = even
6y^2 + 41y = odd
Therefore, in 6y^2 and 41y must be one odd and one even. Y must be odd, otherwise you would have two evens.
Looking back at 1), if Y is odd, this all we know:
x(even) = even
We know nothing.
Answer is E.