This question relies on our understanding of some even/odd multiplication properties:
odd * odd = odd
even * even = even
even * odd = even
We see that if we know we have one even number, we can multiply it by either an even or an odd number and get an even number product. However, if we know we have one odd number, we need to know whether the second number is odd or even - if it is odd, our product will be odd; if it is even, our product will be even.
Statement 1 tells us that x is odd. If y is even, xy will be even. However, if y is odd, xy will be odd. Insufficient.
Statement 2 tells us the y is even. If x is even, xy will be even. If x is odd, xy will still be even. So no matter whether x is even or odd, xy will be even if y is even. Sufficient.
I highly recommend committing these even/odd rules to memory because they come up a lot on the GMAT. However, if you forget, you can try simple one-digit even and odd numbers to test different options.
