GMAT Problem Solving (PS) | Re: x and y are positive integers. When x is divided by 11, the remainder

Hi,

As it is mentioned when x is divided by 11, the remainder is 5, and when x is divided by 34, the remainder is 27. When y is divided by 17, the remainder is 11, and when y is divided by 3, the remainder is 2

Hence, I concluded when X is even (11+5) and Y is even (17+11); Even + Even = Even. Since there is just one option with an Even number. I picked C. Is this approach correct?