If x is a positive even integer, is y odd?
(1) 2y + x is even
(2) 2x + y is even
statement 1) 2y+x is even ==> ( 2y is even and x is even) or ( 2y is odd and x is odd ); but since x is even hence ( 2y is even and x is even) must be true
now 2y is even this does not tell us whether y is even or odd since 2y is always even irrespective of y even or odd ==> insuff
statement 2) 2x + y is even => y must be even because 2x is even. => suff.