Consider statement (1) alone first.
Remainder is 4.
Remainder should always be less than the divisor.
So 4<2y
Or y >2. So y can be 3, 4, 5...
Let the quotient be "a" when x is divided by 2y.
So x = a*2y+4.
Or x/y = 2*a + 4/y.
Hence the remainder depends on the value 4/y.
If y is 3, the remainder is 1 . If y is 4 remainder is 0 and if y is more than 4 say 5, 6.. remainder is 4.
Since nothing definite can be said, (1) alone is not sufficient.

Next consider (2) alone.
Since remainder is less than the divisor, 4<y or y is 5, 6....
Let the quotient when (x+y) is divided by y be "b".
So x+y =b*y+4.
Or x = (b-1)*y+4.
Or x/y = (b-1) + 4/y.
Since y is more than 4 say 5, 6.. remainder is hence 4.
So statement (2) alone is sufficient to answer the question.

The correct answer is hence (B).

That was a mistake. It should be divisor. I have corrected in my earlier post.