banksy wrote:

8. (MH) If x is an integer, is y an integer?

(1) The average (arithmetic mean) of x and y is an integer.

(2) The average (arithmetic mean) of x, y, and y + 4 is x.

1. (x + y)/2 is an integer

i.e x + y => integer

Therefore Y is an integer since x is an integer and X+Y is also an integer

eg . x+y=5 IF x=3 then y will be 2 (both integer)

Similarly if x=2.5 y will be 2.5 (both non integer) sufficient

2. x+y+y+4=3x

x-y=4

x is an integer (x-y) is an integer .... therefore y must also be an integer sufficient