IMO - D

beater wrote:If x is an integer, is y an integer?

1. The average of x, y and y-2 is x
2. The average of x and y is NOT integer

1. (x+y+y-2)/3 = x
2y-2 = 2x
y-1 = x
Hence, if x is an integer and y-1 = x, then y must be an integer. SUFFICIENT.

2. (X+Y)/2 = X
X+Y = 2X
Y=X thus, sufficient.

answer is D.

It should be A
X=7, y=8 then average is 7.5
X=7, y=7.5, average is 7.25

beater wrote:If x is an integer, is y an integer?

1. The average of x, y and y-2 is x
2. The average of x and y is NOT integer

IMO A

Stmt 1

(x + y-2 + y )/3 = x => 2y - 2 = 2 x => y - 1 = x => y = x + 1 And since x belong to integer, hence y belong to integer, as sum of x and 1 should be an integer

Stmt 2

(x+y)/2 is not an integer = > x/2 + y/2 is not an integer.
Now, there are some cases

(a) x/2 is an integer, y/2 is not an integer
(b) y/2 is an integer, x/2 is not an integer as x may not be a multiple of 2
(c) x/y and y/2 both are not integer

so, in case (a) and (c) y is not an integer, case (b) y is an integer. Therefore, stmt 2 does not help us to give the answer of the problem.

Hence stmt 2 is not sufficient