Data Sufficiency

If x is an integer, is y an integer?
(1) The average (arithmetic mean) of
x, y and y - 2 is x.
(2) The average (arithmetic mean) of
x and y is not an integer.

OA is A

grandh01 wrote:If x is an integer, is y an integer?
(1) The average (arithmetic mean) of
x, y and y - 2 is x.
(2) The average (arithmetic mean) of
x and y is not an integer.

OA is A

Option 1. => y-2, x, y are three consecutive integers. SUF
Option 2. => Ix x=2 and y=3, then average in not an integer. If x=2 and y=2.5 then also average is not an integer. INSUF.

Ans A.

Given x is an interger

From Statement (1)

[x + y + (y-2)]/3 = x
=> x + 2y - 2 = 3x
=> 2y - 2 = 2x
=> y - 1 = x
=> y = x + 1 => Since x is an integer, x + 1 (=y) will also be an integer [Sufficient]

From statement (2)

(x + y)/2 => not an integer. Here y can take on both integer as well as non-integer values.
[Not sufficient]

[spoiler]Ans: A[/spoiler]