If x and y are consecutive even integers, is x > y ?

[BTGModeratorVI]

If x and y are consecutive even integers, is x > y ?

(1) x - 2 and y + 2 are consecutive even integers.
(2) x is greater than 2.

Answer: A
Source: Kaplan

[Brent@GMATPrepNow]

If x and y are consecutive even integers, is x > y ?

(1) x - 2 and y + 2 are consecutive even integers.
(2) x is greater than 2.

Answer: A
Source: Kaplan

Given: x and y are consecutive even integers
So, for example it COULD be the case that x = 6 and y = 8 (i.e., x < y)
Alternatively, it could be the case that x = 8 and y = 6 (i.e., x > y)

Target question: Is x > y

Statement 1: x - 2 and y + 2 are consecutive even integers.
This automatically tells us that x > y.

We know this because there are only two possible cases: x < y and y > x (since the given information tells us that x and y are consecutive even integers)
If it were the case that x < y (e.g., x = 6 and y = 8), then subtracting 2 from x (the smaller value) and adding 2 to y (the bigger value) certainly won't yield two numbers that are consecutive even integers.
Since it's impossible for x < y, it must be the case that x > y
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: x is greater than 2
Since we have no information about the value of y, statement 2 is NOT SUFFICIENT

Answer: A

Cheers,
Brent