Data Sufficiency

hypothetically speaking, if the question asks
is the absolute value of x-y greater than 1

this means (i think this logic is correct)
x-y> 1
or x-y <-1

1. x-y>1
2. x = 1/2

hypothetically speaking

since #1 (x-y > 1)matches one of two choices...is this enough to answer "statement 1 alone" or would #1 have to resolve both situations (x-y>1 and x-y<-1)

(A) will be sufficient but you still have to check to find out if the ans is A or D

thanks for the help