Here we have to consider negative and positive value of |2y -5|.

Considering (2y - 5) to be negative

or -(2y - 5) < 1

or 2y - 5 > -1 (equality changes as the sign changes)

or 2y > 4 (adding 5 on both side)

or y > 2

Now consider positive

|2y -5|<1

or 2y - 5 < 1

or 2y < 6 (adding 5 on both side)

or y <3

Therefore the value of y is = 2 < y < 3

Hence statement A.