Data Sufficiency

I find these absolute questions difficult and time consuming! Can anyone help?

OA is D

I have not used this approach before(read in one of Ian's posts on interpreting absolute values). Hoping I have applied it correctly but please do wait for other responses too. I may be off here but anyways let me give it a try

To find if distance between a and y is less than distance between b and y


Stmt I)

|z-a| < |z-b|

Distance between a and z less than distance between b and z

a<y<z<b

Since y is between a and z the distance betwen a and y is indeed less than distance between b and y

SUFF

Stmt II

|y-a| < |z-b|

Distance between a and y is less than distance between b and z

Since distance between b andz itself is greater than distance between a and y therefore the distance between b and y is definitely greater than the distance between a and y since again a<y<z<b

SUFF

D)