IMO E -
This stmt is much more easier to explain with a diagram.Anyways let me try to put this in words.
From the question stem, |x-y| > |x-z|
Stmt 1:
xyz<0
either all must be -ve or any one of the three must be -ve
Case 1: All of 'em are -ve
Let's say x = -5, y = -1, z = -6. This case satisfies the question stem.According to this case, z cannot lie between x and y
Case 2: one of 'em is -ve.Let's say y
Let x = 2, y=-5, z = 1.This case satisfies the question stem.But according to this case , z is between x and y.
Hence Stmt 1 alone is insufficient.
Stmt 2:
xy<0
=> either x or y is -ve
Case 1: x = 1, y = -5, z = 2.Here z does not lie between x and y
Case 2: x = 1 y = -5, z - -2.Here z does lie between x and y.
Hence stmt 2 alone is insufficient.
Combining both Stmt 1 and Stmt 2 -
Since xy<0, z has to be +ve, so as to satisfy the eqn xyz<0
Case 1:
Let's say x = 3 , y = -10, z = 2.Here z lies between x and y.
Case 2:
Let's say x = 3, y = -10, z = 4.Here z does not lie between x and y.
Hence both stmts together are not sufficient.
