There are 3 possible ways you can construct the number line here

1. x ---- z ---- y
2. z ---- x -------- y
3. y -------- x ---- z

In each of the cases above, we have distance xy > distance xz

We cannot arrive at a unique solution using either of the statements.
So, I guess the answer is E

I. xyz<0

Satisfies 1, 2 and 3 above. No unique solution.

II. xy<0

No unique solution.

yes answer is E

The answer would be E. I wish I could explain diagramatically

There are 3 types of scenarios possible: x--z--y, z--x----y, y-----x--z
Statement (1): When xyz<0, we have the following 4 scenarios,
x y z
- - - Line 1, 2, 3 all possible
- + + Line 1 possible
+ - + Line 3 possible
+ + - Line 2 possible

Statement (2): When xy<0, we have the following 2 scenarios,
x y
- + Line 1 or 2
+ - Line 3

Together:
- + + Line 1 possible
+ - + Line 3 possible

There is no clear solution