I used a very long method to solve this, but this is the only way I could think of this problem:
Based on the info given in the question stem, we can deduce 4 possibilities on the number line:
P1) Y____X___Z (Z on the right end, i.e not in between X and Y)
P2) Z___X____Y (Z on the left, i.e. not in between X and Y)
P3) X___Z____Y (Z in the middle, X on the left, Y on the right)
P4) Y____Z___X (Z in the middle, Y on the left, X on the right)
Evaluation each statement separately:
Statement 1: EITHER (X, Y and Z are all < 0) OR (X<0 or Y<0 or Z<0)
If X,Y and Z are all < 0, then P1, P2, P3 and P4 are possible.
If either X, Y or Z is <0, then P1, P2, P3 and P4 are possible.
Not Sufficient.
Statement 2: EITHER (X<0, Y>0) OR (X>0, Y<0)
If X<0, then P2 and P3 are possible
If Y<0, then P1 and P4 are possible.
Not Sufficient.
Evaluating both statements together:
Z must be positive, and either X<0 or Y<0. P1, P3 and P4 are possible. Both together are insufficient, answer E.
