On the number line, the distance between x and y is greater than the distance between x and z. Does z lie between x and y on the number line?
a) xyz < 0
b) xy < 0

When no order is specified, consider different -- especially NON-ALPHABETIC -- orderings of the given points.

The following case satisfies all of the constraints in the problem:
y=-10..............................0..................z=9.....x=10
Here, z lies between x and y.

The following case satisfies all of the constraints in the problem:
y=-10..............................0..............................x=10....z=11
Here, z does NOT lie between x and y.

Thus, the two statements combined are INSUFFICIENT.

The correct answer is E.

Here's an algebraic approach.

Statement 1 tells us that either all three values are negative OR exactly one of them is negative. But which one? We don't know ... insufficient.

Statement 2 tells us that exactly one of x and y is negative and the other is positive. We don't know anything about z, however ... insufficient.

Taking the two together, we know exactly one of the numbers (either x or y) is negative. This tells us z is positive. But z could be on either side of the other positive number! (This is where GMATGuru's approach of trying numbers is helpful.) Hence the two statements together are insufficient.