Uva@90 wrote: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?
(1) xyz<0
(2) xy< 0

Given: Distance between x&y is GREATER than the distance between x&z, ie. on a number line xy is a bigger line segment and xz is a smaller one.



Q: We need to find out whether z lies between x and y or not

St1:
xyz < 0
product is negative so either all could be -ive or two could be -ive and one could be +ive

There could be many possibilities with these combinations and z MAY or MAY not lie inside:


INSUFFICIENT
(All the possibilities need not be visualized here only a few should suffice)

St2:
xy< 0
Either x = +ive & y = -ive
or x = -ive & y = +ive
We know nothing about Z and z could lie inside or outside.
INSUFFICIENT

St1+St2:
Combining the two inequalities we know that Z is +ive

Case1 (x = +ive & y = -ive & Z = +ive) :


Case2 (x = -ive & y = +ive & Z = +ive):


More than one possibility, thus INSUFFICIENT

[spoiler]Answer : E[/spoiler]

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.