DS - distance between x and y

[Xbond]

Hi there,

Could you explain the concept of this DS in the simplest way

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

[pradeepsarathy]

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.