Inequality

[jangojess]

Is |x - z| = |y - z| ???

a) x = y
b) |x| - z = |y| - z

Dont have any OA for this question.....IMO ans is A...Any comments?

[samirpandeyit62]

Is |x - z| = |y - z| ???

This is possible only if x=y or z is midway between x & y or x=y=z

a) x = y

SUFF

b) |x| - z = |y| - z

here |x| & |y| will be always positive

so this will be true only if |x| = |y|

so we have

x =y or x =-y

in first case |x - z| = |y - z|

but in second case i.e x = -y

|x - z| = |y - z| only if z = 0 i.e z is midway between x & y (which we cannot infer)
so |x - z| = |y - z| or |x - z| <> |y - z| depending upon position of z between x & y.

INSUFF

Ans should be A