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vipulgoyal
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Note that is zy < xy < 0, none of x, y, and z can be equal to zero.
This means y and z are of opposite signs and x and y are also of opposite signs.
So, x and z are of same sign.
If |x - z| + |x| = |z|, then |x - z| = |z - x| = |z| - |x|
So, distance between z and x is equal to |z| - |x|, i.e. the difference of the distance of z from 0 and distance of x from 0 on the number line.
This is possible only when both x and z lies on the same side of 0 on the number line.
Also, as |z - x| must be positive, |z| - |x| must be positive, i.e. |z| must be greater than |x|
So, the problem is basically asking whether z < x < 0 or 0 < x < z
Statement 1: z < x
Now it is possible that either 0 < z < x or z < x < 0
So, statement 1 is not sufficient
Statement 2: y > 0
So, x and z are both negative.
Now it is possible that either x < z < 0 or z < x < 0
So, statement 2 is not sufficient
Both statements together: Only possibility is z < x < 0
This in turn means |x - z| + |x| = |z|
So, both statements together is sufficient
Answer : C
