If x - y = 8, then which of the following must be true ? I. Both x and y are positive. II. If x is positive, y must be positive. III. If x is negative, y must be negative.

Answer: Option D

It is given that x - y = 8
I. We may have x = 5 and y = - 3
So, it is not necessary that both x and y are positive.
II. If x positive, then it is not necessary that y is positive, as x = 5 and y = -3
III. If x < 0, then y = x - 8 which is clearly less than 0
So, if x is negative, then y must be negative.