Question

If x > y, and y > z, and all x, y, and z are positive, then which of the following is necessarily correct?

• A. z > x – y
• B. x > y – z
• C. y < x – z
• D. z > x + y

Answer 1

The correct option is B x > y – z

Assume that x = 10, y = 7, z = 1
Then, option a is not correct as 10 – 7 = 3 > 1
Now assume, x = 5, y = 4, z = 3
Then, option c is not correct as 5 – 3 = 2 < 4
Option d is universally incorrect as since both x and y are greater than z, so sum of x and y has to be greater than z.
Option b is always correct as since y and z are both smaller than x, the difference between y and z has to be smaller than x.