buckkitty wrote:

Which of the following CANNOT be the median of the three positive integers x, y, and z?

A) x

B) z

C) x+z

D) (x+z)/2

E) (x+z)/3

This question is from

OG11. Can/should we assume that x, y and z are positive integers such that x<y<z?

i think there is no need for this assumption. The answer is C.

given x > 0, y >0, z > 0

lets look at the answers:

A) x this is possible as the numbers can be y < x < z (or z < x < y)

B) z this is possible (similar reason as in A)

C) x + z

now x + z > x and x + z > z so x+z can not be the median as it is greater than 2 out of the 3 numbers

D) (x + z)/2 , y could be (x + z)/2 hence one seq could be x < y < z

so this could be a median

E) (x + z)/3 , this is also possible (same reason as D)