Data Sufficiency

rjanardhanan wrote:Is Z equal to the median of the 3 positive integers X,Y and Z?

X < Y+Z
Y = Z

Median means the middle value. Now Z can be the median if X < Z < Y or Y < Z < X.

(1) X < Y + Z Let us use the picking numbers approach.
If X = 1, Y = 2, Z = 3, then the median is 2, which means Y is the median value here.
If X = 1, Y = 3, Z = 2, then the median is 2, which means Z is the median value here.
No definite answer; NOT sufficient.

(2) Y = Z implies the 3 positive integers are X, Z, Z.
If all 3 integers are the same, then median will be Z.
If Z is the smallest integer, then also the median will be Z and if Z if the largest integer, then the median will be Z only; SUFFICIENT.

The correct answer is B.