LM
Bunuel
Is z equal to the median of the three positive integers, x,y, and z?
Median of the three numbers is the middle term, hence z would be the median in two cases: \(x\leq{z}\leq{y}\) or \(x\geq{z}\geq{y}\).
(1) x<y+z --> clearly insufficient. If x=1, y=10, z=0, then answer would be NO but x=1, y=10, z=2, then answer would be YES.
(2) y=z --> either the three numbers are z, z, x (in ascending order) --> media=z or the three numbers are x, z, z (in ascending order) --> median=z. Sufficient.
Answer: B.
I just could not think that Z=0 is also possible.
IN this question will it be fair enough to assume that X=Y=Z is also one possibility because it does not say that they each is unique and different!
z may or may not be zero. For (1) you can pick infinite examples x<y+z to hold true. Another example: x=5, y=10, z=3, then answer would be NO but x=6, y=10, z=8, then answer would be YES.
About x=y=z. For statement (2) x=y=z is possible --> three numbers would be z, z, z --> median still z.