Which of the following CANNOT be the median of the 3 positive integers

Question

Which of the following CANNOT be the median of the 3 positive integers x, y, and z, where x<y<z?

A. y
B. z-2x
C. z-x
D. y-x
E. z-y-x

Shahalikhan · Answer

equate each equation to y

IMO D
A.y=y implies true for all integers
D.y-x=y implies

y,y cancels out
implies x=0

which is invalid

3 are positive integers
so x cannot be zero
 option d is righ answer

pkpatro26 · Answer

If Z-X can be a median, Y - X can be one too.

Say X=1, y=4, Z=5, then Z-X is a median
Alternatively, if X=1, Y=5 and Z=5, then Y-X is the median.

Am I missing anything?

unraveled · Answer

For such questions, a option having one of the integers can be eliminated as the integer can be a median. So, A is eliminated.
C and D are similar looking.

Let's say x = 1, y = 2 and z = 3
z - x = 2 
and y = 2
C can be a median. Eliminate.

Similarly, if 
x = 1, z = 2 and y = 3
y - x = 2
and z = 2
D can also be a median. Eliminate.

Out of B and E, the latter looks not possible. 
Let's check B as is it looks like an extension of C and D.
x = 1, y = 2 and z = 4
z - 2x = 4 - 2*1 = 2
and y = 2
Hence B is possible median.

For E, all the three integers are there. Also, median would be positive.
Case I: z - y - x = x  (5 - 1 - 2 = 2) 
z - y = 2x
z - 2x = y
Looks like this can be a median.

Case II:
z - y - x = y  (5 - 2 - 1 = 2) 
z - 2y = x
Looks like this too can be a median.

z - y - x = z
x + y = 0
x = - y
This is not possible as all the integers are positive.

Final note:  
E looks a likely candidate but something is not right with this option.

IMO Answer E.

Shahalikhan · Answer

sorry guys i have updated the question

where x<y<z

Shahalikhan · Answer

you already assumed x=1, y=4, z=5
clearly 4 is the median

as per your considerations
median y-x=3

3 is not in the already assumed set,

bumpbot · Answer

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Which of the following CANNOT be the median of the 3 positive integers

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Which of the following CANNOT be the median of the 3 positive integers

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