AbuRashid wrote:
Bunuel wrote:
Praetorian wrote:
Which of the following CANNOT be the median of the 3 positive integers x, y, and z?
A. x
B. z
C. x+z
D. x+z/2
E. x+z/3
A. x
B. z
C. x+z
D. x+z/2
E. x+z/3
The median of a set with odd number of terms is just a middle term, so it's x, y or z. Eliminate A and B right away. Now, the median can also be (x+y)/2 and (x+y)/3 (for example: {1, 2, 3} and {1, 2, 5}).
But since x, y, and z are positive integers then it no way can be x+y. Why? Because a middle term (the median) cannot possibly be greater than two terms (x and y) in a set with 3 terms.
Answer: C.
Notice that, if we were not told that x, y, and z are positive then x+y could be the median, consider {-1, 0, 1}: -1+1=0=median.
You have assumed x+z/2 ==( x+z)/2.
I really see the question as unclear. Should there be brackets?
Posted from GMAT ToolKitAs brackets were missing from the options, Edited. Thank you.