Which of the following CANNOT be the median of the 3

Sum of two positive integers will make the result fall between the 2nd and 3rd and so can in no way represent the 2nd or the middle number.

Just out of curiosity, is it always to be assumed that the variables are distinct integers? i.e. would there be cases where a gmat question names variables x, y, z without explicitly stating that theyre "distinct" ?

No, we should not assume that. For example here x, y, and z can be the same integer.

If x=1, y=2, z=1 then by (C) x+z=2 which is y
But I suppose trick is to remember the median is the "middle value", when variables are arranged in ascending/descending order

The median of three positive integers must be one of the integers. We see that the quantities in choices A, B, and D can be the median of the integers; since choices A and B are one of the integers, and the quantity in choice D (which is always between x and z) could equal the third integer (which is y). Thus, we can eliminate choices A, B, and D, and the correct answer narrows down to either choice C or E. Let’s analyze each.

If x + z is the median of the three integers, then neither x nor z can be the median since x + z is greater than either of them. This leaves us with y as the only possible candidate for the median. Therefore, y = x + z. However, since y = x + z, then y is greater than both of x and z. Thus y is the greatest integer, and it can’t be the median. Therefore, we see that it’s impossible for x + z to be the median (and we will leave it to the readers as an exercise to show that (x + z)/3 can also be the median).

Answer: C

to this person's point -- why cant x=1, y=2, z=1? How do we know that the 3 variables are in order?

Hi Bunuel, if we had a case where x,y,z are integers but not positive and given your example {-1,0,1}, even x+z could be the median right? Hence making answer choice (C) correct.

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