Which of the following CANNOT be the median of the 3

Question

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

Bunuel · Accepted Answer

The median of a set with odd number of terms is just  the middle term , so it's x, y or z. Eliminate A and B right away. Now, the median can also be (x+z)/2 and (x+z)/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+z. Why? Because a middle term (the median) cannot possibly be greater than two terms (x and z) 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.

KarishmaB · Answer

Simple yet tricky question.

The following would be my train of thought:
Median means middle value (start from the basics). Since there are three numbers, median has to be one of x, y and z. So options a and b are out. 
If answer is c, d or e, then y must be the median i.e. the middle value. The middle value could be (x+z)/2 or (x+y)/3 but not (x+z) (since all the numbers are positive).

ravsg · Answer

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.

essarr · Answer

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" ?

Bunuel · Answer

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

essarr · Answer

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

ScottTargetTestPrep · Answer

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

MBA2020Boys · Answer

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

bumpbot · Answer

Automated notice from GMAT Club BumpBot:

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

This post was generated automatically.

Which of the following CANNOT be the median of the 3

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

Which of the following CANNOT be the median of the 3

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards