Hi, there. I'm happy to help with this.
This is a diabolically evil question, much much harder than anything the GMAT will ask you. In addition to that, the question is flawed. What is the source of this extremely poor question?
First, to answer your parenthetical question --- mean = median does
not imply evenly spaced. Evenly-spaced is an
extremely special condition -- if that's true, it's also true that mean - median, but there are scads of sets with mean = median that don't have this special condition.
In this question, we want a set that satisfies two conditions:
1) mean = median = 50
2) the largest element is 5 greater than 3 times the smallest element
Here are some sets that satisfy those conditions:
{27, 28, 50, 59, 86}
{29, 29, 50, 50, 92}
{30, 30, 45, 50, 50, 50, 95}
{33, 34, 36, 37, 50, 51, 52, 53, 104}
So, I was able to create a set that satisfies this condition with a highest value of 104. I am sure I could make sets with higher values, but I don't know how high could go (possibly 152?) (Notice, BTW, all of those set have mean = median, and none are evenly spaced, or even close)
The point is:
the question, as posed, does not contain the correct answer among the answer choices. It may be that the author intended further restrictions (e.g. only five elements, elements are integers, all elements are distinct, etc etc.) that have not been stated. It is the mark of a poor question when the author has in mind further conditions that are not explicitly stated. The GMAT will never do that to you.
So, don't worry about this particular question ---- and in fact, you might be suspicious of any other question you got from that source. Here's a more GMAT-like question about median:
http://gmat.magoosh.com/admin/questions/845When you submit your answer to that question, the next page will have a video explanation.
Does everything I've set here make sense? Please let me know if you have any further questions.
Mike
_________________
Mike McGarry
Magoosh Test Prep