Question

The mean of a set of 5 different positive integers is 21. How many values are possible for the median of this set of positive integers? Please help:)

Answer 1

This is a hard one. I don't know if this is the right solution, but here's my approach:

The 5 integers must be different. So to find the possible values (range) of the middle integer (the median) we set up the other integers like this, starting from 1:

1+2+c+d+e = 105

Then use algebra to reduce:

c+d+e = 102

Then set up again using DIFFERENT integers than 1 and 2:

3 + 4 + 95 = 102

So the minimum value for the median number is 3.

The equation would look like this: (1+2+3+4+95=105)/5=21

But how to find the max value for the middle integer?

I don't know if there's a mathematical way to approach this. I just assumed that since the numbers must be in order of 0<a<b<c<d<e, then we have to set up MAX so that the three numbers equal 102, but they are different than each other and each one is greater than the previous:

c<d<e, and c+d+e=102

Doing some guesswork, I know that 33 x 3 = 99, so try this:

33+34+35=102

THat works.

So the min value is 3, and the max is 33.

I'd be curious if there's a faster way to do this.

Answer 2

Cool xD

Answer 3

Endo, why did you set up the integers to equal 105, though?