+82 What is the largest possible median for the five number set $\{x, 2x, 3, 2, 5\}$ if $x$ can be any integer?
+122 \(2, 3, 5, x, 2x\) creates the largest median no matter what. \(x\) can be any integer you want it to be, but the median will always be \(5\)
+2095 Correct! Notice that the median must always be the middle numberm and we can already see that 2 and 3 are less than 5. So, 5 will be the middle number, no matter what x and 2x are.
Largest possible median is 5!
+129852 Assuming that x is a positive ineger
Let x be some "large positive integer "
The ordering of the numbers is
2, 3 , 5 , x , 2x
And the median is 5.....just as cryptoaops found !!!
Note that not just ANY integer will produce this....for example...if x = 1 we have
1 2 2 3 5 and the median is 2
And if x = 2 we have 2 2 3 4 5 and the median = 3
If x = 3 we have 2 3 3 5 6 median = 3
If x = 4 we have 2 3 4 5 8 median = 4
In fact x must be an integer greater than 4 to have a median of 5
+122 No problem!
Also, I wanted to notify you that there should be no cheating on Alcumus or Homework as it is not allowed on AoPS.
