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# HALP

+1
58
5
+54

What is the largest possible median for the five number set \$\{x, 2x, 3, 2, 5\}\$ if \$x\$ can be any integer?

Dec 29, 2020

#1
+80
+1

\(2, 3, 5, x, 2x\) creates the largest median no matter what. \(x\) can be any integer you want it to be, but the median will always be \(5\)

Dec 29, 2020
#2
+2197
+4

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!

Dec 29, 2020
#3
+114171
+3

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

Dec 29, 2020
#4
+54
+1

Thanks guys! :D

Dec 29, 2020
#5
+80
+1

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.

cryptoaops  Dec 29, 2020