+0  
 
0
543
1
avatar

If \(S\)  is a subset of \(\{1, 2, \ldots, 100\}\)  with the property that no two distinct elements of \(S\) sum to 120, what is the largest possible value of the sum of the elements of \(S\)?

 Jul 26, 2018
 #1
avatar+111387 
+1

I'm not sure about this, but here's my take

 

Note that any two elements drawn from the  set   { 60, 61, 62, 63,......,98, 99, 100}  will always have a  sum > 120  

 

And  the set  {1, 2, 3,.....,17, 18, 19}   can be combined with the first set such that no two elements drawn from this "combined" set will have a sum of 120

 

So...the sum of the elements of this set will be :

 

(19)(20) / 2    +   [100 + 61] * 40/2 + 60

 

190  + 161* 20 + 60   =

 

190 + 3220 + 60 =

 

3470

 

 

cool cool cool

 Jul 26, 2018

8 Online Users

avatar