All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Just Math
Which integer was removed? (Posted on 2015-06-15) Difficulty: 3 of 5
Precisely one number is removed from the set of positive integers from 1 to n. The average of the remaining numbers is 40.75.

Which integer was removed?

No Solution Yet Submitted by K Sengupta    
No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution | Comment 1 of 2
Let x= the number removed.  
After removing x from the set the sum is n(n+1)/2 - x
For the average to work out this sum must be 40.75(n-1)
Set these equal and solve for x:
x=.5n^2-40.25n+40.75

a quick chart reveals the solution:
...
n=77, x=-94
n=81, x=61
n=85, n=232
...

(You could also solve for n using the quadratic formula and make a chart.  The only integer solution is the same as above.)

  Posted by Jer on 2015-06-15 09:12:18
Please log in:
Login:
Password:
Remember me:
Sign up! | Forgot password


Search:
Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (8)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2017 by Animus Pactum Consulting. All rights reserved. Privacy Information