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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    
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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:

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
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