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?
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.)
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Posted by Jer
on 2015-06-15 09:12:18 |
Solution
