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?

N is obviously near 80. Say n=80, then decreasing values of x{79,78,77,..} increment the average in steps of 1/79. Similarly, if n=82, then decreasing values of x step in increments of 1/81. Neither of these fractions divides 0.25 evenly. So n=81, when decreasing values of x step in increments of 1/80.

Since 0.25=20/80, we need 20 steps. 81-20=61, so x=61

Edited on June 16, 2015, 12:22 am

Posted by broll on 2015-06-16 00:20:57