1986 AIME Problems/Problem 6
Problem
The pages of a book are numbered through . When the page numbers of the book were added, one of the page numbers was mistakenly added twice, resulting in an incorrect sum of . What was the number of the page that was added twice?
Solution
Denote the page number as , with . The sum formula shows that . Since cannot be very large, disregard it for now and solve . The positive root for . Quickly testing, we find that is too large, but if we plug in we find that our answer is .
See also
1986 AIME (Problems • Answer Key • Resources) | ||
Preceded by Problem 5 |
Followed by Problem 7 | |
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