All the page numbers from a book are added, beginning at page 1. However, one-page number was mistakenly added twice. The sum obtained was 1000. Which page number was added twice?Choices:- 44 45 46 10
Question
All the page numbers from a book are added, beginning at page 1. However, one-page number was mistakenly added twice. The sum obtained was 1000. Which page number was added twice?Choices:- 44 45 46 10
Solution
The sum of the first n natural numbers is given by the formula n*(n+1)/2. We know that the sum is 1000 when a page number is added twice. So, we need to find a number n such that n*(n+1)/2 is less than 1000.
If we try n=44, we get 44*(44+1)/2 = 990 which is less than 1000.
If we try n=45, we get 45*(45+1)/2 = 1035 which is more than 1000.
So, the sum of page numbers from 1 to 44 is 990. The difference between 1000 and 990 is 10.
Therefore, the page number that was added twice is 10.
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