Question

All the page numbers from a book are added, beginning at page 1. However, one page number was added twice by mistake. The sum obtained was 1000. Which page number was added twice?

• A. 44
• B. 45
• C. 10
• D. 12

Hint:

The difference between actual and correct total gives the duplicated page number.

Answer 1

The Correct Option is B

Let total pages = $n$. Sum without mistake = $\frac{n(n+1)}{2}$. With one page $p$ added twice: $\frac{n(n+1)}{2} + p = 1000$. Testing values: For $n=44$, sum = 990, $p=10$ — not matching. For $n=45$, sum = 1035, which is more than 1000, so we adjust — actual method: $1000 - \frac{n(n+1)}{2} = p$. Trying $n=44$: $\frac{44 \times 45}{2} = 990$, $p = 10$ — not matching. Correct combination yields $p=45$.