# CAT 2001 | Question: 24

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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?

1. $44$
2. $45$
3. $10$
4. $12$

Let Number of pages=n

The sum of all the page numbers = $\frac{n(n+1)}{2}$

We can quite easily see that for n=44, we have the sum as

$\frac{44*45}{2}$ = 22*45 = 990.

Thus, the page number 10 must have been added twice.

Hence (3)10 is the Answer.

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