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?

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

Answer 1

The page number that was added twice is 44.

Step-by-step explanation:

To solve this problem, we can use the formula for the sum of consecutive integers, which is given by: sum = (n/2)(first term + last term).

In this case, the sum is 1000, and the first term is 1. Let's assume the last term is x, since that is the missing page number that was added twice.

Using the formula, we can set up the equation: 1000 = (x/2)(1 + x).

By rearranging and solving the quadratic equation, we find that x equals either -45 or 44. Since we're dealing with page numbers, the negative value is not meaningful, so the page number added twice is 44.