Question

From a book, a number of consecutive pages are missing. The sum of the page numbers of these pages is 9808. Which pages are missing?

• A. The page 9808 is missing
• B. The pages 291 up to 322 are missing
• C. The pages 291 up to and including 322 are missing
• D. Either a or c

Answer 1

The Correct Option is C

To find which pages are missing, we must determine a sequence of consecutive integers whose sum is 9808. Let's denote the first missing page as \( n \) and the last missing page as \( m \). The sum of the numbers from \( n \) to \( m \) is given by the formula:

\[ \text{Sum} = \frac{(m-n+1)(n+m)}{2} = 9808 \]

After breaking down and simplifying the potential solutions, let's calculate for the suggested options:

1. Pages 291 up to and including 322:

For pages from 291 to 322, \( n = 291 \) and \( m = 322 \).

Number of pages = \( m-n+1 = 322-291+1 = 32 \).

Sum, \( S = \frac{32}{2}(291+322) = 16 \times 613 = 9808 \).

This matches the given sum of page numbers.

Therefore, the missing pages are from 291 to 322, inclusive.