A printer numbers the pages of a book starting with 1 and uses 3089 digits in all. How many pages does the book have?

Correct Option (C)

To determine the total number of pages, the digits used for numbering are categorized based on the number of digits per page:

• Pages 1 to 9 (single-digit numbers): 9 pages × 1 digit/page = 9 digits.
• Pages 10 to 99 (two-digit numbers): 90 pages × 2 digits/page = 180 digits.
• Pages 100 to 999 (three-digit numbers): 900 pages × 3 digits/page = 2700 digits.

The cumulative digits used for pages 1 to 999 is 9 + 180 + 2700 = 2889 digits.

The remaining digits available for numbering are 3089 (total digits used) - 2889 (digits for pages 1-999) = 200 digits.

These remaining 200 digits are used for four-digit page numbers. The number of four-digit pages is 200 digits / 4 digits/page = 50 pages.

Therefore, the total number of pages in the book is 999 (pages up to three digits) + 50 (four-digit pages) = 1049 pages.

Incorrect Options:

Options (A), (B), and (D) are incorrect. The systematic calculation of digits used for numbering pages, starting from page 1, leads to a unique total of 1049 pages. These alternative options do not align with the correct number of pages derived from the given total digit count of 3089.