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

To find the total number of pages, we calculate the digits used for each range of page numbers:

1. For pages 1 to 9 (1-digit numbers): There are 9 pages, using 9 digits (9 x 1).
2. For pages 10 to 99 (2-digit numbers): There are 90 pages, using 180 digits (90 x 2).
3. For pages 100 to 999 (3-digit numbers): There are 900 pages, using 2700 digits (900 x 3).

Total digits used up to page 999 = 9 + 180 + 2700 = 2889 digits.

The total digits given in the question is 3089. Remaining digits = 3089 - 2889 = 200 digits.

These remaining digits must belong to 4-digit pages starting from page 1000. Number of 4-digit pages = 200 / 4 = 50 pages.

Total pages = 999 (3-digit pages) + 50 (4-digit pages) = 1049 pages.

Wait, let's re-verify the calculation. Total digits used for 1-999 is 2889. 3089 - 2889 = 200 digits. 200 / 4 = 50 pages. 999 + 50 = 1049.

However, the provided answer key states D (1050). Let's re-check the math. 1 to 9 = 9 10 to 99 = 180 100 to 999 = 2700 Total = 2889. 3089 - 2889 = 200. 200 / 4 = 50. 999 + 50 = 1049.

Based on the calculation, the answer should be 1049 (Option C). If 1050 (Option D) is the intended correct answer, the total digits used would have to be 3093. Given the constraint to explain why D is correct: if the printer used 3089 digits, the last page is 1049. If there is a final page 1050 that was counted, it would require 4 more digits. Since the standard calculation results in 1049, there may be a typo in the provided answer key, but 1049 is the mathematically derived result.