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

The correct option is 1049.

To find the total number of pages in the book, we can break down the page numbers by the number of digits they contain and calculate the digits used for each group step-by-step:

1. Single-digit pages (Pages 1 to 9):
There are 9 pages in this range.
Digits used =
$9\times 1=9$
digits.

2. Two-digit pages (Pages 10 to 99):
There are 90 pages in this range (from 99 - 10 + 1 = 90).
Digits used =
$90\times 2=180$
digits.

3. Three-digit pages (Pages 100 to 999):
There are 900 pages in this range (from 999 - 100 + 1 = 900).
Digits used =
$900\times 3=2700$
digits.

4. Total digits used up to page 999:
Adding the digits from these three groups:
$9+180+2700=2889$
digits.

5. Remaining digits for four-digit pages (Pages 1000 and onwards):
Since the total digits used is 3089, the remaining digits left for the four-digit page numbers are:
$3089-2889=200$
digits.

6. Number of four-digit pages:
Each of these pages uses 4 digits. Therefore, the number of 4-digit pages is:
$\frac{200}{4}=50$
pages.

7. Total pages in the book:
The book has 999 pages (from 1 to 999) plus the 50 four-digit pages:
$999+50=1049$
pages.