A printer numbers the pages of a book starting with 1 and uses 3089 digits in all. How many pages does the book have ?
- (a) 1040
- (b) 1048
- (c) 1049 ✓ UPSC's answer
- (d) 1050
Why the answer is (c)
• Pages 1 to 9 use 9 digits; pages 10 to 99 use 90 × 2 = 180 digits; pages 100 to 999 use 900 × 3 = 2700 digits.
• Up to page 999 the printer uses 9 + 180 + 2700 = 2889 digits.
• The remaining 3089 − 2889 = 200 digits go on four-digit page numbers, so there are 200 ÷ 4 = 50 more pages.
• The book has 999 + 50 = 1049 pages, option (c).
Why the other options are wrong
- (a) 1040
- Option (a) 1040 implies only 41 four-digit pages (164 digits), resulting in a total of 3053 digits, not 3089.
- (b) 1048
- Option (b) 1048 implies 49 four-digit pages (196 digits), resulting in a total of 3085 digits, not 3089.
- (d) 1050
- Option (d) 1050 implies 51 four-digit pages (204 digits), resulting in a total of 3093 digits, not 3089.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2019, held on 2 June 2019. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.