UPSC Prelims 2019 · CSAT
Question 53: Basic Numeracy
A printer numbers the pages of a book starting with 1 and uses 3089 digits in all. How many pages does the book have ?
AnswerUPSC’s answer is (c).
Pages 1 to 9 use 9 digits, pages 10 to 99 use 90 × 2 = 180, and pages 100 to 999 use 900 × 3 = 2700, a total of 2889 digits. The remaining 3089 - 2889 = 200 digits go to four-digit pages: 200 / 4 = 50 pages, numbered 1000 to 1049. So the book has 1049 pages.
How you could have got this
No shortcut here: in a “how many” question, ruling out options doesn’t help. Every statement has to be judged.
Which options go is worked out from UPSC’s key and the options, not by a model.
Why each option is right or wrong
- (a) Wrong: 1040 pages use 3053 digits.
- (b) Wrong: 1048 pages use 3085 digits.
- (c) Right: 1049 pages use exactly 3089 digits.
- (d) Wrong: 1050 pages use 3093 digits.
Answer: UPSC’s key. Explanation: written by UPSC Grade, not by UPSC.
Source: UPSC, Civil Services (Preliminary) Examination 2019, General Studies Paper II (CSAT), Series A. The paper on upsc.gov.in.