What is the number of fives used in numbering a 260-page book?
- (a) 55
- (b) 56 ✓ UPSC's answer
- (c) 57
- (d) 60
Why the answer is (b)
• Count the digit 5 in the units place from 1 to 260: 5, 15, ..., 255, giving 26 occurrences.
• Count the digit 5 in the tens place: 50-59, 150-159, and 250-259, giving 10 + 10 + 10 = 30 occurrences.
• There is no hundreds-place 5 because the book ends at page 260.
• Total fives = 26 + 30 = 56, so option (b) follows.
Why the other options are wrong
- (a) 55
- Option (a) gives 55, which is one less than the correct total of 56 fives.
- (c) 57
- Option (c) gives 57, which is one more than the correct total of 56 fives.
- (d) 60
- Option (d) gives 60, which overcounts the correct total of 56 fives by 4.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2024, held on 16 June 2024. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.