What is the total number of digits printed, if a book containing 150 pages is to be numbered from 1 to 150?
- (a) 262
- (b) 342 ✓ UPSC's answer
- (c) 360
- (d) 450
Why the answer is (b)
• Pages 1 to 9 are single-digit numbers, contributing 9 × 1 = 9 digits.
• Pages 10 to 99 are two-digit numbers, contributing 90 × 2 = 180 digits.
• Pages 100 to 150 are three-digit numbers, contributing 51 × 3 = 153 digits.
• The total number of digits is the sum of these contributions: 9 + 180 + 153 = 342.
• Therefore, the correct total is 342, which corresponds to option (b).
Why the other options are wrong
- (a) 262
- Option (a) is incorrect because 262 is significantly lower than the calculated total of 342, likely resulting from undercounting the three-digit pages.
- (c) 360
- Option (c) is incorrect because 360 does not match the precise sum of 9 + 180 + 153, indicating a calculation error in the digit count.
- (d) 450
- Option (d) is incorrect because 450 is far higher than the actual total, suggesting a fundamental misunderstanding of how digits accumulate across page ranges.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2017, held on 18 June 2017. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.