279
To count the total digits used in numbering 129 pages, we split the page numbers into groups based on the number of digits.
Pages 1 to 9 (1-digit numbers): There are 9 pages, each using 1 digit.
Digits used = \(9 \times 1 = 9\)
Pages 10 to 99 (2-digit numbers): There are \(99 - 10 + 1 = 90\) pages, each using 2 digits.
Digits used = \(90 \times 2 = 180\)
Pages 100 to 129 (3-digit numbers): There are \(129 - 100 + 1 = 30\) pages, each using 3 digits.
Digits used = \(30 \times 3 = 90\)
Total digits = \(9 + 180 + 90 = 279\)
Hence, the correct answer is 279.
Important Questions from Number System
Consider the following statements :
1. (25)! + 1 is divisible by 26
2. (6)! + 1 is divisible by 7
Which of the above statements is/are correct ?
If the sum S is divided by 8, what is the remainder ?
If the sum S is divided by 60, what is the remainder ?
Find the sum of squares of the greatest value and the smallest value of K in the number so that the number 45082K is divisible by 3.
How many composite numbers are there from 53 to 97 ?
