Question

The pages of Ayhan's book are numbered from 1. The page numbers have a total of 459 digits.

How many pages does the book have?
A) 119
D) 215
B) 189
E) 219
C) 190

Answer 1

Explanation:

the first 9 pages have 1 digit (1 to 9).

the next 90 pages have 2 digits (10 to 99).

that is in total

9×1 + 90×2 = 189 digits.

that leaves us

459 - 189 = 270 digits for pages with 3 digit page numbers (100 and up).

there are 900 pages with 3 digit page numbers = 2700 digits, which is larger than 270.

so, the solution must be in this interval (there are no pages with 4 digit page numbers like 1000).

after how many pages with 3 digit pages numbers do we have a total of 270 digits ?

270/3 = 90 pages.

so, we have 9 + 90 + 90 = 189 pages in the book.