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## A printer numbered consecutively the pages of a book, beginning with 1 on the first page. In numbering the pages, he had to print a total of 187 digits. Find the number of pages in the book. A) 99 B) 98 C) 96 D) 97 E) 95 (GMAT-MATHS)

A printer numbered consecutively the pages of a book, beginning with 1 on the first page. In
numbering the pages, he had to print a total of 187 digits. Find the number of pages in
the book.
A) 99 B) 98 C) 96 D) 97 E) 95 (GMAT-MATHS)

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Option A is correct.
Explanation:
Let's calculate how many digits would be printed if the book had 100 pages.
1-digit pages: 1, 2, 3, . . . 8, 9
TOTAL: 9 digits

2-digit pages: 10, 11, 12, 13, . . . 98, 99
Rule: The number of integers from x to y inclusive = y - x + 1
So, the number of integers from 10 to 99 inclusive = 99 - 10 + 1 = 90
Each of the 90 integers has 2 digits
TOTAL: (90)(2) = 180 digits

3-digit pages: 100
TOTAL: 3 digits

TOTAL number of digits from 1 to 100 = 9 + 180 + 3 = 192
The question tells us that only 189 digits were printed. So, we can conclude that the book has fewer than 100 pages
In fact, notice that our totals for 1-digit and 2-digit pages = 9 + 180 = 189
So, the book must have 99 pages altogether.

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The total number of digits is 187. The total number of single digit page numbers is
9(from 1 to 9). So subtracting this from 187 we get 178. After page number 9 we have 2
digit page numbers. So dividing this by 2 we get 89. So the total number of pages in the
book are 89+9=98.

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