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A printer numbered consecutively

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A printer numbered consecutively [#permalink] New post 06 Dec 2016, 09:01
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Question Stats:

71% (00:53) correct 28% (01:26) wrong based on 57 sessions
A printer numbered consecutively the pages of a book, beginning with 1 on the first page. In numbering the pages, it printed a total of 189 digits.

Quantity A
Quantity B
The number of pages in the book
100


A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
[Reveal] Spoiler: OA

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Re: A printer numbered consecutively [#permalink] New post 29 Dec 2016, 16:21
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Carcass wrote:
A printer numbered consecutively the pages of a book, beginning with 1 on the first page. In numbering the pages, it printed a total of 189 digits.

Quantity A
Quantity B
The number of pages in the book
100




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.

We have:
Quantity A: 99
Quantity B: 100

Answer: B
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Re: A printer numbered consecutively   [#permalink] 29 Dec 2016, 16:21
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