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Question 280949: To number the pages of a volume, 3001 digits were printed. Assuming all pages are
numbered, the number of pages is:
(A) 1021 (B) 1026 (C) 1027 (D) 1028 (E) none of these
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! page numbers 1 to 9 = 1 digit per page * 9 pages = 9 digits total.
page numbers 10 to 99 = 2 digits per page * 90 pages = 180 digits total.
page numbers 100 to 999 = 3 digits per page * 900 pages = 2700 digits total.
page numbers 1000 to 9999 = 4 digits per page * 9000 pages = 36000 digits total.
Since the total number of digits is 3001, then:
we ate up 9 digits to get from 1 to 9.
we ate up another 180 digits to get from 10 to 99.
we ate up another 2700 digits to get from 100 to 999.
So far we used a total of 2700 + 180 + 9 = 2889 digits.
Since we need to eventually use a total of 3001 digits, we have 3001 - 2889 = 112 more digits to go, and all of these digits will have 4 digits per page.
If we divide 112 by 4, we get 28 pages to go.
999 + 28 = 1027 pages in the volume.
If I am correct, that would be selection C.
The fact that 112 divided evenly by 4 was a good sign.
I would go with selection C.
A built in assumption is that the page numbers start at 1 and not 0.
this is a fair assumption I believe.
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