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If the pages of a term paper were numbered consecutively, wi

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fozzzy
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If the pages of a term paper were numbered consecutively, wi [#permalink] New post   Updated on: 11 Sep 2013, 08:07
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If the pages of a term paper were numbered consecutively, with the first page numbered 1, how many pages did the term paper have?

(1) A total of 87 digits were used in numbering the pages

(2) The digit 6 was used only 5 times in numbering the pages.
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Originally posted by fozzzy on 11 Sep 2013, 05:48.
Last edited by fozzzy on 11 Sep 2013, 08:07, edited 1 time in total.
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Bunuel
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Re: If the pages of a term paper were numbered consecutively, wi [#permalink] New post   11 Sep 2013, 06:30
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If the pages of a term paper were numbered consecutively, with the first page numbered 1, how many pages did the term paper have?

(1) A total of 87 digits were used in numbering the pages --> 9 digits for single digit pages + 2 digits for each two-digit pages = 87 --> 9+2x=87 --> x=39 --> total pages 39+9=48. Sufficient.

(2) The digit 6 was used only 5 times in numbering the pages --> the first 5 pages with 6 are: 6, 16, 26, 36 and 46. The sixth is 56. So, we have that \(46\leq{pages}<56\). Not sufficient.

Answer: A.

Hope it's clear.
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If the pages of a term paper were numbered consecutively, wi [#permalink] New post   17 Oct 2023, 04:10
Bunuel wrote:
If the pages of a term paper were numbered consecutively, with the first page numbered 1, how many pages did the term paper have?

(1) A total of 87 digits were used in numbering the pages --> 9 digits for single digit pages + 2 digits for each two-digit pages = 87 --> 9+2x=87 --> x=39 --> total pages 39+9=48. Sufficient.

(2) The digit 6 was used only 5 times in numbering the pages --> the first 5 pages with 6 are: 6, 16, 26, 36 and 46. The sixth is 56. So, we have that \(46\leq{pages}<56\). Not sufficient.

Answer: A.

Hope it's clear.


Hi Bunuel - can you elaborate on the second statement. Why it is not sufficient?

So, we have that 46≤pages<56
46≤Pages<56. Not sufficient.
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Re: If the pages of a term paper were numbered consecutively, wi [#permalink] New post   17 Oct 2023, 04:57
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Uditakaushal1992 wrote:
Bunuel wrote:
If the pages of a term paper were numbered consecutively, with the first page numbered 1, how many pages did the term paper have?

(1) A total of 87 digits were used in numbering the pages --> 9 digits for single digit pages + 2 digits for each two-digit pages = 87 --> 9+2x=87 --> x=39 --> total pages 39+9=48. Sufficient.

(2) The digit 6 was used only 5 times in numbering the pages --> the first 5 pages with 6 are: 6, 16, 26, 36 and 46. The sixth is 56. So, we have that \(46\leq{pages}<56\). Not sufficient.

Answer: A.

Hope it's clear.


Hi Bunuel - can you elaborate on the second statement. Why it is not sufficient?

So, we have that 46≤pages<56
46≤Pages<56. Not sufficient.


For any paper with page numbers ranging from 46 (inclusive) to 56 (exclusive), the digit 6 will appear only 5 times in the numbering, specifically on pages 6, 16, 26, 36, and 46. Therefore, the total number of pages can be anywhere from 46 to 55, inclusive.
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Re: If the pages of a term paper were numbered consecutively, wi [#permalink]
17 Oct 2023, 04:57
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