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Joined: 02 Sep 2009
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Re M0917 [#permalink]
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15 Sep 2014, 23:39



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Re: M0917 [#permalink]
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18 Dec 2014, 23:18
I think that the answer is wrong. The question is asking on how many pages does number 9 appear and not how many times does number 9 appear. Therefore page 99 has to be counted once. Hence correct answer is 18x7= 126



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Re: M0917 [#permalink]
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19 Dec 2014, 07:28
alemazza wrote: I think that the answer is wrong. The question is asking on how many pages does number 9 appear and not how many times does number 9 appear. Therefore page 99 has to be counted once. Hence correct answer is 18x7= 126 That's not correct. Pages with 9 in 100: 9, 19, 29, 39, 49, 59, 69, 79, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, and 99. Total of 19 pages. 19*7 = 133.
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Re: M0917 [#permalink]
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01 Jul 2015, 07:28
Hi,
If I would like to solve with combinatorics, may be slot method _ x _ x _ ... How the method would proceed?
Thanks a lot.
Best regards.
Luis Navarro Looking for 700



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Re: M0917 [#permalink]
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14 Mar 2016, 06:09
Here are the list of numbers 9, 19, 29, 39, 49, 59, 69, 79, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, and 99 Total  20 9's in 1 hundred. Total = 20*7 = 140



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Re: M0917 [#permalink]
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14 Mar 2016, 06:15
deepthit wrote: Here are the list of numbers 9, 19, 29, 39, 49, 59, 69, 79, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, and 99 Total  20 9's in 1 hundred. Total = 20*7 = 140 the Q ask us about the PAGES on which 9 occurs, so 99 will be ONE and not two separately so 19*7
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Re: M0917 [#permalink]
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06 Jul 2016, 04:17
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Another approach:
Pages from 1 to 705.
9 as units digit: 9 first number in set, 699last number in set, set is inclusive. Distance between each occurrence of '9' in units digits = 10. >> Number of occurrences = [(6999)/10] + 1 = 70
9 as tenths digit: if hundredth digit is '0', we have 90first number in set, 98last number in set (omit 99 as already counted above), set is inclusive. >> Number of occurrences: (9890) + 1 = 9 Possible hundredth digits: 0 1 2 3 4 5 6 >> total number of occurrences = 9*7=63
Finally: total pages with '9' = 63 +70 = 133



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Re M0917 [#permalink]
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29 Jul 2016, 09:47
I think this is a highquality question and the explanation isn't clear enough, please elaborate. Hi Bunuel,
Can you please take time to explain how this can be done using combination / permutations ?



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Re: M0917 [#permalink]
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02 Sep 2016, 09:20
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99 NEEDS to be counted as one page as question asks the number of pages on which 9 appears not the total number of 9's



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Re: M0917 [#permalink]
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02 May 2017, 03:25
For those who want to solve this using combinatorics
>> !!!
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