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ds:

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mirhaque
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ds: [#permalink] New post   08 May 2005, 10:28
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any quick fix?



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Re: ds: [#permalink] New post   Updated on: 08 May 2005, 11:21
numbers XX5 are always odd and there is 1 XX5 every 10
so (1000-100)*1/10=90

numbers X5X can be even or odd.
We have 10 of them every 100.
Of these 10, 5 are even and X55 has been already counted.
we have 900*4/100=36

numbers 5XX can be even or odd.
we have 100 of them.
Of these 100, 50 are even and 50 odd.
Of the 50 odd, 10 5X5 have been already counted.
Of the 50 odd, 4 55X have been already counted.
total is 36.

Total with 5 as a digit is 90+36+36=162
Answer is 450-162=288

Hope this helps even if it is wrong.

Originally posted by thearch on 08 May 2005, 10:53.
Last edited by thearch on 08 May 2005, 11:21, edited 1 time in total.
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Re: ds: [#permalink] New post   Updated on: 08 May 2005, 11:17
total no of integers from 100 to 1000=(1000-100)+1=901
no of odd integers from 100 to 1000=(901-1)/2=450
total= 162
the required number=450-162=288

Originally posted by MA on 08 May 2005, 11:02.
Last edited by MA on 08 May 2005, 11:17, edited 1 time in total.
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Re: ds: [#permalink] New post   Updated on: 08 May 2005, 12:24
total # = 901
even # = 451

so odd # = 450

100 to 200: 14 5's
so 14 * 8 = 112 (not counting the 500's)

500's: 100 numbers; out of which half is odd with 5 = 50 numbers.

total = 112 + 50 = 162

odd and no 5's = 450 - 162= 288. Sooooo Easy!!! :-D

Originally posted by Dan on 08 May 2005, 11:04.
Last edited by Dan on 08 May 2005, 12:24, edited 1 time in total.
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Re: ds: [#permalink] New post   08 May 2005, 11:18
MA wrote:
total no of integers from 100 to 1000=(1000-100)+1=901
no of odd integers from 100 to 1000=(901-1)/2=450

aa5=9X9=81
a55=5x9=45
5xx=50
total=81+45+1+36= 176
the required number=450-176=274


Hi MA.
isnt it 163 (and the answer 287)? :)

PS In my previous post the answer should be 450-162=288 and not 162
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Re: ds: [#permalink] New post   08 May 2005, 12:00
thearch wrote:
MA wrote:
total no of integers from 100 to 1000=(1000-100)+1=901
no of odd integers from 100 to 1000=(901-1)/2=450

aa5=9X9=81
a55=5x9=45
5xx=50
total=81+45+1+36= 176
the required number=450-176=274


Hi MA.
isnt it 163 (and the answer 287)? :)

PS In my previous post the answer should be 450-162=288 and not 162


163 or 162? :lol:

i edited because i was messed up. :wink:
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Re: ds: [#permalink] New post   08 May 2005, 12:45
ok agreed on 162 :-D
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Re: ds: [#permalink] New post   08 May 2005, 13:27
hundreds digit can be: 12346789 => 8
tens digit can be: 123467890 => 9
units digit can be: 1379 => 4

9*8*4=288
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Re: ds: [#permalink] New post   08 May 2005, 13:29
christoph wrote:
hundreds digit can be: 12346789 => 8
tens digit can be: 123467890 => 9
units digit can be: 1379 => 4

9*8*4=288


wow, brilliant solution! thanks
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Re: ds: [#permalink] New post   08 May 2005, 15:48
christoph wrote:
hundreds digit can be: 12346789 => 8
tens digit can be: 123467890 => 9
units digit can be: 1379 => 4
9*8*4=288


miracle!!!!!!!!!!!!!!!!!!!!!!!!!! :roll:
is it a rule or just co-incident? :wink:
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Re: ds: [#permalink] New post   08 May 2005, 16:52
seriously is that a rule?
otherwise amazing!

christoph wrote:
hundreds digit can be: 12346789 => 8
tens digit can be: 123467890 => 9
units digit can be: 1379 => 4

9*8*4=288
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Re: ds: [#permalink] New post   08 May 2005, 23:25
IMO this way is applicable to all kind of these questions...i ever did it like this :)



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This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
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Thank you for understanding, and happy exploring!
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Re: ds: [#permalink]
08 May 2005, 23:25
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