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# 5). How many times is the digit "3" written while

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Manager
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5). How many times is the digit "3" written while [#permalink]  16 May 2008, 07:06
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5). How many times is the digit "3" written while numbering the pages of a book from 1 to 1000?
A. 243
B. 252
C. 271
D. 293
E. 300

Any easy/quick way to solve this?
Director
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Re: PS: Counting the Digits [#permalink]  16 May 2008, 09:19
not sure if this is a quick way

<edit>from 30 to 39, there are 11 3s <edit>
from 0 to 100 there are 20 3's (with the 30s)

not counting 300s, 20*9 = 180 3s between 0 and 1000

from 300 to 399, there are a 100 3s from the hundreds digit
and 20 3s from the tens digit

what is the oa?

Last edited by gmatnub on 16 May 2008, 09:42, edited 1 time in total.
Manager
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Re: PS: Counting the Digits [#permalink]  16 May 2008, 09:36
OA is 300. You are darn right, GMATnub. Good job, mate.
Current Student
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Re: PS: Counting the Digits [#permalink]  16 May 2008, 09:44
number of ways to have 3s..hmm

well we can have 3 as the unit digit..in that case we can have 10 different hundreds and 10 different ways of tens...10*10*1+10*1*10 (this case when 3 is the ten digit)+1*10*10 (this case when 3 is hundred digit)..total 100+100+100=300
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Re: PS: Counting the Digits [#permalink]  16 May 2008, 10:37
Expert's post
in the set of the numbers {001,002,003,...,999} we have 1000 numbers with 3 digits, totally 3000. Appearance of 3 is 1/10. So, N=3000*1/10=300
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Director
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Re: PS: Counting the Digits [#permalink]  17 May 2008, 04:40
we have:

1000 numbers with probability of a 3 appearing in each respective place equal to 0, 1/10, 1/10 ,1/10

so our overall probablity = 3/10. multiplying this with our 1000 numbers gives us 300.
Re: PS: Counting the Digits   [#permalink] 17 May 2008, 04:40
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