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# Starting with 1, positive integers are written one after the

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Senior Manager
Joined: 04 Jan 2006
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Starting with 1, positive integers are written one after the [#permalink]  10 Feb 2007, 11:33
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Starting with 1, positive integers are written one after the other. What is the 40,000th digit that will be written?

A. 4
B. 2
C. 1
D. 0
E. 3
SVP
Joined: 05 Jul 2006
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I CANT UNDERSTAND THE QUESTION , ARE U SURE OF THE WORDING??

OR IS IT ME
Intern
Joined: 02 Jan 2007
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Do you mean if you to write very large number like this:

1234567901234567890.... to 40,000 in length, what would the 40,000th digit be???

Wouldn't it be 0? Or that would be too easy.
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Beginning with the end in mind. Aiming to join the 700+ club.

Senior Manager
Joined: 04 Jan 2006
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yezz wrote:
I CANT UNDERSTAND THE QUESTION , ARE U SURE OF THE WORDING??

OR IS IT ME

Here is the sample.

1 then 2 then 3 then 4

123456789 10 11 12 13 14 15 16 17 18 19... keep writing and what is number in the 40,000th digit
VP
Joined: 22 Oct 2006
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Schools: Chicago Booth '11
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this is probably an 800 level question, i cant imagine anyone solving this in under 2 minutes
Senior Manager
Joined: 23 Jun 2006
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the answer would be 1.... however i agree that this is not a GMAT question....

here is the trick:
there are 9 1-digit numbers
there are 90 2-digit numbers
there are 900 3-digit numbers
and 9000 4-digit numbers
writing them all gives us 38889 digits.
so the 38890th digit is 1 of the number 10000, the first 5 digit number.
from here on, for the next 10000 numbers (or 50000 digits), each 5th digit would be 1. so 1 is the 38890th digit and 38895th digit etc... and also the 40000th digit.
GMAT Instructor
Joined: 04 Jul 2006
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Re: PS: Hard Question [#permalink]  12 Feb 2007, 11:12
devilmirror wrote:
Starting with 1, positive integers are written one after the other. What is the 40,000th digit that will be written?

A. 4
B. 2
C. 1
D. 0
E. 3

1-9 -9 digits total
10-99 -180 digits total ( 2 for each of the 90 two-digit numbers)
100-999 - 2700 digits total (3 for each of the 900 3-digit numbers)

1000-9999 - 36,000 digits total (......)

Clearly, the number containing the 40,000th digit will be a five digit number

Up to 999, we have written 38889 digits
Since 40,000-38,889= 1,111 and 1,111/5 =222 with a remainder of 1,

So, the 40,000th digit is the first digit in 10,222 i.e. 1
A tedious solution- has anybody got another?
VP
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hobbit wrote:
the answer would be 1.... however i agree that this is not a GMAT question....

here is the trick:
there are 9 1-digit numbers
there are 90 2-digit numbers
there are 900 3-digit numbers
and 9000 4-digit numbers
writing them all gives us 38889 digits.
so the 38890th digit is 1 of the number 10000, the first 5 digit number.
from here on, for the next 10000 numbers (or 50000 digits), each 5th digit would be 1. so 1 is the 38890th digit and 38895th digit etc... and also the 40000th digit.

you rule...........amazing solution hobbit
Manager
Joined: 12 Feb 2007
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they would never give this on the GMAT's would they?
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