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# How many times will the digit 7 be written when listing the

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VP
Joined: 09 Jul 2007
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How many times will the digit 7 be written when listing the [#permalink]  12 Nov 2007, 06:42
How many times will the digit 7 be written when listing the integers from 1 to 1000?

110
111
271
300
304
Manager
Joined: 01 Nov 2007
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D

300 times

100 times at units place
100 times at tens place
100 times at hundreds place
VP
Joined: 09 Jul 2007
Posts: 1108
Location: London
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Kudos [?]: 74 [0], given: 0

Senior Manager
Joined: 01 Sep 2006
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Re: 7 [#permalink]  12 Nov 2007, 09:51
Ravshonbek wrote:
How many times will the digit 7 be written when listing the integers from 1 to 1000?

110
111
271
300
304

b/1 1-100 10 times + 1 for (77) =11
b/w 101-200 10 times + 1 more time (177) =11
b/w 201-300 10 times + 1 more time (277) = 11
b/w301-400 10 times + 1 more time (377) =11
b/w401-400 10 times + 1 more time (477) = 11
b/w501-600 10 times + 1 more time (577)= 11
b/w601-700 10 times + 1 more time (677)=11
b/w701-800 10 times + 10 times (for 7 being 1st digit) + 1 (777)=21
b/w 801-900 10 times + 1 more time (877) =11
b/w 901-1000 10 times + 1 more time (977) =11

99+11+1= 111
Director
Joined: 25 Oct 2006
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a) Unit’s place : i.e. 7,17,27,37…..97 = 10 times (between 1 to 100)
b) Tenth’s place: i.e. 70,71…79 = 10 times (between 1 to 100)
c) Hundred’s place: i.e. 700,701…..799= 100 times

So Upto 1000 it would be ten times for a and b: 10*10+10*10+100 = 300

D
CEO
Joined: 21 Jan 2007
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Location: New York City
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Re: [#permalink]  07 Jan 2008, 11:40
Ravshonbek wrote:

1000 is a 4 digit integer. XXXX
control for each of the digits.

the first digit cannot be 7 so we only have xxx to control for.

controlling for hundreds digit
7xx - the tens place can be 10C1 and the ones place can be 10C1. therefore, 10*10 = 100 possibilities
x7x - same logic
xx7 - same logic

100 + 100 + 100 = 300
_________________

You tried your best and you failed miserably. The lesson is 'never try'. -Homer Simpson

Intern
Joined: 07 Jan 2008
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Re: 7 [#permalink]  07 Jan 2008, 13:35
300..

between
1 and 100 – 20 times
101 and 200 – 20
201 and 300 – 20
301 and 400 – 20
401 and 500 – 20
501 and 600 – 20
601 and 700 – 20 + 1
701 and 800 – 20 + 99
801 and 900 – 20
901 and 1000 – 20

i.e 300
Re: 7   [#permalink] 07 Jan 2008, 13:35
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