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

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VP
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How many times will the digit 7 be written when listing the [#permalink] New post 10 Oct 2008, 16:23
How many times will the digit 7 be written when listing the integers from 1 to 1000?

* 110
* 111
* 271
* 300
* 304

I took a long long time to solve this and finally threw a hail mary pass. I want to look at different or easy approaches to solve this.

Thanks
Senior Manager
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Re: Number 7 [#permalink] New post 10 Oct 2008, 17:01
D - 300

1to100 : 20 times
101to200 : 20 times
.
.
.
.
901to1000:20times
Total = 200
plus
700's = 100
= 300

PS: If someone could come up with a better implementation/answer, I would appreciate it too...
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Re: Number 7 [#permalink] New post 10 Oct 2008, 17:20
please remaimber this thing:

how many time 7 or 8 or 5 comes between 1 to 1000

I think each number(except 0) will come 20 times from1 to 100 ".................1

so in 1 to 1000 mulitply this by 10:20 *10 =200

now each number hase its own series for 3 digitnumber :1xx,2xx,9xx

again each number will come 100 times.

so total 100 +200 = 300
* This thing can certainly save your 2min.in exam :)

Someone please confirm/correct this:
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Re: Number 7 [#permalink] New post 10 Oct 2008, 19:08
icandy wrote:
How many times will the digit 7 be written when listing the integers from 1 to 1000?

* 110
* 111
* 271
* 300
* 304

I took a long long time to solve this and finally threw a hail mary pass. I want to look at different or easy approaches to solve this.

Thanks


Unfortunately, we don't have any formulaic approach here. Go by the Unit, tens and hundreds approach so that you don't miss any number.

The number 7 at units place appears once in every 10 digits. So in the first 100 numbers, 7 appears 10 times. We have 10 100s here (100*10= 1000) so we have 7 at units place in 10*10 =100

Next tens place. Again we have 7 appearing 10 times in tens place in the first 100. We have 10 100s(100*10= 1000) here. So 7 at tens place = 10*10 = 100

Next hundreds place. In the first 100 numbers, We have 7 appearing 100 times in hundreds place (from 700 to 799) so that makes another 100.

Add up the three 100s we get 300
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Re: Number 7   [#permalink] 10 Oct 2008, 19:08
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