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

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by mbawisdom » Sat Mar 10, 2018 7:40 am
ardz24 wrote:How many times will the digit 7 be written when listing the integers from 1 to 1000?

(A) 110
(B) 111
(C) 271
(D) 300
(E) 304

Is there a strategic approach to this question? Can any experts help?
hi ardz24, how did you approach the question? Where did you run into difficulty?
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by swerve » Sat Mar 10, 2018 10:03 am
Hi ardz24,

Many approaches are possible, for example:

Consider numbers from 0 to 999 written as follows:

1. 000
2. 001
3. 002
4. 003
...
...
...
1000. 999

We have 1000 numbers. We used 3 digits per number, hence used a total of 3*1000 = 3000 digits. Now, why should ANY digit have preference over another? We used each of 10 digits equal # of times, thus we used each digit (including 7) 3000/10 = 300 times. Hence D should be the correct answer.

Regards!
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by Brent@GMATPrepNow » Mon Mar 12, 2018 7:23 am
ardz24 wrote:How many times will the digit 7 be written when listing the integers from 1 to 1000?

(A) 110
(B) 111
(C) 271
(D) 300
(E) 304

Here's one way to look at it.
Write all of the numbers as 3-digit numbers.
That is, 000, 001, 002, 003, .... 998, 999

NOTE: Yes, I have started at 000 and ended at 999, even though though the question asks us to look at the numbers from 1 to 1000. HOWEVER, notice that 000 and 1000 do not have any 7's so the outcome will be the same.

First, there are 1000 integers from 000 to 999
There are 3 digits in each integer.
So, there is a TOTAL of 3000 individual digit. (since 1000 x 3 = 3000)

Each of the 10 digits is equally represented, so the 7 will account for 1/10 of all digits.

1/10 of 3000 = 300

So, there are 300 0's, 300 1's, 300 2's, 300 3's, . . ., and 300 9's in the integers from 000 to 999

Answer: D

Cheers,
Bren
Brent Hanneson - Creator of GMATPrepNow.com
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