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?
How many times will the digit 7 be written when listing the
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hi ardz24, how did you approach the question? Where did you run into difficulty?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,
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!
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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 Brent@GMATPrepNow
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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 3digit 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