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How many times will the digit 7 be written?

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Re: How many times will the digit 7 be written? [#permalink]

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New post 10 Mar 2018, 06:24
seekmba 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


_ _ _

1. When all are 7, we have 1 combination i.e. 7 7 7 and since 7 appears 3 times we have 1*3= 3

2. When we have 2 7s, 7 7 _, we can fill the dash with 9 remaining digits and these can be further arranged in 3 ways.
Total ways = 9*3=27; but 7 appears 2 times in each combination; thus we have 27*2 = 54

3. When we have 1 7; 7 _ _ , we can fill the remaining dashes with remainng 9 digits.
Total ways = 9*9*3= 243

Thus Final Total = 243+54+3 = 300
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Re: How many times will the digit 7 be written? [#permalink]

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New post 12 Mar 2018, 08:26
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seekmba 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
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Re: How many times will the digit 7 be written?   [#permalink] 12 Mar 2018, 08:26

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