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How many times will the digit 7 be written?

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BSchool Forum Moderator
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Joined: 28 Mar 2017
Posts: 1161
Location: India
GMAT 1: 730 Q49 V41
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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
Top Contributor
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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How many times will the digit 7 be written?  [#permalink]

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New post 11 Sep 2018, 17:21
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


The digit 7 as the hundreds digit appears 100 times (700 to 799). As the tens digit, it appears 100 times also (ten times each in the 70s, 170s, 270s, …, 970s). As the units digit, it appears 100 times also (7, 17, 27, …, 997). Therefore, the digit 7 has appeared a total of 300 times.

Answer: D
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How many times will the digit 7 be written? &nbs [#permalink] 11 Sep 2018, 17:21

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