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

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Re: How many times will the digit 7 be written when listing the integers [#permalink] New post   11 Sep 2018, 17:21
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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


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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Re: How many times will the digit 7 be written when listing the integers [#permalink] New post   12 Dec 2020, 11:49
I did by total combinations- restricted (no 7's).

Total combination=10*10*10=1000
no 7's in the digit= 9*9*9=729

no of times 7 will be written from 1-1000= 1000-729=271. But the answer is 300. What mistake did i do here?
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Re: How many times will the digit 7 be written when listing the integers [#permalink] New post   12 Dec 2020, 21:55
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Hi Zeus666,

Your approach calculated the number of integers that had AT LEAST ONE '7' in the digits. However, that's not what the question asked for. We need to total all of the 7's that appear in the first 1,000 positive integers - and your solution does not consider numbers that include more than one 7 as digits (for example, 717, 778 or 777).

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Re: How many times will the digit 7 be written when listing the integers [#permalink] New post   22 May 2021, 04:19
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Solution:

Total 3 digit numbers from 1-1000,if we represent each number as abc (where a and b are 0 for double and single digit numbers respectively)
=3*1000 = 3000

Every digit must be equally used and hence each digit is used 3000/10 =300 times
=>7 shall be used as a digit 300 times too. (option d)

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Re: How many times will the digit 7 be written when listing the integers [#permalink] New post   10 May 2023, 20:43
KarishmaB What is wrong with below approach?
XX7 -> This way 100 numbers are possible.
X7X -> This way 100 numbers are possible.
7XX -> This way 100 numbers are possible.
Total 300. But there will few same number such as 777 (counted thrice), 77 (counted twice). So we will have to subtract it.
Answer will come 297
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Re: How many times will the digit 7 be written when listing the integers [#permalink] New post   10 May 2023, 22:52
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saketkandoi wrote:
KarishmaB What is wrong with below approach?
XX7 -> This way 100 numbers are possible.
X7X -> This way 100 numbers are possible.
7XX -> This way 100 numbers are possible.
Total 300. But there will few same number such as 777 (counted thrice), 77 (counted twice). So we will have to subtract it.
Answer will come 297



There are two different concepts:

How many times is the number 7 written? You will write 7 three times in 777 so it will be counted 3 times. You are not to remove 2 out of it.

How many numbers will have 7 in them? Now 777 is only one such number so you will count it only once.

Since our question asks us to find how many times 7 was written, it was written 100 times in hundreds place, 100 times in tens place and 100 times in units place so total 300 times.
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Re: How many times will the digit 7 be written when listing the integers [#permalink]
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