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quant question

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quant question [#permalink] New post 31 May 2010, 12:16
hi everyone,
is there any other way to do the following question? i understand the explanation provided by the GMAT club. however i think this is a time-consuming approach. any short cut to this question? thanks!

How many times will the digit 7 be written when listing the integers from 1 to 1000?
• 110
• 111
• 271
• 300
• 304
There are several ways to count the number of times 7 appears between 7 and 997. One way is to consider the number of 7's in single, double, and triple digit numbers separately.
One-digit numbers: 7 is the only one-digit number.
Two-digit numbers: 7 could be the first digit or the second digit. Case 1: 7 is the first digit. There are 9 ways to place 7 as the first digit of a two-digit number. Case 2: There are 10 ways to place the second digit, i.e. 0-9. Remember that we have counted 07 already. Thus, for two-digit numbers we have: numbers that contain a 7.
Three-digit numbers: Use the knowledge from the previous two scenarios: each hundred numbers will contain one 7 in numbers such as 107 or 507 and also 19 other sevens in numbers such as 271 or 237. Thus a total of 20 sevens per each hundred and 200 sevens for 1000. Since we have 700's within the range, that adds another 100 times that a seven will be written for a total of 300 times.
The correct answer is D.
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Re: quant question [#permalink] New post 31 May 2010, 12:43
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Re: quant question   [#permalink] 31 May 2010, 12:43
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