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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.