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11 Sep 2018, 17:21
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seekmba
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
(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
12 Dec 2020, 11:49
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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?
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?
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).
GMAT assassins aren't born, they're made,
Rich
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).
GMAT assassins aren't born, they're made,
Rich
