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The sum of all the digits of the positive integer q is equal to the

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The sum of all the digits of the positive integer q is equal to the [#permalink] New post   07 Apr 2021, 00:13
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The sum of all the digits of the positive integer q is equal to the three-digit number x13. If \(q = 10^n – 49\), what is the value of \(n\)?

(A) 24
(B) 25
(C) 26
(D) 27
(E) 28
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B
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Re: The sum of all the digits of the positive integer q is equal to the [#permalink] New post   08 Apr 2021, 16:57
solution plz
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The sum of all the digits of the positive integer q is equal to the [#permalink] New post   08 Apr 2021, 19:33
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\(10^n\) - 49 starts producing a series of 9s (as n increases) with a 5 in the tens position and a 1 in the units position.

At 10^3 - 49, you end up with 951
At 10^4 - 49, you end up with 9951

1000 - 49 = 951, sum of digits = 15
10,000 - 49 = 9951, sum of digits = 24
on and on

Hence formula is: 9*(n-2) + 6 is the sum of the digits of \(10^n\) - 49 .

9*(25 - 2) + 6 = 213

Answer is B
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Re: The sum of all the digits of the positive integer q is equal to the [#permalink] New post   01 Oct 2022, 10:51
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Re: The sum of all the digits of the positive integer q is equal to the [#permalink]
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