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M16-36

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Bunuel
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M16-36 [#permalink] New post   16 Sep 2014, 01:00
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Question Stats:

63% (01:27) correct 37% (01:49) wrong based on 226 sessions
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What is the sum of the digits in the decimal notation of the number \(10^{20} - 16\)?

A. 158
B. 162
C. 165
D. 174
E. 183
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D
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Bunuel
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Re M16-36 [#permalink] New post   16 Sep 2014, 01:00
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Official Solution:

What is the sum of the digits in the decimal notation of the number \(10^{20} - 16\)?

A. 158
B. 162
C. 165
D. 174
E. 183


\(10^{20}\) has 21 digits: a 1 followed by 20 zeros.

\(10^{20}-16\) has 20 digits: eighteen 9's and 84 at the end.

So, the sum of the digits of \(10^{20}-16\) equals \(18*9+8+4=174\).


Answer: D
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123Avi
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Re: M16-36 [#permalink] New post   07 Nov 2014, 07:38
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Bunuel wrote:
Official Solution:

What is the sum of digits in decimal notation of number \(10^{20} - 16\) ?

A. 158
B. 162
C. 165
D. 174
E. 183


\(10^{20}\) has 21 digits: 1 followed by 20 zeros;

\(10^{20}-16\) has 20 digits: 18 9's and 84 in the end;

So, the sum of the digits of \(10^{20}-16\) equals to \(18*9+8+4=174\).


Answer: D
Just one comment or perhaps it is my ignorance but I got confused by the text in decimal notation

They could had just written What is the sum of digits of number XXXXXXXXXXX?
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Re: M16-36 [#permalink] New post   07 Nov 2014, 07:54
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mayankpant wrote:
Bunuel wrote:
Official Solution:

What is the sum of digits in decimal notation of number \(10^{20} - 16\) ?

A. 158
B. 162
C. 165
D. 174
E. 183


\(10^{20}\) has 21 digits: 1 followed by 20 zeros;

\(10^{20}-16\) has 20 digits: 18 9's and 84 in the end;

So, the sum of the digits of \(10^{20}-16\) equals to \(18*9+8+4=174\).


Answer: D
Just one comment or perhaps it is my ignorance but I got confused by the text in decimal notation

They could had just written What is the sum of digits of number XXXXXXXXXXX?


Based 10 notation, or decimal notation, is just a way of writing a number using 10 digits: 1, 2, 3, 4, 5, 6, 7, 8, and 0 (usual way), in contrast, for example, to binary numeral system (base-2 number system) notation.

Similar questions to practice:
the-sum-of-all-the-digits-of-the-positive-integer-q-is-equal-126388.html
the-sum-of-the-digits-of-64-279-what-is-the-141460.html
what-is-the-sum-of-all-digits-for-the-number-147057.html
10-25-560-is-divisible-by-all-of-the-following-except-126300.html
if-x-is-a-positive-integer-and-10-x-74-in-decimal-notation-61013.html

Hope it helps.
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GeetikaR
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Re: M16-36 [#permalink] New post   02 Oct 2017, 00:22
Please explain - 10^20-16 has 20 digits: 18 9's and 84 in the end
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Bunuel
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Re: M16-36 [#permalink] New post   02 Oct 2017, 00:31
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GeetikaR wrote:
Please explain - 10^20-16 has 20 digits: 18 9's and 84 in the end


Take a simple example: 10^3 has 4 digits: 1,000.

10^3 - 16 has three digits: 984 - one 9 followed by 84.

Practice similar questions from the post above.

Hope it helps.
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GeetikaR
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Re: M16-36 [#permalink] New post   02 Oct 2017, 00:38
yea it definitely helped. Thanks a lot.
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Bunuel
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Re: M16-36 [#permalink] New post   04 Jul 2023, 00:29
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I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.
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Re: M16-36 [#permalink]
04 Jul 2023, 00:29
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