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# M16-36

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Math Expert
Joined: 02 Sep 2009
Posts: 47221

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16 Sep 2014, 01:00
00:00

Difficulty:

35% (medium)

Question Stats:

65% (00:48) correct 35% (00:48) wrong based on 81 sessions

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

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

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Math Expert
Joined: 02 Sep 2009
Posts: 47221

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16 Sep 2014, 01:00
1
1
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 $$18*9+8+4=174$$.

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Joined: 25 Feb 2014
Posts: 47
GMAT 1: 730 Q50 V39
GPA: 3.83

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07 Nov 2014, 07:38
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 $$18*9+8+4=174$$.

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?
Math Expert
Joined: 02 Sep 2009
Posts: 47221

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07 Nov 2014, 07:54
1
1
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 $$18*9+8+4=174$$.

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.

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Hope it helps.
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02 Oct 2017, 00:22
Please explain - 10^20-16 has 20 digits: 18 9's and 84 in the end
Math Expert
Joined: 02 Sep 2009
Posts: 47221

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02 Oct 2017, 00:31
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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Joined: 09 Apr 2017
Posts: 6

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02 Oct 2017, 00:38
yea it definitely helped. Thanks a lot.
Re: M16-36 &nbs [#permalink] 02 Oct 2017, 00:38
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# M16-36

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