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# 100^15 - 3^5 is written as an integer. What is the sum of the digits

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Math Expert
Joined: 02 Sep 2009
Posts: 56307
100^15 - 3^5 is written as an integer. What is the sum of the digits  [#permalink]

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25 Jun 2019, 03:25
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Difficulty:

55% (hard)

Question Stats:

63% (03:04) correct 37% (02:52) wrong based on 49 sessions

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$$100^{15}-3^5$$ is written as an integer. What is the sum of the digits of this integer?

A. 225
B. 234
C. 243
D. 262
E. 272

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Director
Joined: 20 Jul 2017
Posts: 563
Location: India
Concentration: Entrepreneurship, Marketing
WE: Education (Education)
100^15 - 3^5 is written as an integer. What is the sum of the digits  [#permalink]

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25 Jun 2019, 03:39
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1
Bunuel wrote:
$$100^{15}-3^5$$ is written as an integer. What is the sum of the digits of this integer?

A. 225
B. 234
C. 243
D. 262
E. 272

3^5 = 243

100^2 - 3^5 = 9757, Sum = 9*1 + 7 + 5 + 7 = 9*1 + 19
100^3 - 3^5 = 999757, Sum = 9*3 + 19
100^4 - 3^5 = 99999757, Sum = 9*5 + 19
.
.
.
100^15 - 3^5 = Sum = 9*27 + 19 = 243 + 19 = 262

IMO Option D

Pls Hit kudos if you like the solution

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Manager
Joined: 03 Mar 2017
Posts: 98
Location: India
Re: 100^15 - 3^5 is written as an integer. What is the sum of the digits  [#permalink]

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25 Jun 2019, 03:45
1
100^15-3^5
=10^30-243
10^30 will have 30 zeros and when subtracted by 243 will have (30-3) number of 9s
=27*9+7+5+7=262
(9-2=7,9-4=5,10-3=7)
IMO option D
Manager
Joined: 01 Feb 2017
Posts: 230
Re: 100^15 - 3^5 is written as an integer. What is the sum of the digits  [#permalink]

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28 Jun 2019, 11:47
1
3^5= 243

10^15= 100.....

Now, 100....-243= 999..757

So, sum= 9+9+9...+7+5+7= 9*something + 19

Subtracting 19 from each answer choice to check whether the remainder is divisible by 9.

A) 225-19= 206; no
B) 234-19= 215; no
C) 243-19= 224; no
D) 262-19= 243; yes
E) 272-19= 253; no

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Re: 100^15 - 3^5 is written as an integer. What is the sum of the digits   [#permalink] 28 Jun 2019, 11:47
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