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

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

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New post 27 Mar 2018, 21:21
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Q. \(100^{15}-3^5\) 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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100^15-3^5 is written as an integer. What is the sum of the digits of  [#permalink]

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New post Updated on: 28 Mar 2018, 00:55
rishabhmishra wrote:
Q. \(100^{15}-3^5\) 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


I think the OA on this one is incorrect. IMO D.

\(3^5 = 243\) ( \(3^2 * 3^3 = 9 * 27 = 243\))

100^15 = 10^30, 1 followed by 30 zeros

So when we subtract 243 from that big number.. the carry over would lead to 27 9's followed by \(1000-243 = 757\)

So it will be 999...27 times...757

Hence sum of digits = \(27*9 + 7 + 5 + 7 = 243 + 19 = 262\)

Best,
Gladi

Originally posted by Gladiator59 on 28 Mar 2018, 00:36.
Last edited by Gladiator59 on 28 Mar 2018, 00:55, edited 1 time in total.
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Re: 100^15-3^5 is written as an integer. What is the sum of the digits of  [#permalink]

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New post 28 Mar 2018, 00:47
Gladiator59 wrote:
rishabhmishra wrote:
Q. \(100^{15}-3^5\) 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


I think the OA on this one is incorrect. Please look into my solution Bunuel chetan2u

IMO it should be 127. The units place must be a 7!! as we are subtracting 3 from 10... that itself told me OA was wrong without solving completely. :-D

\(3^5 = 243\) ( \(3^2 * 3^3 = 9 * 27 = 243\))

10^15 = 1 followed by 15 zeros

So when we subtract 243 from that big number.. the carry over would lead to 12 9's followed by \(1000-243 = 757\)

So it will be 999...12 times...757

Hence sum of digits = \(12*9 + 7 + 5 + 7 = 108 + 19 = 127\)

Please point out if I am wrong somewhere...

Thanks!

Best,
Gladi

yes you made mistake in counting number of nine's as you can see its \(100^{15}\) then we can write it as \(10^{30}\) and last 3 digits are 757 then number of nine are 27
so 9*27+7+5+7=262 (hope you got my point)
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100^15-3^5 is written as an integer. What is the sum of the digits of  [#permalink]

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New post 28 Mar 2018, 00:52
rishabhmishra wrote:
yes you made mistake in counting number of nine's as you can see its \(100^{15}\) then we can write it as \(10^{30}\) and last 3 digits are 757 then number of nine are 27
so 9*27+7+5+7=262 (hope you got my point)


Thanks for pointing out that I read the Q wrong. Silly me. I have edited my original post.

Best,
Gladi
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Re: 100^15-3^5 is written as an integer. What is the sum of the digits of  [#permalink]

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New post 28 Mar 2018, 01:50
Gladiator59 wrote:
rishabhmishra wrote:
yes you made mistake in counting number of nine's as you can see its \(100^{15}\) then we can write it as \(10^{30}\) and last 3 digits are 757 then number of nine are 27
so 9*27+7+5+7=262 (hope you got my point)


Thanks for pointing out that I read the Q wrong. Silly me. I have edited my original post.

Best,
Gladi

hey first time i did the same silly mistake that is why i posted this question. I always make such silly mistakes that is why i am struggling right now and don't know how to over come.
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Re: 100^15-3^5 is written as an integer. What is the sum of the digits of &nbs [#permalink] 28 Mar 2018, 01:50
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