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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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Manager
Joined: 23 Sep 2016
Posts: 217
100^15-3^5 is written as an integer. What is the sum of the digits of  [#permalink]

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27 Mar 2018, 21:21
00:00

Difficulty:

55% (hard)

Question Stats:

61% (02:25) correct 39% (02:09) wrong based on 47 sessions

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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
PS Forum Moderator
Status: It always seems impossible until it's done.
Joined: 16 Sep 2016
Posts: 417
GMAT 1: 740 Q50 V40
100^15-3^5 is written as an integer. What is the sum of the digits of  [#permalink]

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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,

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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Joined: 23 Sep 2016
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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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28 Mar 2018, 00:47
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.

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

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,

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)
PS Forum Moderator
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Joined: 16 Sep 2016
Posts: 417
GMAT 1: 740 Q50 V40
100^15-3^5 is written as an integer. What is the sum of the digits of  [#permalink]

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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,
Manager
Joined: 23 Sep 2016
Posts: 217
Re: 100^15-3^5 is written as an integer. What is the sum of the digits of  [#permalink]

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28 Mar 2018, 01:50
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,

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.
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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