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What is the sum of all digits for the number 10^30 - 37

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What is the sum of all digits for the number 10^30 - 37  [#permalink]

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New post Updated on: 11 Feb 2013, 10:05
3
15
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

63% (01:35) correct 37% (01:44) wrong based on 325 sessions

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What is the sum of all digits for the number 10^30 - 37 ?

A. 63
B. 252
C. 261
D. 270
E. 337

Edit: Sorry, I meant to have this in the PS sub-forum.

Originally posted by exploringm on 11 Feb 2013, 10:01.
Last edited by Bunuel on 11 Feb 2013, 10:05, edited 1 time in total.
Moved to PS forum.
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Re: What is the sum of all digits for the number 10^30 - 37  [#permalink]

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New post 11 Feb 2013, 10:15
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exploringm wrote:
What is the sum of all digits for the number 10^30 - 37 ?

A. 63
B. 252
C. 261
D. 270
E. 337

Edit: Sorry, I meant to have this in the PS sub-forum.


10^30 is a 31-digit number: 1 followed by 30 zeros.

10^30 - 37 is a 30-digit number: 28 9's and 63 in the end. Thus the sum of the digits is 28*9+6+3=261.

Answer: C.

Similar question to practice:
10-25-560-is-divisible-by-all-of-the-following-except-126300.html

Hope it helps.
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Re: What is the sum of all digits for the number 10^30 - 37  [#permalink]

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New post 06 Oct 2016, 12:32
Bunuel wrote:
exploringm wrote:
What is the sum of all digits for the number 10^30 - 37 ?

A. 63
B. 252
C. 261
D. 270
E. 337

Edit: Sorry, I meant to have this in the PS sub-forum.


10^30 is a 31-digit number: 1 followed by 30 zeros.

10^30 - 37 is a 30-digit number: 28 9's and 63 in the end. Thus the sum of the digits is 28*9+6+3=261.

Answer: C.

Similar question to practice:
10-25-560-is-divisible-by-all-of-the-following-except-126300.html

Hope it helps.


Hello Bunuel,

How you are able to figure out that it will be having "28 9's and 63 in the end" ?

Thanks.
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Re: What is the sum of all digits for the number 10^30 - 37  [#permalink]

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New post 06 Oct 2016, 12:39
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exploringm wrote:
What is the sum of all digits for the number 10^30 - 37 ?

A. 63
B. 252
C. 261
D. 270
E. 337


10^30 = 1000000...thirty 0's in total....000000
In other words, 10^30 is a 31-digit number.

So, for example, 10^30 - 1 is a 30-digit number.
In fact, 10^30 - 1 = 9999...thirty 9's in total...99999

Likewise, 10^30 - 37 is a 30-digit number.
Since 100 - 37 = 63, we know that 10^30 - 37 = 9999999.....9999963
Since 10^30 - 37 is a 30-digit number, we know that this value has 28 nines followed by 63
That is 100 - 37 = 999,999,999,999,999,999,999,999,999,963

The sum of all digits = (28)(9) + 6 + 3
= 261
=

Cheers,
Brent
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Re: What is the sum of all digits for the number 10^30 - 37  [#permalink]

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Re: What is the sum of all digits for the number 10^30 - 37   [#permalink] 17 Feb 2019, 02:28
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