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What is the sum of all digits for the number 10^30 - 37 ?
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08 Jan 2021, 07:48
08 Jan 2021, 07:48
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Question Stats:
55% (01:41) correct
44% (01:24) wrong based on 78 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
Kudos for the right answer and explanation
A. 63
B. 252
C. 261
D. 270
E. 337
Kudos for the right answer and explanation
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: What is the sum of all digits for the number 10^30 - 37 ?
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08 Jan 2021, 07:56
08 Jan 2021, 07:56
1
Carcass wrote:
What is the sum of all digits for the number \(10^{30} - 37\) ?
A. 63
B. 252
C. 261
D. 270
E. 337
Kudos for the right answer and explanation
A. 63
B. 252
C. 261
D. 270
E. 337
Kudos for the right answer and explanation
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
Answer: C
Cheers,
Brent
Re: What is the sum of all digits for the number 10^30 - 37 ?
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13 Jan 2021, 00:12
13 Jan 2021, 00:12
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We have,
100 - 37 = 63 (For 10^2 - 37, Sum of digits = 1 x 9)
1000 - 37 = 963 (For 10^3 - 37, Sum of digits = 2 x 9)
10000 - 37 = 9963 (For 10^4 - 37, Sum of digits = 3 x 9)
Similarly,
For 10^30 - 37, Sum of digits = (30-1) x 9 = 270 - 9 = 261
100 - 37 = 63 (For 10^2 - 37, Sum of digits = 1 x 9)
1000 - 37 = 963 (For 10^3 - 37, Sum of digits = 2 x 9)
10000 - 37 = 9963 (For 10^4 - 37, Sum of digits = 3 x 9)
Similarly,
For 10^30 - 37, Sum of digits = (30-1) x 9 = 270 - 9 = 261
