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

Question

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

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

Bunuel · Accepted Answer

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.

BrentGMATPrepNow · Answer

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.....99999 63 
Since 10^30 - 37 is a 30-digit number, we know that this value has 28 nines followed by  63 
That is 100 - 37 = 999,999,999,999,999,999,999,999,999,9 63

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

Cheers,
Brent

Nanobotstv · Answer

Hello Bunuel,

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

Thanks.

CrackverbalGMAT · Answer

Any number of the form  10^n  will have (n+1) digits viz a 1 followed by n zeroes. The first thing we can infer in this question, therefore, is the fact that  10^{30}  will have 31 digits – a 1 followed by 30 zeroes.

When 37 is subtracted from  10^{30} , the last 2 digits will be 63 and each of the remaining digits will be 9. Because we had to take a carry over, we will only be left with 30 digits now. 
Therefore, 9 appears 28 times followed by a 6 followed by a 3. The sum of these digits = (28*9) + 6 + 3 = 261.
The correct answer option is C.

A question like you tests your knowledge of basic mathematical operations like subtraction, addition and multiplication and hence, the only mistakes that can happen on such questions are calculation mistakes. Therefore, be very careful while doing the calculations. Even if you spend 1 minute on this question, make sure that you get it right, else the algorithm may penalize you for having gone wrong with such simple questions.

Hope this helps!

QuantMadeEasy · Answer

Sum of the digits = Number of 9's is 28 + 6 + 3
= (28*9) + 9
= 261

C is correct.

PrafulLata · Answer

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

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

Solution:

10^2 - 37 = 63
10^3 - 37 = 963
10^4 - 37 = 9963
.
.
10^n - 37 = 9 (n-2 times) 63

So 10^30 - 37 = 9*28 + 6 + 3 = 261

Option C is correct

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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

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