Base notation Problem

[sanalnnair]

Hi, Can anyone help me to solve this problem

Source- Previous GMAT question

Note "~" means raise to

If 10~1050 - 74 is written as an integer in base 10 notation, what is the sum of the digits in
that integer?

A. 424
B. 433
C. 440
D. 449
E. 467

Ans C


@ Sanju09, I tried hiding texts, but not able to do so..

[Rahul@gurome]

I think the question should be what is the sum of digits of the integer 10^50 - 74?

Now 10^50 = (10^48)*100.
Or 10^50 - 74 = (10^48)*100 - 74 = (10^48)*100 - 100 + 26 = 100*(10^48 - 1) + 26.

10^1 - 1 = 9.
10^2 - 1 = 99.
10^3 - 1 = 999.
Or 10^n - 1 = 99999....(n times).

Or 10^48 - 1 = 999.....(48 times).
Or 100*(10^48 - 1 ) = 9999....(48 times)00.
Or 100*(10^48 - 1) + 26 = 9999....(48 times)26. (last two digits are 26)

So the sum of digits is 9*48 + 2 + 6 = 432 + 8 = 440.

[sanalnnair]

Thanks a lot Rahul..