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base 10 notation - Set 10 Q14

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arocks: Master | Next Rank: 500 Posts; Posts: 127; Joined: Tue Oct 02, 2007 9:35 am; Thanked: 1 times

by arocks » Sun Oct 07, 2007 5:01 am

If 10^50 – 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

Not sure how to go about this one...Pls explain. Thanks.

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Source: Beat The GMAT — Problem Solving | Sun Oct 07, 2007 5:01 am

samirpandeyit62: Master | Next Rank: 500 Posts; Posts: 460; Joined: Sun Mar 25, 2007 7:42 am; Thanked: 27 times

by samirpandeyit62 » Sun Oct 07, 2007 5:20 am

10^ 5 -74

now 10^3 -74 = 1000 -74 = 926 i.e (3 digits against 4 of 1000)

similarly

10^50 -74 = 10....(50 zeros) -74 =(9999...(48 times)..26) (total 50 digits with last two as 26 & first 50-2 =48 as 9)

sum = 48*9 +2+6 =440

ans should be C

Regards
Samir

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arocks: Master | Next Rank: 500 Posts; Posts: 127; Joined: Tue Oct 02, 2007 9:35 am; Thanked: 1 times

by arocks » Sun Oct 07, 2007 5:52 am

Thanks...you rock!!

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