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# sum of digits

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Manager
Joined: 01 Jan 2009
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sum of digits [#permalink]  10 Oct 2009, 21:06
00:00

Difficulty:

5% (low)

Question Stats:

100% (02:26) correct 0% (00:00) wrong based on 2 sessions
what is the sum of the digits in 10^50 - 74 ?
A. 424
B. 433
C. 440
D. 449
e. 467
_________________

The Legion dies, it does not surrender.

Senior Manager
Joined: 31 Aug 2009
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Location: Sydney, Australia
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Kudos [?]: 90 [0], given: 20

Re: sum of digits [#permalink]  10 Oct 2009, 21:12
May not be the most elegant method but here goes:

10^50 = 1 followed by 50 trailing 0's.
The resulting number is 48 9's followed by 26
So the number will be 2+6+48(9) = 2+6+432 = 440
ANS = C
Math Expert
Joined: 02 Sep 2009
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Kudos [?]: 17564 [0], given: 2183

Re: sum of digits [#permalink]  10 Oct 2009, 21:32
Expert's post
yangsta8 wrote:
May not be the most elegant method but here goes:

10^50 = 1 followed by 50 trailing 0's.
The resulting number is 48 9's followed by 26
So the number will be 2+6+48(9) = 2+6+432 = 440
ANS = C

Well, think found more elegant solution:

10^50-76=10^2*10^48-10^2+26=10^2(10^48-1)+26 --> we'll have the number with 48 nines 2 zeros +26, so the number would be 48 nines and 26 at the end --> number of digits=48*9+2+6=440

C.
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Manager
Joined: 15 Sep 2009
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Re: sum of digits [#permalink]  11 Oct 2009, 07:06
I have solved the foll way :

100 - 74 = 26
1000 - 74 = 926

10^50 - 74 will have 48 9's and 26.so adding we get the sum of digits as 440

I will go with option C
Director
Joined: 01 Apr 2008
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Re: sum of digits [#permalink]  11 Oct 2009, 09:40
One more way:)
10^50 has 51 digits... 10^50-76 will have 50 digits ( as the first digit '1' will be borrowed ) and the last two digits will be '2' and '6'. So we have 48*9 + 2 + 6 = 440
Manager
Joined: 04 Sep 2009
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Re: sum of digits [#permalink]  12 Oct 2009, 07:50
Got there the same way as economist. For around 20 sec, though, pondered on why I was getting 448, then realised that I added 432 and 26, while should have 432+2+6
Director
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Re: sum of digits [#permalink]  12 Oct 2009, 19:45
Got there the same way as economist. For around 20 sec, though, pondered on why I was getting 448, then realised that I added 432 and 26, while should have 432+2+6

I know , these are the silly silly silly mistakes that suck !!
Senior Manager
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Re: sum of digits [#permalink]  12 Oct 2009, 20:26
Looks like the solution offered by Economist is shortest, thus saves the most time.
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Manager
Joined: 12 Oct 2009
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Re: sum of digits [#permalink]  13 Oct 2009, 09:50
Economist wrote:
Got there the same way as economist. For around 20 sec, though, pondered on why I was getting 448, then realised that I added 432 and 26, while should have 432+2+6

I know , these are the silly silly silly mistakes that suck !!

did the same but I was adding 432+26 =458 and it was not in option

Regards
Asterix
Remember the golden rule "2+2 = 4"
Manager
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Re: sum of digits [#permalink]  13 Oct 2009, 10:11
9 x 48 +2+6 = 440
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Bhushan S.
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Senior Manager
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Kudos [?]: 30 [0], given: 23

Re: sum of digits [#permalink]  09 Nov 2009, 08:58
C.

99,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,926

math is a bitch
Re: sum of digits   [#permalink] 09 Nov 2009, 08:58
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