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Re: What is the sum of the digits in 10^50 - 74 ? [#permalink]

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10 Oct 2009, 22:12

May not be the most elegant method but here goes:

10^50 = 1 followed by 50 trailing 0's. Question asks: 1.....000 - 74 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

10^50 = 1 followed by 50 trailing 0's. Question asks: 1.....000 - 74 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

Re: What is the sum of the digits in 10^50 - 74 ? [#permalink]

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11 Oct 2009, 10:40

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

Re: What is the sum of the digits in 10^50 - 74 ? [#permalink]

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12 Oct 2009, 08:50

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

Re: What is the sum of the digits in 10^50 - 74 ? [#permalink]

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12 Oct 2009, 20:45

arkadiyua 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 !!

Re: What is the sum of the digits in 10^50 - 74 ? [#permalink]

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13 Oct 2009, 10:50

Economist wrote:

arkadiyua 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"