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The set X consists of the following terms : {4,44,444,4444,. [#permalink]
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15 Jun 2013, 08:37
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The set X consists of the following terms: {4,44,444,4444,.....), where the nth term has n 4's in it for example 10th term is 4444444444. what is the hundreds digit of the sum of the first 45 terms of set S? A. 5 B. 3 C. 1 D. 6 E. 9
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Last edited by Bunuel on 15 Jun 2013, 09:20, edited 1 time in total.
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Re: The set X consists of the following terms : {4,44,444,4444,. [#permalink]
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15 Jun 2013, 08:50
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You can write the sum as \(4(1+11+111+...)\). Consider now the terms in the brackets: they go from 1 to 1x45 times. Since the question asks for the hundereds digit of the sum you should not bother of any futher digit, so consider the sum of the terms as \(1+11+111+111+111+...\) , so the sum can be written as \(1+11+(111*43=4773)\). As I said before you can discard any digit beyond the hundereds so you have \(4(1+11+773)\). \(773+1+11=785\) and \(4*785=3140\). \(C)1\) Hope it's clear
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Re: The set X consists of the following terms : {4,44,444,4444,. [#permalink]
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15 Jun 2013, 09:19
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fozzzy wrote: The set X consists of the following terms : {4,44,444,4444,.....), where the nth term has n 4's in it for example 10th term is 4444444444. what is the hundreds digit of the sum of the first 45 terms of set S?
A. 5 B. 3 C. 1 D. 6 E. 9 45*4=180, thus the units digit will be 0 and 18 will be carried over to the tens digit; 44*4+18=194, thus the tens digit will be 4 and 19 will be carried over to the hundreds digit; 43*4+19=191, thus the hundreds digit is 1. Answer: C. Similar question to practice: sistheinfinitesequences12s222s397477.htmlHope it helps.
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Re: The set X consists of the following terms : {4,44,444,4444,. [#permalink]
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17 Jun 2013, 17:59
Hi Bunuel,
Sorry i could not understand y we r doing this 45*4? 44*4+18? 43*4+19?
Thanks in Advance, Rrsnathan.



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Re: The set X consists of the following terms : {4,44,444,4444,. [#permalink]
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17 Jun 2013, 22:05
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rrsnathan wrote: Hi Bunuel,
Sorry i could not understand y we r doing this 45*4? 44*4+18? 43*4+19?
Thanks in Advance, Rrsnathan. Here is how the question works if you write the number down 4444444444 ( 45 4's 444444444 (44 4's ... .. 44444444 4444444 444444 44444 4444 444 44 4 ( 1 4 If you take the sum it will be 45 *4 = 180 the digit will be 0 and there will be a carryover of 18 then to calculate the next set it will be 44*4 + 18 = 194 so this digit is 4 and the carry over is 19 then for the next set it will be 43* 4 + 19 = 191 so this digit is 1, which is the hundreds digit
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Re: The set X consists of the following terms : {4,44,444,4444,. [#permalink]
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17 Jun 2013, 22:55
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rrsnathan wrote: Hi Bunuel,
Sorry i could not understand y we r doing this 45*4? 44*4+18? 43*4+19?
Thanks in Advance, Rrsnathan. 4 44 444 ...  4,444,444,444,444,444,444,444,444  44,444,444,444,444,444,444,444,444 444,444,444,444,444,444,444,444,444 Total 45 numbers. For the first digit (units place) we should add 45 2's > 45*4=180, thus the units digit will be 0 and 18 will be carried over to the tens digit; For the second digit (tens place) we should add 44 4's > 44*4+18=194, thus the tens digit will be 4 and 19 will be carried over to the hundreds digit; For the third digit (hundreds place) we should add 43 4's > 43*4+19=191, thus the hundreds digit is 1. Similar question to practice: sistheinfinitesequences12s222s397477.htmlHope it helps.
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The set X consists of the following terms : {4,44,444,4444,. [#permalink]
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08 Dec 2017, 00:29
We only need to be concerned about 45 numbers. So, in your notebook, write down how the addition would look like, for our set: {4+44+444+...4444} 4 +44 +444 ... Now, you don't really need to write so much, it's just for visualization. So, if there are 45 numbers, we have 45 4's in the Unit's place, 451=44 4's in the Ten's place and 441=43 4's in the Hundred's place. So, we need to write down the digits of the sum one by one in the following manner: 45*4=180, write down 0 in the Unit's place, and 18 is carried over. Then, 44*4=176, so add 18 to 176, we get 194, so write down 4 in the Ten's place and carry over 19. Then, 43*4=172, so add 19 to 172, we get 191, so write down 1 in the Hundred's place. We have arrived at our answer choice, C. Do this method on paper for easier understanding. Hope it helps.
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