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The set X consists of the following terms : {4,44,444,4444,. [#permalink]

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15 Jun 2013, 07:37

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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?

Re: The set X consists of the following terms : {4,44,444,4444,. [#permalink]

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15 Jun 2013, 07:50

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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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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.

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.

The set X consists of the following terms : {4,44,444,4444,. [#permalink]

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07 Dec 2017, 23:29

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, 45-1=44 4's in the Ten's place and 44-1=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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