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by [email protected] » Sun Nov 24, 2013 7:55 am
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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by Brent@GMATPrepNow » Sun Nov 24, 2013 8:08 am
[email protected] 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
Since we're trying to find hundreds digit of the sum, we can ignore the thousands digit, the ten-thousands digit, (etc) since these values will have no effect on the hundreds digit of the sum.

So, we need only find the hundreds digit of 4 + 44 + 444 + 444 + 444 + . . . + 444, where 444 appears 43 times in the sum.

Let's first find the sum of the 444's
We get (43)(444) = 19092
To the sum of 19092, we'll add 4 and 44 to get 19140

The hundreds digit is [spoiler]1[/spoiler], so the correct answer is C

Cheers,
Brent
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by [email protected] » Sun Nov 24, 2013 8:19 am
Brent,

But why dint we directly multiply with 45?

Brent@GMATPrepNow wrote:
[email protected] 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
Since we're trying to find hundreds digit of the sum, we can ignore the thousands digit, the ten-thousands digit, (etc) since these values will have no effect on the hundreds digit of the sum.

So, we need only find the hundreds digit of 4 + 44 + 444 + 444 + 444 + . . . + 444, where 444 appears 43 times in the sum.

Let's first find the sum of the 444's
We get (43)(444) = 19092
To the sum of 19092, we'll add 4 and 44 to get 19140

The hundreds digit is [spoiler]1[/spoiler], so the correct answer is C

Cheers,
Brent
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by Brent@GMATPrepNow » Sun Nov 24, 2013 8:23 am
[email protected] wrote:Brent,

But why dint we directly multiply with 45?

Brent@GMATPrepNow wrote:
[email protected] 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
Since we're trying to find hundreds digit of the sum, we can ignore the thousands digit, the ten-thousands digit, (etc) since these values will have no effect on the hundreds digit of the sum.

So, we need only find the hundreds digit of 4 + 44 + 444 + 444 + 444 + . . . + 444, where 444 appears 43 times in the sum.

Let's first find the sum of the 444's
We get (43)(444) = 19092
To the sum of 19092, we'll add 4 and 44 to get 19140

The hundreds digit is [spoiler]1[/spoiler], so the correct answer is C

Cheers,
Brent
The sum 4 + 44 + 444 + 444 + 444 + . . . + 444 has one 4, one 44 and forty-three 444's

So, I added the forty-three 444's and then added the one 4, one 44

Cheers,
Brent
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