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What is the sum of the numbers common to the two series

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What is the sum of the numbers common to the two series  [#permalink] New post 13 Mar 2004, 16:25
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What is the sum of the numbers common to the two series
3,6,9,12,....100 terms & 4,8,12,....80 terms?

7800
3640
3900
5799
None of the above
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 [#permalink] New post 13 Mar 2004, 18:33
3900

If we combine the series we get a new series with 12,24....300
Then, Sn = 1/2 n (a1+an) {n-count ; a1 - first number, an -last number}
As 25 times 12 is 300 I took n as 25.
1/2(25)*(12+300)
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 [#permalink] New post 13 Mar 2004, 18:49
I'm :stupid & :?
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 [#permalink] New post 15 Mar 2004, 08:18
3900.

Take the first series. every 4th number is the same as every third number in the second series.

For the first series, 100/4 = 25.
Second series, 80/3 = ~26.6

So they'll have 25 numbers in common. All you have to do is find the sum of these 25 numbers using the first series.

Sum = (2a + (n-1)d) * n/2
a = 12; n = 25; d = 12.

Solve to get 3900.
  [#permalink] 15 Mar 2004, 08:18
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