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# What is the sum of the first 50 common numbers between the

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Intern
Joined: 11 Dec 2003
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Location: IN
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What is the sum of the first 50 common numbers between the [#permalink]  13 Apr 2005, 14:21
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What is the sum of the first 50 common numbers between the series 15,19,23....... and 14,19,24.........?

A) 25550
B) 24540
C) 24450
D) 25450
E) 25540
VP
Joined: 25 Nov 2004
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Re: PS old qn. [#permalink]  13 Apr 2005, 19:45
D) 25450

Series I: 15,19,23,27,31,35,39,43,47,51,55,59................................
Series II: 14,19,24,29,34,39, 44,49,54,59........................................

The common numbers are 19, 39,59. Note here the pattren, 19-39-59: the difference between two sucessive common numbers is 20.
the last common number is =19+(49x20)=999
the average of the 50 common numbers = (19+999)/2=509
sum = 509x50=25450. will correct if any and this is the shortest method i have.
Intern
Joined: 11 Dec 2003
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MA Thanks a lot for the expln.

"the last common number is =19+(49x20)=999"

How did you get 49 here there are 50 numbers ? Could you please explain this part alone. Rest is clear.
VP
Joined: 18 Nov 2004
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"B"

remember this formula for summation of equally spaced numbers

S = n/2 ((2a + (n-1)*d)

n = number of elements (50 here)
a = first element (19 here)
d = difference between successive elements (20 here)

S = 50/2 (38 + 49*20)

S = 25450
Senior Manager
Joined: 19 Feb 2005
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Location: Milan Italy
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Hey guys, look at this:
MA said
Series I: 15,19,23,27,31,35,39,43,47,51,55,59................................
Series II: 14,19,24,29,34,39, 44,49,54,59........................................
the difference between two sucessive common numbers is 20

this is 4*5 (note that there are no common factors bw the two numb)

If I say
Series I: 16,19,22,25,28,31,34,37,40,43,46,49................................
Series II: 12,19,26,33,40,47, 54,61,68,75........................................
the difference between two sucessive common numbers is 21

this is 3*7

this is something I can't explain, but my bells rang and I just shared their sound with you
VP
Joined: 25 Nov 2004
Posts: 1494
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TS wrote:
How did you get 49 here there are 50 numbers ? Could you please explain this part alone. Rest is clear.

you forget to count first one i.e. 19.
the first one is 19 and rest are 49 numbers, total 50.
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