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Prime Factors in a number sequence

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Junior | Next Rank: 30 Posts
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by beatthe800 » Sun Apr 07, 2013 10:50 am
[email protected] wrote:Hi

Anyone know a quick way to solve this - took me way too long?

If integer k is equal to the sum of all even multiples of 15 between 295 and 615, what is the greatest prime factor of k?

1)5
2)7
3)11
4)13
5)17

Thanks in advance!
Please correct me if I am wrong.
15{20,22,24,..34..,40}
15*20*22*24*.....*34*...40
15*20*22*24*.....*2*17*...40

Here highest prime number is 17. So Answer is E
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by Anju@Gurome » Sun Apr 07, 2013 10:57 am
beatthe800 wrote:Please correct me if I am wrong.
15{20,22,24,..34..,40}
15*20*22*24*.....*34*...40
15*20*22*24*.....*2*17*...40

Here highest prime number is 17. So Answer is E
The problem said 'sum' of the numbers.
Required sum = 15*(20 + 21 + 22 + ... + 40) = 15*(Sum of all the integers from 20 to 40, both inclusive) = 15*[11*(20 + 40)/2] = 15*11*30

Highest prime factor is 11.
Anju Agarwal
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Backup Methods : General guide on plugging, estimation etc.
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Junior | Next Rank: 30 Posts
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by beatthe800 » Sun Apr 07, 2013 11:34 am
Thanks Anju..
Got it now..
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