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Even multiples of 15

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Manager
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Joined: 04 Dec 2008
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Even multiples of 15 [#permalink]

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New post 21 May 2009, 06:11
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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?

(A) 5
(B) 7
(C) 11
(D) 13
(E) 17

Kudos [?]: 223 [0], given: 2

Manager
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Joined: 16 Apr 2009
Posts: 233

Kudos [?]: 99 [0], given: 10

Schools: Ross
Re: Even multiples of 15 [#permalink]

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New post 21 May 2009, 09:56
Quote:
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?

(A) 5
(B) 7
(C) 11
(D) 13
(E) 17


Answer =A ?

I have done in the most lengthiest way.Could someone tell the shorest way to do these kind of problems?

I overlook the question.I was looking at the number of the prime number factors instead of the greatest prime factor.Mere carelessness...The answer would be C...
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Keep trying no matter how hard it seems, it will get easier.


Last edited by vannu on 21 May 2009, 12:28, edited 1 time in total.

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Joined: 13 May 2008
Posts: 141

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Re: Even multiples of 15 [#permalink]

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New post 21 May 2009, 10:58
even multiples of 15 b/w 295 and 615 means... multiples of 30 b/w the same range which are from 300 (30x10) to 600 (30x20). I think the key is to find their sum, checking for the greatest prime factor would be easier.

so the sum can be written as : 30(10+11+12+...20) ...this is equal to 4950... there is a very easy and short way to calculate it... if you don't know I will explain it in a follow-up post ... Anyway 4950 is divisible by 11 but not 13 or 17 .. so 11 (C) is your answer... do let me know if I am correct or not...

Kudos [?]: 25 [0], given: 6

Manager
Manager
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Joined: 04 Dec 2008
Posts: 103

Kudos [?]: 223 [0], given: 2

Re: Even multiples of 15 [#permalink]

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New post 21 May 2009, 21:35
MJ2009 wrote:
even multiples of 15 b/w 295 and 615 means... multiples of 30 b/w the same range which are from 300 (30x10) to 600 (30x20). I think the key is to find their sum, checking for the greatest prime factor would be easier.

so the sum can be written as : 30(10+11+12+...20) ...this is equal to 4950... there is a very easy and short way to calculate it... if you don't know I will explain it in a follow-up post ... Anyway 4950 is divisible by 11 but not 13 or 17 .. so 11 (C) is your answer... do let me know if I am correct or not...


Yes, answer is C. Is the short method go to do with sum=average*terms?

Kudos [?]: 223 [0], given: 2

Current Student
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Joined: 13 May 2008
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Re: Even multiples of 15 [#permalink]

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New post 21 May 2009, 22:00
joyseychow wrote:
MJ2009 wrote:
even multiples of 15 b/w 295 and 615 means... multiples of 30 b/w the same range which are from 300 (30x10) to 600 (30x20). I think the key is to find their sum, checking for the greatest prime factor would be easier.

so the sum can be written as : 30(10+11+12+...20) ...this is equal to 4950... there is a very easy and short way to calculate it... if you don't know I will explain it in a follow-up post ... Anyway 4950 is divisible by 11 but not 13 or 17 .. so 11 (C) is your answer... do let me know if I am correct or not...


Yes, answer is C. Is the short method go to do with sum=average*terms?


yup, its average*terms... the reasoning is quite self-explanatory if you try it a couple of times. I hope the explanation helped!

Kudos [?]: 25 [0], given: 6

Re: Even multiples of 15   [#permalink] 21 May 2009, 22:00
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