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# If integer k is equal to the sum of all even multiples of 15

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Manager
Joined: 20 Dec 2004
Posts: 246
If integer k is equal to the sum of all even multiples of 15  [#permalink]

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03 Apr 2008, 15:10
1
00:00

Difficulty:

(N/A)

Question Stats:

100% (00:04) correct 0% (00:00) wrong based on 50 sessions

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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?

5
7
11
13
17

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Joined: 28 Dec 2004
Posts: 3222
Location: New York City
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Re: PS: Greatest prime factor  [#permalink]

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03 Apr 2008, 15:16
we need to find how many such terms exists..

soo let n=number of even multiples of 15..

600=300+(n-1)30

n=11

sum =11/2 (2*300+(10)30)=11(300+150)=11(450) as you can see biggest prime is 11
Senior Manager
Joined: 16 Aug 2004
Posts: 297
Location: India
Re: PS: Greatest prime factor  [#permalink]

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03 Apr 2008, 23:52
maximum=600, lowest=300 difference between the numbers=30, n=11 (30-20 + 1)
Sum= n x (lowest+maximum)/2= 11(300+600)/2, therefore 11 will be the greatest prime factor.
Intern
Joined: 05 Apr 2008
Posts: 2
Re: PS: Greatest prime factor  [#permalink]

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05 Apr 2008, 10:45
how did you get 30?
is this an equation?
what is the format for this equation?
Intern
Joined: 05 Apr 2008
Posts: 2
Re: PS: Greatest prime factor  [#permalink]

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05 Apr 2008, 10:59
u guys r like math geniuses, let me clarify my question.

lets say the numbers are X = 15 AND Y = 45

20+30+40 = 90

90 = (1)(3)(3)(5)(2)

K = GREATEST PRIME BETWEEN X AND Y = 5

how do i come up with the number 5? using your method? with harder #'s? like the ones you've used. I've just simplified the same question with these easier numbers so i can see if my answer is correct.

Based on your method, I'm thinking this.

50=20+(n-1)not sure what number to put here <--??
so n = 5
SVP
Joined: 04 May 2006
Posts: 1658
Schools: CBS, Kellogg
Re: PS: Greatest prime factor  [#permalink]

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05 Apr 2008, 18:48
neelesh wrote:
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?

5
7
11
13
17

D
Even multiple of 15 btw 295 and 615 starts: 300..., and ends at 610
There are (610-300)/30 = 7 numbers
and sum of them is (610+300)/2 * 7 = 5*7*13*7

So D
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Concentration: Finance, Strategy
Re: PS: Greatest prime factor  [#permalink]

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05 Apr 2008, 19:58
it is not 610, n u forgot adding 1
(600-300)/30 + 1 =11
SVP
Joined: 04 May 2006
Posts: 1658
Schools: CBS, Kellogg
Re: PS: Greatest prime factor  [#permalink]

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05 Apr 2008, 20:09
AlbertNTN wrote:
it is not 610, n u forgot adding 1
(600-300)/30 + 1 =11

You are right! I checked it again already

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Re: If integer k is equal to the sum of all even multiples of 15  [#permalink]

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05 Aug 2018, 00:50
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Re: If integer k is equal to the sum of all even multiples of 15 &nbs [#permalink] 05 Aug 2018, 00:50
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