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# For any integer n, denotes the product of all of the

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Manager
Joined: 07 Dec 2006
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For any integer n, denotes the product of all of the [#permalink]

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25 Jan 2008, 23:39
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For any integer n, [n] denotes the product of all of the positive even numbers' from 2 to n. What is the largest prime factor of [23] + [21]?

A) 23
B) 19
C) 11
D) 7
E) 5

Do you have shortcut to solve this problem?

OA is A.

Kudos [?]: 103 [0], given: 0

CEO
Joined: 17 Nov 2007
Posts: 3584

Kudos [?]: 4574 [0], given: 360

Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
Re: PS - Product of all the positive even numbers [#permalink]

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26 Jan 2008, 00:51
A

[23] + [21] = [22] + [20] = [20]*(22+1) = 2*10!*23
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Kudos [?]: 4574 [0], given: 360

Senior Manager
Joined: 22 Sep 2005
Posts: 278

Kudos [?]: 241 [0], given: 1

Re: PS - Product of all the positive even numbers [#permalink]

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26 Jan 2008, 09:44
It must be A (23), because the balance possible prime numbers are in both series.

A too!!!

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Intern
Joined: 14 Sep 2007
Posts: 42

Kudos [?]: 5 [0], given: 0

Re: PS - Product of all the positive even numbers [#permalink]

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26 Jan 2008, 16:54
i dont understand either explanation...

i could do the grunt math out but theres gotta bea faster way that im not seeing

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SVP
Joined: 04 May 2006
Posts: 1886

Kudos [?]: 1395 [0], given: 1

Schools: CBS, Kellogg
Re: PS - Product of all the positive even numbers [#permalink]

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26 Jan 2008, 18:54
GMAT4Lyfe wrote:
i dont understand either explanation...

i could do the grunt math out but theres gotta bea faster way that im not seeing

[23]=2*4*6*8*10*12*14*16*18*20*22
[21]=2*4*6*8*10*12*14*16*18*20

[23]+[21]=2*4*6*8*10*12*14*16*18*20*(22+1)
[23]+[21]=2*4*6*8*10*12*14*16*18*20*23
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Kudos [?]: 1395 [0], given: 1

Re: PS - Product of all the positive even numbers   [#permalink] 26 Jan 2008, 18:54
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