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lt;n> stands for the product of all even integers from 2 [#permalink ]
27 Oct 2005, 05:53

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<n> stands for the product of all even integers from 2 to n.
For example, <4> = 2 * 4, <6> = 2 * 4 * 6.
What is the greatest prime factor of <20>+<22>?

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Greatest prime number [#permalink ]
27 Oct 2005, 06:09

Ans: 463
Here is the solution:
<20> + <22> = <20> (1 + 21*22) = <20>*463
As 463 is a prime, that is the greatest prime factor of <20>+<22>

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Re: Greatest prime number [#permalink ]
27 Oct 2005, 06:14

dogbert wrote:

Here is the solution: <20> + <22> = <20> (1 + 21*22) = <20>*463 As 463 is a prime, that is the greatest prime factor of <20>+<22>

<22>= 2*4*6*...*22

<20>= 2*4*6*...*20

<20>+<22>= 2*4*6....*20*(1+22)= 2*4*6*...*23

23 is the greatest prime.

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I get 23 too...
<20>(1+22)=<20>(23)

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Sorry... I should not have included 21 in my calculations as it is only for even numbers.... 23 is the right answer...

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Well, this was question number 4 in my actual GMAT!!

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I agree with 23, but I thought I'd give a longer explanation than has been posted so far, in case anybody's trying to figure out the reasoning:
<20>+<22>
(2^10)(10!) + (2^11)(11!)
(2^10)(10!) + (2)(2^10)(10!)(11)
(2^10)(10!)[1 + 2(11)]
(2^10)(10!)(23)
The largest prime factors in each part of this equation are:
2^10: 2
10!: 7
23: 23
Thus, 23 is the greatest prime factor

Last edited by

BumblebeeMan on 28 Oct 2005, 03:10, edited 1 time in total.

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rahulraao wrote:

Well, this was question number 4 in my actual GMAT!!

Well...this question was in my pocket for monthes...

Should have posted this question earlier...

Anyways,

Good job, everyone.

The OA is 23.

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Can someone break this problem down even more for a moron like me??? I am still not seeing it. Thanks!!

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BumblebeeMan wrote:

I agree with 23, but I thought I'd give a longer explanation than has been posted so far, in case anybody's trying to figure out the reasoning: <20>+<22> (2^10)(10!) + (2^11)(11!) (2^10)(10!) + (2)(2^10)(10!)(11) (2^10)(10!)[1 + 2(11)] (2^10)(10!)(23) The largest prime factors in each part of this equation are: 2^10: 2 10!: 7 23: 23 Thus, 23 is the greatest prime factor

Could you explain how you got (2^10)(10!)?

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TeHCM wrote:

BumblebeeMan wrote:

I agree with 23, but I thought I'd give a longer explanation than has been posted so far, in case anybody's trying to figure out the reasoning: <20>+<22> (2^10)(10!) + (2^11)(11!) (2^10)(10!) + (2)(2^10)(10!)(11) (2^10)(10!)[1 + 2(11)] (2^10)(10!)(23) The largest prime factors in each part of this equation are: 2^10: 2 10!: 7 23: 23 Thus, 23 is the greatest prime factor

Could you explain how you got (2^10)(10!)?

<20> = 2*4*6*8*10*12*14*16*18*20

<22> = 2*4*6*8*10*12*14*16*18*20*22

<20>+<22> = 2*4*6*8*10*12*14*16*18*20 + 2*4*6*8*10*12*14*16*18*20*22

= (2*4*6*8*10*12*14*16*18*20*22)(1+22)

=(2*4*6*8*10*12*14*16*18*20*22)(23)

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