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If {x} is the product of all even integers from 1 to x inclusive, what

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If {x} is the product of all even integers from 1 to x inclusive, what [#permalink]

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If {x} is the product of all even integers from 1 to x inclusive, what is the greatest prime factor of {22} + {20}?

A) 23
B) 20
C) 11
D) 5
E) 2
[Reveal] Spoiler: OA

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Re: If {x} is the product of all even integers from 1 to x inclusive, what [#permalink]

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duahsolo wrote:
If {x} is the product of all even integers from 1 to x inclusive, what is the greatest prime factor of {22} + {20}?

A) 23
B) 20
C) 11
D) 5
E) 2


{22} + {20} = 22*{20} +{20} = 23*{20}


A

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Re: If {x} is the product of all even integers from 1 to x inclusive, what [#permalink]

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New post 19 Aug 2017, 08:24
{22} + {20} = 22*{20*18*-------*2} + {20*18*16-------*2} = 23*{20}

Hence 23

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Re: If {x} is the product of all even integers from 1 to x inclusive, what [#permalink]

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New post 19 Aug 2017, 09:18
duahsolo wrote:
If {x} is the product of all even integers from 1 to x inclusive, what is the greatest prime factor of {22} + {20}?

A) 23
B) 20
C) 11
D) 5
E) 2



hi..

two ways..

1) as given above..
{22} + {20} = 22*(20*18......*2)+(20*18....*2)=(22+1)(20*18...*2)=23{20}

2) {22} + {20}
\(2*4*.....*22+2*4...20 = 2^{11}*(1*2*3...*11)+2^{10}*(1*2*3....*10) = 2^{11}*11!+2^{10}*10! = 2*2^{10}*11*10!+2^{10}*10!=2^{10}*10!*(2*11+1)=2^{10}*10!*23\)
so 23
A
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Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

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Re: If {x} is the product of all even integers from 1 to x inclusive, what   [#permalink] 19 Aug 2017, 09:18
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