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# All of the following are factors of 8!9! + 9!10! except:

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Re: All of the following are factors of 8!9! + 9!10! except: [#permalink]
8!9!+9!10! = 8!*(9!+9*10!) = 8!*9!*(1+9*10)=8!9!*(91)

91 can be split into 13*7, hence the actual question is what is not a factor of 8!*9!*13*7
From the answer choices 7, 8, 9 and 13 are all factors if 8!*9!*13*7.

17 cannot be a factor, so answer E
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Re: All of the following are factors of 8!9! + 9!10! except: [#permalink]
All of the following are factors of $$8!9! + 9!10!$$ except:

A. 7
B. 8
C. 9
D. 13
E. 17

$$8!9! + 9!10!$$ = $$8!9! (1 + 9*10)$$ = $$8!9! (91)$$

Let's check if 91 is divisible by 13.....91/13 =7

one choice left

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Re: All of the following are factors of 8!9! + 9!10! except: [#permalink]
The equation when simplified:
9! (8! + 10!)
= 9! (8! (1+(10*9)))
= 9! * 8! * 91

hence, 7,8,9,13 all are factors, 17 is not.

IMO E
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Re: All of the following are factors of 8!9! + 9!10! except: [#permalink]
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Re: All of the following are factors of 8!9! + 9!10! except: [#permalink]
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