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Bunuel
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All of the following are factors of 8!9! + 9!10! except: 16 Jun 2017, 04:05
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E
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Difficulty:

25% (medium)

Question Stats:

75% (01:29) correct 25% (01:52) wrong based on 214 sessions

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All of the following are factors of \(8!9! + 9!10\)! except:

A. 7
B. 8
C. 9
D. 13
E. 17
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E
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All of the following are factors of 8!9! + 9!10! except: 16 Jun 2017, 04:58
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Bunuel
All of the following are factors of \(8!9! + 9!10!\) except:

A. 7
B. 8
C. 9
D. 13
E. 17
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\(8!9! + 9!10\)!
= \(8!9! + 9.8!10.9!\)
= \(8!9!(1 + 9.10)\)
= \(8!9!(91)\)

Every option except E is a factor of \(8!9!(91)\).
Hence Answer E
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All of the following are factors of 8!9! + 9!10! except: 16 Jun 2017, 04:59
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Bunuel
All of the following are factors of \(8!9! + 9!10!\) except:

A. 7
B. 8
C. 9
D. 13
E. 17
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\(8!9! + 9!10!\) = \(8!9! (1 + 9*10)\) = \(8!9! (91)\)

Answer: Option E
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All of the following are factors of 8!9! + 9!10! except: 16 Jun 2017, 05:05
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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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All of the following are factors of 8!9! + 9!10! except: 17 Jun 2017, 12:07
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All of the following are factors of \(8!9! + 9!10!\) except:

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

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

Scanning the answers choices:

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

one choice left

Answer: E
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All of the following are factors of 8!9! + 9!10! except: 21 Jun 2017, 01:18
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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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All of the following are factors of 8!9! + 9!10! except: 11 Jun 2023, 01:55
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