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10! + 9! can be rewritten as:

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10! + 9! can be rewritten as: [#permalink]

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New post 25 Apr 2017, 02:16
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A
B
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E

Difficulty:

  25% (medium)

Question Stats:

69% (01:04) correct 31% (00:49) wrong based on 109 sessions

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10! + 9! can be rewritten as:

A. 9!(10)
B. 11!/10
C. (10!)^2*9
D. (9!)^2 + 10
E. 19!
Spoiler: OA

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Re: 10! + 9! can be rewritten as: [#permalink]

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New post 25 Apr 2017, 02:27
1
10! + 9!
= (10*9!)+ 9!
=9! (10+1)
=9!(11)
=(9!*11*10)/10
=11!/10

Hence B

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Re: 10! + 9! can be rewritten as: [#permalink]

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New post 07 Mar 2018, 10:16
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Top Contributor
Bunuel wrote:
10! + 9! can be rewritten as:

A. 9!(10)
B. 11!/10
C. (10!)^2*9
D. (9!)^2 + 10
E. 19!


First recognize that 10! = (10)(9!)
Here's why:
10! = (10)(9)(8)(7)(6)(5)(4)(3)(2)(1)
= (10)(9!)

So....
10! + 9! = (10)(9!) + 9!
= 9!(10 + 1) [I factored out the 9!]
= 9!(11)
Check the answer choice.....9!(11) isn't there! So, we'll need to check each answer choice to see which one can be expressed as (9!)(11)



A. 9!(10)
We can clearly see that this is not equal to (9!)(11)
ELIMINATE A


B. 11!/10
11!/10 = (11)(10)(9)(8)(7)(6)(5)(4)(3)(2)(1)/(10)
= (11)(9)(8)(7)(6)(5)(4)(3)(2)(1)
= (11)(9!) PERFECT!!
= B

Cheers,
Brent
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Re: 10! + 9! can be rewritten as: [#permalink]

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New post 12 Mar 2018, 10:55
Bunuel wrote:
10! + 9! can be rewritten as:

A. 9!(10)
B. 11!/10
C. (10!)^2*9
D. (9!)^2 + 10
E. 19!


10! + 9! = 10 x 9! + 9! = 9!(10 + 1) = 9!(11) = 11!/10

Answer: B
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Re: 10! + 9! can be rewritten as:   [#permalink] 12 Mar 2018, 10:55
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