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# 10! + 9! can be rewritten as:

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Math Expert
Joined: 02 Sep 2009
Posts: 64242
10! + 9! can be rewritten as:  [#permalink]

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25 Apr 2017, 01:16
11
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Difficulty:

35% (medium)

Question Stats:

63% (01:24) correct 37% (01:24) wrong based on 182 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!

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Joined: 11 Sep 2015
Posts: 4878
GMAT 1: 770 Q49 V46
Re: 10! + 9! can be rewritten as:  [#permalink]

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07 Mar 2018, 09:16
4
Top Contributor
1
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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##### General Discussion
Intern
Joined: 13 Sep 2015
Posts: 25
Re: 10! + 9! can be rewritten as:  [#permalink]

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25 Apr 2017, 01:27
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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12 Mar 2018, 09:55
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

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

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09 Feb 2020, 06:34
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Re: 10! + 9! can be rewritten as:   [#permalink] 09 Feb 2020, 06:34