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What is the value of (11! - 10!)/9!

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What is the value of (11! - 10!)/9!  [#permalink]

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New post 25 Apr 2019, 03:33
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A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

80% (00:35) correct 20% (00:59) wrong based on 35 sessions

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Intern
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Joined: 27 Nov 2018
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Location: India
Schools: Erasmus '21 (S)
GMAT 1: 640 Q47 V31
GPA: 3.5
WE: Project Management (Manufacturing)
What is the value of (11! - 10!)/9!  [#permalink]

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New post 25 Apr 2019, 03:47
1
--> (11!/9!) - (10!/9!)
= (10x11) - (10) [all values from 1 to 9 get cancelled out in Nr. and Dr.]
= 110 - 10
= 100

Hope this is correct
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Re: What is the value of (11! - 10!)/9!  [#permalink]

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New post 25 Apr 2019, 07:00
(11!-10!)/9!= (11*10!-10!)/9!
11! Can be written as 11*10!
(10!(11-1))/9!=(10*10!)/9!
10!=10*9!
(10*10*9!)/9!
9! Will be canceled in the numerator & denominator
Answer is 10*10=100

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Re: What is the value of (11! - 10!)/9!  [#permalink]

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New post 25 Apr 2019, 08:09
Top Contributor
Bunuel wrote:
What is the value of (11! - 10!)/9!

(A) 99
(B) 100
(C) 110
(D) 121
(E) 132


Useful (and often-tested) concept: \(\frac{a - b}{c}=\frac{a}{c}-\frac{b}{c}\)

So, \(\frac{11! - 10!}{9!}=\frac{11!}{9!}-\frac{10!}{9!}\)

\(=\frac{(11)(10)(9)(8)(7)(6)(5)(4)(3)(2)(1)}{(9)(8)(7)(6)(5)(4)(3)(2)(1)}-\frac{(10)(9)(8)(7)(6)(5)(4)(3)(2)(1)}{(9)(8)(7)(6)(5)(4)(3)(2)(1)}\)

\(= (11)(10)-(10)\)

\(= 110-10\)

\(= 100\)

Answer: B

Cheers,
Brent
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Re: What is the value of (11! - 10!)/9!   [#permalink] 25 Apr 2019, 08:09
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