10! + 9! can be rewritten as:

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Re: 10! + 9! can be rewritten as:

by Brent@GMATPrepNow » Mon Sep 07, 2020 7:10 am

BTGModeratorVI wrote: ↑
Mon Sep 07, 2020 7:03 am
10! + 9! can be rewritten as:

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

Answer: B
Source: Veritas Prep

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

Brent Hanneson - Creator of GMATPrepNow.com

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