10! + 9! can be rewritten as:

Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pm; Location: Vancouver, BC; Thanked: 5254 times; Followed by:1268 members; GMAT Score:770

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

by Brent@GMATPrepNow » Tue Mar 16, 2021 7:00 am

BTGmoderatorDC wrote: ↑
Tue Mar 09, 2021 6:19 pm
10! + 9! can be rewritten as:

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

OA 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

Quote

swerve: Legendary Member; Posts: 2499; Joined: Sun Oct 29, 2017 2:04 pm; Followed by:6 members

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

by swerve » Tue Mar 16, 2021 9:50 am

BTGmoderatorDC wrote: ↑
Tue Mar 09, 2021 6:19 pm
10! + 9! can be rewritten as:

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

OA B

Source: Veritas Prep

\begin{align*}
10! + 9! &= (10\cdot 9!)+ 9! \\
&=9! (10+1) \\
&=9!(11)\\
&=\dfrac{9!\cdot 11\cdot 10}{10}\\
&=\dfrac{11!}{10}
\end{align*}

Therefore, B

Quote

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

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

by Scott@TargetTestPrep » Sat Mar 20, 2021 12:01 pm

BTGmoderatorDC wrote: ↑
Tue Mar 09, 2021 6:19 pm
10! + 9! can be rewritten as:

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

OA B

Source: Veritas Prep