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10! + 9! can be rewritten as:

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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
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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
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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
Solution:

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

Answer: B

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