NEW HERE? LEARN MORE
closeclose
Last visit was: 28 Apr 2024, 04:27 It is currently 28 Apr 2024, 04:27
Decision Tracker
My Rewards
New posts
New comers' posts

Close
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

[(n+3)!]^5/[(n+2)!]^5 =

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92964
Own Kudos [?]: 619601 [2]
Given Kudos: 81613
Send PM
CAT Tests Forum Quiz Mode
[(n+3)!]^5/[(n+2)!]^5 = [#permalink] New post   29 Apr 2021, 09:00
2
Bookmarks
Expert Reply
00:00
A
B
C
D
E

Difficulty:

5% (low)

Question Stats:

94% (00:47) correct 6% (00:43) wrong based on 67 sessions
Hide Show timer Statistics
\(\frac{[(n+3)!]^5}{[(n+2)!]^5} =\)

A. 2
B. (n+1)^5
C. (n+2)^5
D. (n+3)^5
E. ((n+3/(n+2))^5
ShowHide Answer
Official Answer
D
User avatar
B
Dashingnightmare
Intern
Intern
Joined: 25 Jan 2019
Posts: 15
Own Kudos [?]: 13 [0]
Given Kudos: 40
Send PM
[(n+3)!]^5/[(n+2)!]^5 = [#permalink] New post   29 Apr 2021, 10:08
[[(n+3)(n+2)!]^5]/[(n+2)!]^5= (n+3)^5
Hence D.
User avatar
P
Showmeyaa
Senior Manager
Senior Manager
Joined: 24 Jun 2019
Posts: 432
Own Kudos [?]: 437 [0]
Given Kudos: 117
Location: India
Concentration: Marketing, Strategy
Send PM
Reviews Badge
Re: [(n+3)!]^5/[(n+2)!]^5 = [#permalink] New post   29 Apr 2021, 12:35
Bunuel wrote:
\(\frac{[(n+3)!]^5}{[(n+2)!]^5} =\)

A. 2
B. (n+1)^5
C. (n+2)^5
D. (n+3)^5
E. ((n+3/(n+2))^5


\(\frac{(n+3)!^{5}}{(n+2)!^5}\) = \(\frac{(n+2)!^{5}(n+3)^{5}}{(n+2)!^{5}}\) = \((n+3)^{5}\)
avatar
B
shiva90
Intern
Intern
Joined: 20 Jan 2018
Posts: 2
Own Kudos [?]: 1 [0]
Given Kudos: 7
Location: India
Concentration: Finance, Technology
Schools: S.P.Jain Institute XLRI IIMC PGPEX'22 IIML-IPMX '22 IIM
Send PM
Re: [(n+3)!]^5/[(n+2)!]^5 = [#permalink] New post   30 Apr 2021, 10:43
n! can be written as n*(n-1)!
so (n+3)!^5 can be written as (n+3)^5*(n+2)^5!
on simplifying we get
option-D
User avatar
B
gmatmonk7
Intern
Intern
Joined: 21 Oct 2018
Posts: 3
Own Kudos [?]: 0 [0]
Given Kudos: 8
Location: India
GMAT 1: 750 Q50 V40
GRE 1: Q169 V166
Send PM
Re: [(n+3)!]^5/[(n+2)!]^5 = [#permalink] New post   30 Apr 2021, 11:18
It is useful to note: k! = k * (k-1)! = k * (k-1) * (k-2)!.....

Therefore, (n+3)! = (n+3) * (n+2)!

This leaves us with (n+3) inside the bracket.

Thus the expression becomes (n+3)^5.

Hence (D) is the answer.

Glad to help!
GMAT Club Bot
gmatclubot
Re: [(n+3)!]^5/[(n+2)!]^5 = [#permalink]
30 Apr 2021, 11:18
Moderators:
Bunuel
Math Expert
92964 posts
yashikaaggarwal
Senior Moderator - Masters Forum
3137 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions