Last visit was: 27 May 2024, 00:31 It is currently 27 May 2024, 00:31
Toolkit
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

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.

If ¡n! = (n!)^2, then ¡17! - ¡16! =

SORT BY:
Tags:
Show Tags
Hide Tags
Manager
Joined: 26 Sep 2013
Posts: 149
Own Kudos [?]: 605 [50]
Given Kudos: 40
Concentration: Finance, Economics
GMAT 1: 670 Q39 V41
GMAT 2: 730 Q49 V41
Manager
Joined: 26 Sep 2013
Posts: 149
Own Kudos [?]: 605 [11]
Given Kudos: 40
Concentration: Finance, Economics
GMAT 1: 670 Q39 V41
GMAT 2: 730 Q49 V41
General Discussion
Manager
Joined: 04 Sep 2012
Posts: 138
Own Kudos [?]: 49 [3]
Given Kudos: 17
Location: United States
GMAT 1: 760 Q50 V42
GPA: 3.3
SVP
Joined: 27 Dec 2012
Status:The Best Or Nothing
Posts: 1559
Own Kudos [?]: 7242 [0]
Given Kudos: 193
Location: India
Concentration: General Management, Technology
WE:Information Technology (Computer Software)
Re: If ¡n! = (n!)^2, then ¡17! - ¡16! = [#permalink]
Bunuel, can you please tell if factorial questions are asked in GMAT? Thanks!!
Math Expert
Joined: 02 Sep 2009
Posts: 93470
Own Kudos [?]: 627010 [2]
Given Kudos: 81958
Re: If ¡n! = (n!)^2, then ¡17! - ¡16! = [#permalink]
2
Bookmarks
PareshGmat wrote:
Bunuel, can you please tell if factorial questions are asked in GMAT? Thanks!!

Yes, most definitely. I'd suggest you to go through Official Guide to know the concepts tested on the GMAT.
Board of Directors
Joined: 17 Jul 2014
Posts: 2160
Own Kudos [?]: 1182 [0]
Given Kudos: 236
Location: United States (IL)
Concentration: Finance, Economics
GMAT 1: 650 Q49 V30
GPA: 3.92
WE:General Management (Transportation)
Re: If ¡n! = (n!)^2, then ¡17! - ¡16! = [#permalink]
J17! = 17! * 17!
THIS can be rewritten as: 16! * 17 * 16! * 17.

now, 16! * 16! is j16!.

we can factor out j16!
we are left with j16! (17*17 - 1) = j16! * 288
288=144 *2 or 12^2 * 2.
Intern
Joined: 31 Oct 2016
Posts: 1
Own Kudos [?]: 2 [2]
Given Kudos: 3
Re: If ¡n! = (n!)^2, then ¡17! - ¡16! = [#permalink]
1
Kudos
Can someone tell me why you subtract the 1 when you're factoring out 16!
Intern
Joined: 14 Sep 2017
Posts: 29
Own Kudos [?]: 116 [0]
Given Kudos: 23
Location: Italy
Re: If ¡n! = (n!)^2, then ¡17! - ¡16! = [#permalink]
Can someone explain me why D is not correct, I can't get it: the only difference in (17!)^2 and (16!)^2 isn't just the 17^2??
Math Expert
Joined: 02 Sep 2009
Posts: 93470
Own Kudos [?]: 627010 [0]
Given Kudos: 81958
Re: If ¡n! = (n!)^2, then ¡17! - ¡16! = [#permalink]
Fedemaravilla wrote:
Can someone explain me why D is not correct, I can't get it: the only difference in (17!)^2 and (16!)^2 isn't just the 17^2??

No. $$(17!)^2 - (16!)^2 = 126075783368849775132672000000$$ not 17^2
Intern
Joined: 06 Jul 2019
Posts: 2
Own Kudos [?]: 0 [0]
Given Kudos: 11
Re: If ¡n! = (n!)^2, then ¡17! - ¡16! = [#permalink]
Not sure why we subtract the 1 can someone help Bunuel
Manager
Joined: 10 May 2018
Posts: 60
Own Kudos [?]: 35 [0]
Given Kudos: 99
Re: If ¡n! = (n!)^2, then ¡17! - ¡16! = [#permalink]
¡n! = (n!)^2
¡17! - ¡16!

(17!)^2 - (16!)^2

(17! * 17!) - (16! * 16!)

Can be written as
17*16! *17* 16! -16! *16!
Taking common
16!*16! (17*17 -1)

(16!)^2 (289-1)

¡16!(288)

E

Posted from my mobile device
Intern
Joined: 01 Jan 2016
Posts: 28
Own Kudos [?]: 37 [0]
Given Kudos: 1128
Location: India
Re: If ¡n! = (n!)^2, then ¡17! - ¡16! = [#permalink]
Did a different way and got a wrong result - Pls help

(17!)^2 - (16!)^2
(17! + 16!) * (17! - 16!)
16!(17+1) * 16! (17-1)
16!*16!*18*16
2*16!*18*16, which is 2 times the right answer choice.
Manager
Joined: 10 May 2018
Posts: 60
Own Kudos [?]: 35 [1]
Given Kudos: 99
If ¡n! = (n!)^2, then ¡17! - ¡16! = [#permalink]
1
Kudos
cptholt wrote:
Did a different way and got a wrong result - Pls help

(17!)^2 - (16!)^2
(17! + 16!) * (17! - 16!)
16!(17+1) * 16! (17-1)
16!*16!*18*16
2*16!*18*16, which is 2 times the right answer choice.

16!*16!*18*16 is (16!)^2 * 288
Its 16!*16! not 16!+16!

Posted from my mobile device
Non-Human User
Joined: 09 Sep 2013
Posts: 33229
Own Kudos [?]: 830 [0]
Given Kudos: 0
Re: If ¡n! = (n!)^2, then ¡17! - ¡16! = [#permalink]
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
Re: If ¡n! = (n!)^2, then ¡17! - ¡16! = [#permalink]
Moderator:
Math Expert
93470 posts