GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 23 Jun 2018, 16:31

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.

Close

Request Expert Reply

Confirm Cancel

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

If n!/(n-2)!<100, what is the greatest possible value of n?

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Expert Post
Math Revolution GMAT Instructor
User avatar
D
Joined: 16 Aug 2015
Posts: 5600
GMAT 1: 800 Q59 V59
GPA: 3.82
If n!/(n-2)!<100, what is the greatest possible value of n? [#permalink]

Show Tags

New post 05 Mar 2018, 01:41
00:00
A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

82% (00:30) correct 18% (00:39) wrong based on 65 sessions

HideShow timer Statistics

[GMAT math practice question]

If \(\frac{n!}{(n-2)!}<100\), what is the greatest possible value of \(n\)?

\(A. 8\)
\(B. 9\)
\(C. 10\)
\(D. 11\)
\(E. 12\)

_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $99 for 3 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"

Manager
Manager
avatar
S
Joined: 31 Oct 2013
Posts: 236
Concentration: Accounting, Finance
GPA: 3.68
WE: Analyst (Accounting)
CAT Tests
Re: If n!/(n-2)!<100, what is the greatest possible value of n? [#permalink]

Show Tags

New post 05 Mar 2018, 03:14
MathRevolution wrote:
[GMAT math practice question]

If \(\frac{n!}{(n-2)!}<100\), what is the greatest possible value of \(n\)?

\(A. 8\)
\(B. 9\)
\(C. 10\)
\(D. 11\)
\(E. 12\)



i would like to use back solving strategy. !
but before doing so , a simple thing that must be mentioned is that numerator is n! and denominator is (n-2)!
it means that 2 no. will always be extra in numerator part.

how?

a) 8 as a value of n
so, 8!/ (8-2)!
= 8!/6!
= 8*7*6*5*4*3*2*1/6*5*4*3*2*1
= 8*7
=56 <100 , it meets our condition .
now , we have to remember that we are looking for max value of n
it must be 10

10!/(10-2)!
=10*9*8*7*6*5*4*3*2*1/8*7*6*5*4*3*2*1
=10*9
=90 <100
the correct answer is C.
Manager
Manager
avatar
B
Joined: 02 Jan 2016
Posts: 82
Reviews Badge
Re: If n!/(n-2)!<100, what is the greatest possible value of n? [#permalink]

Show Tags

New post 05 Mar 2018, 20:53
MathRevolution wrote:
[GMAT math practice question]

If \(\frac{n!}{(n-2)!}<100\), what is the greatest possible value of \(n\)?

\(A. 8\)
\(B. 9\)
\(C. 10\)
\(D. 11\)
\(E. 12\)



n!/(n-2)!, will be the last two factors of N!, and it has to be such that it is less than 100, 9*10 = 90, less than 100, if we go further 10*11 = 110 this is beyond the restriction. thus 10! is the answer
Expert Post
Math Revolution GMAT Instructor
User avatar
D
Joined: 16 Aug 2015
Posts: 5600
GMAT 1: 800 Q59 V59
GPA: 3.82
Re: If n!/(n-2)!<100, what is the greatest possible value of n? [#permalink]

Show Tags

New post 07 Mar 2018, 03:39
=>

We must have
\(\frac{n!}{(n-2)!} = n(n-1) < 100.\)
If \(n = 10, n(n-1) = 10*9 = 90 < 100.\)
If \(n = 11, n(n-1) = 11*10 = 110 > 100.\)

\(10\) is the greatest value of n for which \(\frac{n!}{(n-2)!} < 100.\)

Therefore, C is the answer.

Answer: C
_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $99 for 3 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"

Manager
Manager
User avatar
S
Joined: 23 May 2017
Posts: 226
Concentration: Finance, Accounting
WE: Programming (Energy and Utilities)
CAT Tests
Re: If n!/(n-2)!<100, what is the greatest possible value of n? [#permalink]

Show Tags

New post 07 Mar 2018, 04:15
Equation can be reduced to n ( n - 1) < 100

Best way is to "Test the Numbers"

Lets pick from the largest number -

[E] : 12 * 11 = 132 < 100 : No
[D] : 11 * 10 = 110 < 100 : No
[C] : 10 * 9 = 90 < 100 : Yes - This is the answer
_________________

If you like the post, please award me Kudos!! It motivates me

Expert Post
Math Revolution GMAT Instructor
User avatar
D
Joined: 16 Aug 2015
Posts: 5600
GMAT 1: 800 Q59 V59
GPA: 3.82
Re: If n!/(n-2)!<100, what is the greatest possible value of n? [#permalink]

Show Tags

New post 21 Mar 2018, 11:29
Leo8 wrote:
Equation can be reduced to n ( n - 1) < 100

Best way is to "Test the Numbers"

Lets pick from the largest number -

[E] : 12 * 11 = 132 < 100 : No
[D] : 11 * 10 = 110 < 100 : No
[C] : 10 * 9 = 90 < 100 : Yes - This is the answer


For this question, your way is the best one.
_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $99 for 3 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"

Re: If n!/(n-2)!<100, what is the greatest possible value of n?   [#permalink] 21 Mar 2018, 11:29
Display posts from previous: Sort by

If n!/(n-2)!<100, what is the greatest possible value of n?

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.