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Buy "All-In-One Standard ($149)", get free Daily quiz (2 mon). Coupon code : SPECIAL # 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 Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6962 GMAT 1: 760 Q51 V42 GPA: 3.82 If n!/(n-2)!<100, what is the greatest possible value of n? [#permalink] ### Show Tags 05 Mar 2018, 00:41 00:00 Difficulty: 5% (low) Question Stats: 86% (00:51) correct 14% (01:06) wrong based on 73 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$149 for 3 month Online Course"
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VP
Joined: 31 Oct 2013
Posts: 1128
Concentration: Accounting, Finance
GPA: 3.68
WE: Analyst (Accounting)
Re: If n!/(n-2)!<100, what is the greatest possible value of n?  [#permalink]

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05 Mar 2018, 02:14
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
Manager
Joined: 02 Jan 2016
Posts: 123
Re: If n!/(n-2)!<100, what is the greatest possible value of n?  [#permalink]

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05 Mar 2018, 19:53
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
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6962
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: If n!/(n-2)!<100, what is the greatest possible value of n?  [#permalink]

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07 Mar 2018, 02:39
=>

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 $$\frac{n!}{(n-2)!} < 100.$$

_________________

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 $149 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 Joined: 23 May 2017 Posts: 240 Concentration: Finance, Accounting WE: Programming (Energy and Utilities) Re: If n!/(n-2)!<100, what is the greatest possible value of n? [#permalink] ### Show Tags 07 Mar 2018, 03:15 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 Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6962 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: If n!/(n-2)!<100, what is the greatest possible value of n? [#permalink] ### Show Tags 21 Mar 2018, 10:29 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$149 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, 10:29
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# If n!/(n-2)!<100, what is the greatest possible value of n?

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