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# If 11!/(11-r)!<1,000, what is the greatest possible value of r? A. 1 B

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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GMAT 1: 760 Q51 V42
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If 11!/(11-r)!<1,000, what is the greatest possible value of r? A. 1 B  [#permalink]

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22 Aug 2017, 01:23
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Difficulty:

25% (medium)

Question Stats:

76% (01:20) correct 24% (01:39) wrong based on 81 sessions

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If 11!/(11-r)!<1,000, what is the greatest possible value of r?

A. 1
B. 2
C. 3
D. 4
E. 5

_________________
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"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" Math Expert Joined: 02 Aug 2009 Posts: 7579 Re: If 11!/(11-r)!<1,000, what is the greatest possible value of r? A. 1 B [#permalink] ### Show Tags 22 Aug 2017, 02:44 MathRevolution wrote: If 11!/(11-r)!<1,000, what is the greatest possible value of r? A. 1 B. 2 C. 3 D. 4 E. 5 $$\frac{11!}{(11-r)!}<1000......11*10*(11-r+1)=11*10*9=990<1000$$ So 11-r+1=9...12-9=R=3 C _________________ Manager Joined: 27 Dec 2016 Posts: 232 Concentration: Marketing, Social Entrepreneurship GPA: 3.65 WE: Marketing (Education) Re: If 11!/(11-r)!<1,000, what is the greatest possible value of r? A. 1 B [#permalink] ### Show Tags 22 Aug 2017, 04:27 MathRevolution wrote: If 11!/(11-r)!<1,000, what is the greatest possible value of r? A. 1 B. 2 C. 3 D. 4 E. 5 - We start to calculate the number of 11! from the beginning. - 11 X 10 = 110 ~ 110 still < 1.000 - 11 X 10 X 9 = 990 ~ 990 still < 1.000 - 11 X 10 X 9 X 8 = clearly > 1.000 - So we must eliminate 8! with the right denominator. 11-X = 8, so X = 3. C. _________________ There's an app for that - Steve Jobs. Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 7240 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: If 11!/(11-r)!<1,000, what is the greatest possible value of r? A. 1 B [#permalink] ### Show Tags 24 Aug 2017, 01:29 => 11! / (11-r)! = 11*(11-1)*…*(11-r+1) r = 1 : 11 < 1,000 r = 2 : 11*10 = 110 < 1,000 r = 3 : 11*10*9 = 990 < 1,000 r = 4 : 11*10*9*8 = 7290 > 1,000 r = 3 Ans: 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$149 for 3 month Online Course"
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Re: If 11!/(11-r)!<1,000, what is the greatest possible value of r? A. 1 B   [#permalink] 24 Aug 2017, 01:29
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