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# If 10!/(10-r)!<1,000, what is the greatest possible value of r?

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Math Revolution GMAT Instructor
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If 10!/(10-r)!<1,000, what is the greatest possible value of r?  [#permalink]

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10 Jul 2017, 01:02
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81% (01:47) correct 19% (01:14) wrong based on 58 sessions

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If $$\frac{10!}{(10-r)!}<1,000$$, what is the greatest possible value of r?

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

_________________
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" Director Joined: 04 Dec 2015 Posts: 750 Location: India Concentration: Technology, Strategy WE: Information Technology (Consulting) If 10!/(10-r)!<1,000, what is the greatest possible value of r? [#permalink] ### Show Tags 10 Jul 2017, 07:43 1 MathRevolution wrote: If $$\frac{10!}{(10-r)!}<1,000$$, what is the greatest possible value of r? A. 1 B. 2 C. 3 D. 4 E. 5 $$\frac{10!}{(10-r)!}<1,000$$ By Checking the options the Greatest possible value of $$r$$ is $$= 5$$ Lets check the value of $$r = 5$$ $$\frac{10!}{(10-5)!}$$ $$=> \frac{10!}{5!}$$ $$\frac{10*9*8*7*6 * 5!}{5!}$$ $$=> 10*9*8*7*6$$ $$(10*9 = 90)$$ and $$(8*7 = 56)$$ ------------ (i) $$90*50 = 4500$$ ------- (This value is greater than $$1000$$) Therefore (i) will have value greater than $$1000$$. Hence $$5$$ cannot be the value of $$r$$. If we have the value without $$7$$ in (i), we will get a value less than $$1000$$. Lets check for value of $$r = 3$$ $$\frac{10!}{(10-3)!}$$ $$=> \frac{10!}{7!}$$ $$\frac{10*9*8*7!}{7!}$$ $$10*9*8 = 720$$ ------------- (Less than $$1000$$) Therefore greatest possible value of $$r = 3$$ Answer (C)... _________________ Please Press "+1 Kudos" to appreciate. Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 7367 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: If 10!/(10-r)!<1,000, what is the greatest possible value of r? [#permalink] ### Show Tags 12 Jul 2017, 01:10 ==>If you substitute r=1, 2, 3, 4.., for r=4, you get 10!/(10-4)!=10*9*8*7=5,040>1,000, and for r=3, you get 10!/(10-3)!=10*9*8=720<1,00. Thus, the greatest possible value of r is r=3. The answer is C. 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$149 for 3 month Online Course"
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Re: If 10!/(10-r)!<1,000, what is the greatest possible value of r?   [#permalink] 12 Jul 2017, 01:10
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# If 10!/(10-r)!<1,000, what is the greatest possible value of r?

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