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# If r is an integer, and 700 < 10!/(10-r)!<1,000, then r=

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6832
GMAT 1: 760 Q51 V42
GPA: 3.82
If r is an integer, and 700 < 10!/(10-r)!<1,000, then r=  [#permalink]

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21 Nov 2017, 17:23
1
00:00

Difficulty:

25% (medium)

Question Stats:

74% (01:28) correct 26% (01:34) wrong based on 72 sessions

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[GMAT math practice question]

If r is an integer, and $$700 < \frac{10!}{(10-r)!}<1,000$$, then 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" Math Expert Joined: 02 Aug 2009 Posts: 7212 Re: If r is an integer, and 700 < 10!/(10-r)!<1,000, then r= [#permalink] ### Show Tags 21 Nov 2017, 18:37 MathRevolution wrote: [GMAT math practice question] If r is an integer, and $$700 < \frac{10!}{(10-r)!}<1,000$$, then r= A. 1 B. 2 C. 3 D. 4 E. 5 Hi.... $$\frac{10!}{(10-r)!}=10*9*8..*(10-(r-1)$$ Now it is given this value is more than 700 and less than 1000 10*9*8=720 So 10-(r-1)=8.....r-1=10-8=2....r=2+1=3 C _________________ 1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372 2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html 3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html GMAT online Tutor Intern Status: Prepping for GMAT Joined: 06 Nov 2017 Posts: 21 Location: France GPA: 4 Re: If r is an integer, and 700 < 10!/(10-r)!<1,000, then r= [#permalink] ### Show Tags 22 Nov 2017, 04:27 MathRevolution wrote: [GMAT math practice question] If r is an integer, and $$700 < \frac{10!}{(10-r)!}<1,000$$, then r= A. 1 B. 2 C. 3 D. 4 E. 5 An easy way to solve this question is to plug in the answers given, calculate the value of $$\frac{10!}{(10-r)!}$$ and see whether it satisfies or violates the inequality in the problem prompt. A/$$r = 1$$ This gives us: $$\frac{10!}{(10-r)!} = \frac{10!}{9!} = 10$$. This violates the inequality given in the problem prompt. B/ $$r = 2$$ This gives us: $$\frac{10!}{(10-r)!} = \frac{10!}{8!} = 10*9 = 90$$. This also violates the inequality given in the problem prompt. C/ $$r = 3$$ This gives us: $$\frac{10!}{(10-r)!} = \frac{10!}{7!} = 10*9*8 = 720$$. This satisfies the inequality given in the problem prompt, therefore, this is our answer (we can afford to stop here since this is not a DS question nor is the unknown a polynomial/non-integer with multiple potential values). Thus, the answer is C. Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6832 GMAT 1: 760 Q51 V42 GPA: 3.82 If r is an integer, and 700 < 10!/(10-r)!<1,000, then r= [#permalink] ### Show Tags 22 Nov 2017, 18:54 => Note that $$\frac{10!}{(10-r)!} = 10 * (10-1) * … * (10-r+1)$$. Test different values of $$r$$: $$r=1 : 10$$ $$r=2 : 10 * 9 = 90$$ $$r=3 : 10 * 9 * 8 = 720$$ $$r=4 : 10 * 9 * 8 * 7 = 5040$$ Therefore,$$r = 3$$. 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"
"Free Resources-30 day online access & Diagnostic Test"
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Joined: 11 Mar 2017
Posts: 12
Re: If r is an integer, and 700 < 10!/(10-r)!<1,000, then r=  [#permalink]

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06 Feb 2018, 10:55
chetan2u wrote:
MathRevolution wrote:
[GMAT math practice question]

If r is an integer, and $$700 < \frac{10!}{(10-r)!}<1,000$$, then r=

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

Hi....

$$\frac{10!}{(10-r)!}=10*9*8..*(10-(r-1))$$
Now it is given this value is more than 700 and less than 1000
10*9*8=720
So 10-(r-1)=8.....r-1=10-8=2....r=2+1=3
C

Hi Chetan,

Can you please explain how did you derive $$\frac{10!}{(10-r)!}=10*9*8..*(10-(r-1)$$
Re: If r is an integer, and 700 < 10!/(10-r)!<1,000, then r= &nbs [#permalink] 06 Feb 2018, 10:55
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# If r is an integer, and 700 < 10!/(10-r)!<1,000, then r=

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