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# N is the product of the first 5 prime numbers. If 12!/n is divisible b

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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GMAT 1: 800 Q59 V59
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N is the product of the first 5 prime numbers. If 12!/n is divisible b [#permalink]

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30 May 2016, 19:46
1
KUDOS
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Difficulty:

55% (hard)

Question Stats:

62% (01:07) correct 38% (01:35) wrong based on 97 sessions

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N is the product of the first 5 prime numbers. If 12!/n is divisible by 2^k, what is the greatest value of a positive integer k?
A. 6
B. 7
C. 8
D. 9
E. 10

*An answer will be posted in 2 days.
[Reveal] Spoiler: OA

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"Only $79 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Last edited by MathRevolution on 01 Jun 2016, 07:09, edited 1 time in total. Senior Manager Joined: 18 Jan 2010 Posts: 256 Re: N is the product of the first 5 prime numbers. If 12!/n is divisible b [#permalink] ### Show Tags 30 May 2016, 23:29 1 This post received KUDOS MathRevolution wrote: N is the product of the first 5 prime numbers. If 12!/n is divisible by 2k, what is the greatest value of a positive integer k? A. 6 B. 7 C. 8 D. 9 E. 10 *An answer will be posted in 2 days. N = 2.3.5.7.11. 12! / N = 12. 10. 9. 8. 6. 4 Expressing this as $$2^9$$*$$3^4$$* 5 --> This number is divisible by 2 k. $$2^8$$*$$3^4$$*5 is divisible by k. Out of given options 10 is the biggest possible option. Answer E Manager Joined: 18 May 2016 Posts: 67 Concentration: Finance, International Business GMAT 1: 720 Q49 V39 GPA: 3.7 WE: Analyst (Investment Banking) Re: N is the product of the first 5 prime numbers. If 12!/n is divisible b [#permalink] ### Show Tags 31 May 2016, 02:39 1 This post received KUDOS N = 2 x 3 x 5 x 7 x 11 12! / N = (12 x 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1) / (2 x 3 x 5 x 7 x 11) = 12 x 10 x 9 x 8 x 6 x 4 x 1 Here we get rid of 2 in the denominator by dividing 12 by 2: (12! / N) / 2K = (12 x 10 x 9 x 8 x 6 x 4 x 1) / 2K = (6 x 10 x 9 x 8 x 6 x 4 x 1) / K Hence, largest K from the given options can be 10 Would very much like to hear why the correct answer is D. Answer: E _________________ Please kindly +Kudos if my posts or questions help you! My debrief: Self-study: How to improve from 620(Q39,V36) to 720(Q49,V39) in 25 days! Intern Joined: 05 Jan 2014 Posts: 26 GMAT 1: 610 Q47 V26 WE: Information Technology (Computer Software) Re: N is the product of the first 5 prime numbers. If 12!/n is divisible b [#permalink] ### Show Tags 31 May 2016, 08:16 Its 2^k not 2k please correct it. Intern Joined: 01 Mar 2016 Posts: 1 Re: N is the product of the first 5 prime numbers. If 12!/n is divisible b [#permalink] ### Show Tags 31 May 2016, 22:00 HI, Here given is 1)N is product of first five prime numbers , that is : 2*3*5*7*11 2)12!/N divisible by 2k and that is multiple of 2 and k should be highest value so , 12!/N = (12*11*10*9*8*7*6*5*4*3*2*1)/(2*3*5*7*11) and now we have 12!/N = 12*10*9*8*6*4 i.e 2k = 12*10*9*8*6*4 [here except 9 all others are multiples of 2 and can be written in 2 multiples as below] 2k = 2(6*5*4*3*2)*9 2k=2()*9 similar to the given expression as 2k and hence the highest value for K is 9 So D is the option Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 5062 GMAT 1: 800 Q59 V59 GPA: 3.82 Re: N is the product of the first 5 prime numbers. If 12!/n is divisible b [#permalink] ### Show Tags 01 Jun 2016, 18:03 From 12!/n=12!/(2)(3)(5)(7)(11)=2^k(integer), the value of k is the number in which one of 2 in 12! is taken out. 12! has 2,4,6,8,10,12. In other words, 2^1(2), 2^2(4), 2^1(6), 2^3(8), 2^1(10), 2^2(12). Since it is multiplication, we can add 1+2+1+3+1+2=10. Since we need to take one of 2 out, the number become 10-1=9. Hence, the correct answer is D. _________________ 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$79 for 3 month Online Course"
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Re: N is the product of the first 5 prime numbers. If 12!/n is divisible b [#permalink]

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23 Oct 2017, 14:50
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Re: N is the product of the first 5 prime numbers. If 12!/n is divisible b   [#permalink] 23 Oct 2017, 14:50
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