Factorial Question

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awilhelm: Master | Next Rank: 500 Posts; Posts: 117; Joined: Fri Oct 17, 2008 7:41 am

by awilhelm » Sun Dec 14, 2008 8:26 pm

Which of the following is an integer?

I. 12!/6!
II. 12!/8!
III. 12!/(7!)(5!)

Is there a quick way to calculate whether III is an integer? After canceling out 7-1 I'm left with

(12*11*10*9*8)/(5*4*3*2*1)

Thank you!

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Source: Beat The GMAT — Problem Solving | Sun Dec 14, 2008 8:26 pm

acecoolan: Master | Next Rank: 500 Posts; Posts: 139; Joined: Wed May 07, 2008 12:27 pm; Thanked: 8 times

by acecoolan » Sun Dec 14, 2008 8:42 pm

Cancel from numerator and denominator

(12*11*10*9*8)/(5*4*3*2*1)

so 5*2 is 10 - that cancels
and 4*3 is 12 - that cancels ..u r left with 3 integers in the numerator. Hence III. 12!/(7!)(5!) is also an integer

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awilhelm: Master | Next Rank: 500 Posts; Posts: 117; Joined: Fri Oct 17, 2008 7:41 am

by awilhelm » Sun Dec 14, 2008 8:51 pm

Thanks!

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ronniecoleman: Legendary Member; Posts: 546; Joined: Sun Nov 16, 2008 11:00 pm; Location: New Delhi , India; Thanked: 13 times

by ronniecoleman » Wed Dec 17, 2008 11:14 pm

12! / 5! 7!

Have a rule if a!/b!d! if a = b+ d

then a!/b!d! is a integer !
otherwise...we need to check it out

Admission champion, Hauz khaz
011-27565856

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parallel_chase: Legendary Member; Posts: 1153; Joined: Wed Jun 20, 2007 6:21 amFollowed by: 2 members; Thanked: 146 times

by parallel_chase » Thu Dec 18, 2008 3:29 am

Here is another rule

Product of n consecutive integers will always be divisible by n!

12! /5! 7!

we know that 7! cancels out, whats left is

(8*9*10*11*12)/5!

if we follow the above rule, we have product of 5 consecutive integers, therefore the result will be an integer.

Hope this helps.

No rest for the Wicked....

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PVtrainer: Newbie | Next Rank: 10 Posts; Posts: 3; Joined: Fri Dec 12, 2008 10:46 pm; Location: India

Re: Factorial Question

by PVtrainer » Thu Dec 18, 2008 9:20 am

awilhelm wrote:Which of the following is an integer?

I. 12!/6!
II. 12!/8!
III. 12!/(7!)(5!)

Is there a quick way to calculate whether III is an integer? After canceling out 7-1 I'm left with

(12*11*10*9*8)/(5*4*3*2*1)

Thank you!

The value of option III is nothing but the value of 12C7 which always comes as integer or you can see that after canceling 7! we are left with 5! in denominator which is equal to 120 and in numerator it comes from product of 12 and 10 so it comes as integer . Hence all the values are integers

P. V. Singh
+ve Approach, +ve Attitude will give +ve result.

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