Easier way of simplifying this factorial equation?

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ssy: Senior | Next Rank: 100 Posts; Posts: 66; Joined: Sat Sep 29, 2007 7:17 pm; Thanked: 5 times; GMAT Score:660

by ssy » Sat Oct 20, 2007 10:36 pm

Is there a way to tell if 12! / (7!5!) is an integer without fully working it out?

In my calculations, I've only managed to simplify it to:

12 x 11 x 10 x 9 x 8 / 5 x 4 x 3 x 2 x 1

..which would still take around 40 precious seconds to work out if it equals an integer..is there a shortcut?

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Source: Beat The GMAT — Problem Solving | Sat Oct 20, 2007 10:36 pm

jimbow: Newbie | Next Rank: 10 Posts; Posts: 3; Joined: Sun Oct 21, 2007 12:49 pm

Re: Easier way of simplifying this factorial equation?

by jimbow » Mon Oct 22, 2007 4:37 am

ssy wrote:Is there a way to tell if 12! / (7!5!) is an integer without fully working it out?

In my calculations, I've only managed to simplify it to:

12 x 11 x 10 x 9 x 8 / 5 x 4 x 3 x 2 x 1

..which would still take around 40 precious seconds to work out if it equals an integer..is there a shortcut?

you've got it:

5x2=10
4x3=12

you simplify and you have 11x9x8 / 1 (you don't need to calculate this). You know that 11x9x8 is an integer (product of integers)

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ssy: Senior | Next Rank: 100 Posts; Posts: 66; Joined: Sat Sep 29, 2007 7:17 pm; Thanked: 5 times; GMAT Score:660

by ssy » Mon Oct 22, 2007 4:49 am

Great, thanks guys!

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agni_mba: Junior | Next Rank: 30 Posts; Posts: 18; Joined: Mon Aug 13, 2007 3:04 am; Location: india

by agni_mba » Mon Oct 22, 2007 3:00 pm

another way of looking at this is: 12!/(7!.5!) is 12C5 i.e. no. of different ways of picking 5items from a set of 12. Obviously that can't be a non-integer...

cheers
agni

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