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Rule: The product of k consecutive integers is always divisi

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diananah
 Post subject: Rule: The product of k consecutive integers is always divisi
 Post Posted: Sun Aug 07, 2011 7:29 pm 
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Course Students


Posts: 3
Rule: The product of k consecutive integers is always divisible by k factorial (k!).
(Guide 1, Chapter 4 - Consecutive Integers, Page 31)

In this section, in order to prove this rule, the chapter asks us at first to come up with a series of 3 consecutive integers in which none of the integers is a multiple of 3 and then lists a string of examples like:

1 x 2 x 3 = 6
2 x 3 x 4 = 24
3 x 4 x 5 = 60
4 x 5 x 6 = 120

But, what about the three consecutive integers: 0 x 1 x 2? Are we saying that this rule applies because technically 0 is a multiple of 3? Or the consec integers: -1 x 0 x 1 --- which numbers do we consider to be multiplies of 3 and 2 in the series?

Can we only apply this rule to consecutive integers that don't include 0?
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tim
 Post subject: Re: Rule: The product of k consecutive integers is always divisi
 Post Posted: Fri Aug 12, 2011 11:22 pm 
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ManhattanGMAT Staff


Posts: 2242
Location: Southwest Airlines, seat 21C
although i have not seen the GMAT do it, you can definitely apply this principle to 0. as you correctly observe, 0 is technically a multiple of every number..

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Tim Sanders
Manhattan GMAT Instructor
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