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# If n is an integer greater than 6, which of the following

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VP
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If n is an integer greater than 6, which of the following [#permalink]  07 Jan 2008, 05:18
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If n is an integer greater than 6, which of the following must be divisible by 3?

A. n (n+1) (n-4)
B. n (n+2) (n-1)
C. n (n+3) (n-5)
D. n (n+4) (n-2)
E. n (n+5) (n-6)
Director
Joined: 12 Jul 2007
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Re: intgers [#permalink]  07 Jan 2008, 06:16
As long as one of these terms is divisible by 3 the whole mess will be divisible by 3 once it's multiplied out. Since n is an integer, anything that covers 3 consecutive integers MUST be divisible by 3. This means that these terms will work:

n(n+1)(n+2)
n(n-1)(n+1)
n(n-1)(n-2)

will work.

Of course the GMAT wouldn't make it so easy that one of these options is actually an answer, but that's OK. Since we're dealing with multiples of 3, if we add 3 or subtract 3 from any of these terms the answer will still work.

Example:

Let's say n = 7

n(n+1)(n+2) = 7(8)(9)
BUT, adding or subtracting 3 to any of these terms will get the same answer
n(n+4)(n-1) = 7(11)(6)

so we're looking for one of these options that's just had 3 added or subtracted from it

Quote:
n(n+1)(n+2)
n(n-1)(n+1)
n(n-1)(n-2)

Right off the bat A works.

n(n+1)(n-4) = n(n+1)(n-1-3)

VP
Joined: 22 Nov 2007
Posts: 1104
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Re: intgers [#permalink]  20 Feb 2008, 01:11
eschn3am wrote:
As long as one of these terms is divisible by 3 the whole mess will be divisible by 3 once it's multiplied out. Since n is an integer, anything that covers 3 consecutive integers MUST be divisible by 3. This means that these terms will work:

n(n+1)(n+2)
n(n-1)(n+1)
n(n-1)(n-2)

will work.

Of course the GMAT wouldn't make it so easy that one of these options is actually an answer, but that's OK. Since we're dealing with multiples of 3, if we add 3 or subtract 3 from any of these terms the answer will still work.

Example:

Let's say n = 7

n(n+1)(n+2) = 7(8)(9)
BUT, adding or subtracting 3 to any of these terms will get the same answer
n(n+4)(n-1) = 7(11)(6)

so we're looking for one of these options that's just had 3 added or subtracted from it

Quote:
n(n+1)(n+2)
n(n-1)(n+1)
n(n-1)(n-2)

Right off the bat A works.

n(n+1)(n-4) = n(n+1)(n-1-3)

good, i solve it by guessing in few seconds but feel that smtms guessing could drive me to mistakes. your way is better
Re: intgers   [#permalink] 20 Feb 2008, 01:11
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