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# GMATPrep - DS - Remainder and divisibility

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Director
Joined: 28 Dec 2005
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GMATPrep - DS - Remainder and divisibility [#permalink]  16 Dec 2006, 12:19
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This question might have been asked before, but I am not able to find it in a search.

If n is a positive integer and r is the remainder when (n-1)(n+1) is divided by 24, what is the value of r?

1) n is not divisible by 2
2) n is not divisible by 3

Thanks
Director
Joined: 26 Feb 2006
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Re: GMATPrep - DS - Remainder and divisibility [#permalink]  16 Dec 2006, 14:46
hsampath wrote:
This question might have been asked before, but I am not able to find it in a search.

If n is a positive integer and r is the remainder when (n-1)(n+1) is divided by 24, what is the value of r?

1) n is not divisible by 2
2) n is not divisible by 3

Thanks

seems C since n is a prime integer greater tham 3, r when (n-1)(n+1) is divided by 24 is 0.
Senior Manager
Joined: 08 Jun 2006
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Location: Washington DC
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Good one ... Going for C
r = 0, even when n = 1
Manager
Joined: 18 Nov 2006
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C)

r=0 ..arrived at only by insp.
take n=1,5,7,11,13,17,19...

looks like its a strange property of primes greater than 2 and 3
n^2-1 is div by 24 if n is prime other than 2 and 3..
Director
Joined: 28 Dec 2005
Posts: 921
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Kudos [?]: 38 [0], given: 0

Thanks guys, OA is C. So did you know about this property of divisibility by 24, or did you arrive at it only by plugging in numbers? Blissful, I know you did.

Thanks again
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