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# If n is a positive integer and r is the remainder when

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Senior Manager
Joined: 05 Jun 2008
Posts: 291
If n is a positive integer and r is the remainder when [#permalink]

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25 Sep 2008, 10:55
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Question Stats:

0% (00:00) correct 0% (00:00) wrong based on 0 sessions

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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) 2 is not a factor of n.
(2) 3 is not a factor of n.

Good question, i got it wrong but got the solution while reviewing it...

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VP
Joined: 17 Jun 2008
Posts: 1479
Re: DS - Number Properties [#permalink]

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25 Sep 2008, 11:16
I think, this question is already posted here.

I get the answer as C using the substitution method.

Stmt 1 says that n is an odd number and hence there will be different remainder when (n-1)(n+1) are divided by 24. Hence, insufficient. Similarly, for stmt2.

However, combining stmt1 and 2, n will be 1, 5, 7, 11, ......and remainder will always be 0.
Director
Joined: 23 May 2008
Posts: 743
Re: DS - Number Properties [#permalink]

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25 Sep 2008, 11:26
I agree with C

24x + r =(n^2) - 1

1) 2 is not a factor of n
means n is odd

say n=7

24x + r =48 so r=0

say n=9

24x + r=80 so r=8

insuff.

2) n is not a factor of 3

say n is 10, r=3
say n is 5, r=0

insuff.

together:
n is not a factor of 2 or 3

examples above, n=5 then r=0, n=7 then r=0

sufficient
Manager
Joined: 28 Aug 2008
Posts: 95
Re: DS - Number Properties [#permalink]

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25 Sep 2008, 17:11
C .. In all cases n^2-1 / 24 = integer where n is not a factor of 2 or 3

--== Message from GMAT Club Team ==--

This is not a quality discussion. It has been retired.

If you would like to discuss this question please re-post it in the respective forum. Thank you!

To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.
Re: DS - Number Properties   [#permalink] 25 Sep 2008, 17:11
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