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

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Senior Manager
Senior Manager
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If n is a positive integer and r is the remainder when [#permalink]

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New post 25 Sep 2008, 10:55
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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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SVP
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Re: DS - Number Properties [#permalink]

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New post 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.

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Director
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Re: DS - Number Properties [#permalink]

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New post 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

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Manager
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Re: DS - Number Properties [#permalink]

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

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Re: DS - Number Properties   [#permalink] 25 Sep 2008, 17:11
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If n is a positive integer and r is the remainder when

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