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

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Intern
Joined: 08 Oct 2007
Posts: 33
If n is a positive integer and r is the remainder when  [#permalink]

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30 Nov 2008, 07:20
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.

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Manager
Joined: 23 Nov 2008
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30 Nov 2008, 07:43
C - together sufficient

1) If 2 is not a factor of n, then (n-1) and (n+1) must both be even.
But they could be small numbers (like 2*4), or larger numbers (like 6*8), so no distinct remainder => NOT SUFF

2) 3 is not a factor of n, not enough info again, (1*3) or (6*8)
Together, we know=>
n-1 = even ; n+1 = even ; one of these numbers is divisible by 3 (since n is not)
Now, since 2&3 are not factors of n, n>4
n+1> 5, hence, for any n, with n+1 or n-1 will be multiple of 4

therefore, 3,4,2 are def factors.
Hence remainder will be 0.

The only case not considered above is if n is 1, but there remainder =0 as well.

hence C.
Manager
Joined: 18 Nov 2008
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Updated on: 01 Dec 2008, 08:50
Quote:
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.

(n-1)(n+1) = n^2-1

1) if 2 is not a factor of n, n^2-1 can give different reminders when divided by 24, Insuff.
2) again, no enough info, Insuff.

Combined, we know that n is any prime number other than 2 and 3. Any such squared prime number minus 1 gives 0 as a reminder when divided by 24. Suff.

C

Originally posted by atletikos on 30 Nov 2008, 07:52.
Last edited by atletikos on 01 Dec 2008, 08:50, edited 1 time in total.
Manager
Joined: 27 May 2008
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30 Nov 2008, 08:26
a repeat Q

7-t68277
Intern
Joined: 08 Oct 2007
Posts: 33

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30 Nov 2008, 08:29
Atletikos,

how do you that any prime, other than 2 and 3, minus 1 is divided by 24. What is this number property?

I tried 5^2-1=24. It really works. I just want to know what these properties are
Manager
Joined: 18 Nov 2008
Posts: 109

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30 Nov 2008, 08:35
Quote:
how do you that any prime, other than 2 and 3, minus 1 is divided by 24. What is this number property?

I tried 5^2-1=24. It really works. I just want to know what these properties are

Not be surprised, I've just discovered it picking numbers

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

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Re: number property &nbs [#permalink] 30 Nov 2008, 08:35
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