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If x and n are positive integers , and when (n+1)(n-1) is

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If x and n are positive integers , and when (n+1)(n-1) is [#permalink] New post 26 Nov 2006, 22:52
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If x and n are positive integers , and when (n+1)(n-1) is divided by 24, the quotient is x and the remainder is r. r=?
1) 2 is not the factor of n
2) 3 is not the factor of n
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 [#permalink] New post 26 Nov 2006, 23:02
I got C.

1) means that n is odd. then n + 1 and n - 1 both will be even.
then it has a factor of 2*2 = 4. then we can deduce r is from 1 to 5.

InSuff.

2) means (n+1)(n-1) must have a factor of 3. then r is from 1 to 7.
InSuff.


Both put together, it has a factor or 2*2*3 = 12.
then the remainder can only be 1. C.
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 [#permalink] New post 26 Nov 2006, 23:13
Both choices together are sufficient C.

Since n does not have 2 and 3 as factor - it must be a prime number.

Also it must be a prime > 3.

picking primes > 3 we can see that n+1 * n-1 will always be divisible by 24 and hence r = 0.
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 [#permalink] New post 26 Nov 2006, 23:53
Thanks for explanation.

OA is C
  [#permalink] 26 Nov 2006, 23:53
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If x and n are positive integers , and when (n+1)(n-1) is

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