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

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14 Apr 2006, 16:54
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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
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14 Apr 2006, 18:02
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

Statement 1:

Insufficient: if n=3, you get 8; if n=7, you get 48 (no remainder)

Statement 2:

Insufficient: if n=2, you get 3; if n=7, again you get 48.

Statement Combined: Sufficient. All values that are neither a factor of 2 or 3, will give us multiples of them in (n-1)*(n+1). This will always give us a multiple of 24. Therefore sufficient.
14 Apr 2006, 18:02
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# If n is a positive integer and r is the remainder when

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