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.

(1)

if 2 is not a factor of n, one of (n-1) or (n+1) must be mutiples of 2, the other must be mutiple of 4.

so (n-1)(n+1) must be multiple of 8

when (n-1)(n+1) = 24, r =0

when (n-1)(n+1) = 32, r =8

Not Suff.

(1)

if 3 is not a factor of n, either (n-1) or (n+1) must be mutiples of 3

so (n-1)(n+1) must be multiple of 3

when (n-1)(n+1) = 24, r =0

when (n-1)(n+1) = 27, r =3

Not Suff

(1)&(2)

Since (n-1)(n+1) is a multiple of 8 and 3, it must be a multiple of 24.

So r = 0

Suff.

Ans is C

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