Question rephrased: If n is a positive integer, what is the remainder when (n+1)(n-1) is divided by 8?
Statement 1: n is odd.
Thus,(n-1)(n+1) = the product of two consecutive even integers.
Of every two consecutive even integers, exactly one will be a multiple of 4:
0,2,4,6,8,10,12...
Thus, the product of any two consecutive even integers = (multiple of 4)(even) = multiple of 8.
When a multiple of 8 is divided by 8, R=0.
SUFFICIENT.
Statement 2: n is not a multiple of 8.
If n=3, then (n-1)(n+1) = 2*4 = 8.
8/8 = 1 R0.
If n=4, then (n-1)(n+1) = 3*5 = 15.
15/8 = 1 R7.
Since R can be different values, INSUFFICIENT.
The correct answer is A.
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