If n is a positive integer greater than 6, what is the remainder when n is divided by 6? (1) n2 – 1 is not divisible by 3. (2) n2 – 1 is even.

The remainder is 3

Step-by-step explanation:

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

When n^2 -1 is not divisible by 3, it implies that neither (n-1) nor (n+1) is divisible by 3.

From any three consecutive integers, one must be divisible by 3.

The consecutive integers are n, (n-1), (n+1)

n is divisible by 3.

If n is even, the remainder is 0.

If n is odd, the remainder is 3 if divided by 6.

2) n^2-1 is even

n^2 - 1 = even

n^2 = even + 1

n^2 = odd

For 1 + 2 , n is odd.

3,9,15,21,

The remainder when n is divided by 6 is odd

in your question which ask for the statement that best fit in your theorem that a parallel line to one side of a triangle divides the other two proportionately which states that segment de is parallel to segment bc and segment ef is parallel to ab so the answer is bf=15