A. (n − 1)( n + 1)

If n is even , n-1 and n+1 will both be odd.

If n = 2

(n − 1)( n + 1) = 1*3 = 3

Not even

B. (n − 2)( n + 1)

If n = 4 (Even)

2*5 = 10 is even

If n = 5 (Odd)

3*6 = 18 is even

If n = Odd , n+1 will be even and n-2 will be Odd . Product will be Even

If n = even , n+1 will be odd and n-2 will be Even . Product will be Even .

C. (n − 2)( n + 4)

If n is odd , n-2 and n+4 will both be odd .Product will be Odd .

D. (n − 3)( n + 1)

If n is even , n-3 will be odd and n+1 will also be odd.

Product will be Odd .

E. (n − 3)( n + 5)

If n is even , n-3 and n+5 will both be odd .

Product will be Odd .

Answer B

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