If N is a positive integer, then n(n+1)(n+2) is
A. even only when n is even
B. even only when n is odd
C. odd whenever is odd
D. divisible by 3 only when n is odd
E. divisible by 4 whenever n is even

If n is odd
then n+1 = even
and n+2 = odd

Ans =O*E*O=E

If n is even
then n+1=Odd
n+2 = Even

Ans =E*O*E=E

Hence ans will always be even no matter what. So eliminate A,B&C
If n=Even then it would mean E*O*E and that is clearly divisible by 4(sample 2,3,4 or 8,9,10 or 34,35,36).

You can try D,but it wont be the right choice. If n =21 then 21*22*23 is divisible by 3. hence it is not only when n is odd that the equation is divisible by 3

Definitely E..

if N is an even integer..it is multiply of 2..in addition n+2 is a second multiple of 2...thus the product is multiple of 4

must remeber the following, very easy if you follow the rythm that's going on.

E(+-)E = E
E(+-)O= O
O(+-)O = E
O-E = O

ExE = E
Ex O= E
OxO = O