单选题 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 n is odd
(D) divisible by 3 only when n is odd
(E) divisible by 4 whenever n is even

【正确答案】 E
【答案解析】[解析] n(n+1)(n+2)是三个连续正整数的乘积，而根据连续整数的性质可知，无论n取何数，他们三个数中一定有一个偶数，且一定有一个数是3的倍数，所以n(n+1)(n+2)一定是偶数，且能被3整除；若n是偶数时，则n+2也一定是偶数，所以此时n(n+1)(n+2)也一定能被4整除。