number properties

[sud21]

M, N and K are integers. Is the product of them divisible by 3?
1) The sum of them is divisible by 3
2) M, N, and K are consecutive integers.

[Anurag@Gurome]

M, N and K are integers. Is the product of them divisible by 3?
1) The sum of them is divisible by 3
2) M, N, and K are consecutive integers.

Statement 1:
# Say, M = N = K = 1 --> (M + N + K) = 3 is divisible by 3 but MNK is not
# Say, M = N = K = 3 --> (M + N + K) = 9 and MNK = 27 are both divisible by 3

Not sufficient

Statement 2: If M, N, and K are consecutive integers then at least one of them must be divisible by three. Hence, their product is also divisible by 3.

Sufficient

The correct answer is B.