If j and k are positive integers, is j divisible by 6?

1: j is the product of 3 consecutive integers, therefore, j is divisible by 3 and 2 and therefore 6. Sufficient.
2: Tells nothing about J. Insufficient.
Answer is A.

MANHATTAN GMAT OFFICIAL SOLUTION:

In order to determine whether j is divisible by 6, we need to know whether j is divisible by 2 (even) and also divisible by 3.

Statement (1) is SUFFICIENT: k + 1, k + 2, and k + 3 are 3 consecutive integers. The product of 3 consecutive integers will always be divisible by 3, because one of the 3 integers must be a multiple of 3.

Additionally, at least one of those integers must be even (it's possible that two of them are even), so the product will be even.

Statement (2) is INSUFFICIENT: knowing that k is even tells us nothing about j.

You might Spot One Statement Adding Nothing here. Knowing that k is even adds no information to Statement (1), because the product (k + 1)(k + 2)(k + 3) is going to be even for any value of k. Therefore, C can be eliminated.

You might also Judge by Appearance on this problem. We need to know whether j is divisible by 2 and 3, and since Statement (1) tells us that j is the product of 3 consecutive integers, it seems as though this statement is likely to be sufficient.

You could also use Discrete Number Listing to test numbers for k and prove to yourself that j must be divisible by 6.

The correct answer is A.

Statement 1

The product of 3 consecutive integers is always a multiple of 3; moreover, one of the numbers is even so so it it must be divisible by 2 and thus a product of 6.

A

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