First, in this particular question, the GMAT wants you to recognize that(x)(x + 2)(x + 4) is the same thing as saying "3 consecutive even integers" or "3 consecutive odd integers". Whether x is even or odd will determine which is true. If x is even, these are three consecutive even integers (e.g. x=2, x+2=4, x+4=6). Conversely, if x is odd, these are three consecutive odd integers (e.g. x=1, x+2=3, x+4=5). It's worth remembering that three consecutive even integers will be divisible by 2, 3, and 4. It will be divisible by 2 because the product will always be even (even * even * even = even), it will be divisible by 3 because there are three numbers (the product of n numbers will always be divisible by n), and it will be divisible by 4 because one of the three terms must be divisible by 4 (you cannot find 3 consecutive even integers in which one of the integers is not divisible by 4).

To say that the product of these three numbers is divisible by twelve is to say: When these three numbers are multiplied together, can they evenly be divided by 12? Or, is the product of these three integers a multiple of 12 (12, 24, 36, etc.). Or, if you took the product of these three numbers, and then divided it by 12, would the remainder be 0 (as you pointed out at the bottom of your post)?

Statement one tells us that the product of the first two numbers (x and x+2) is a multiple of three; however, we are not told whether x is even or odd. Without knowing whether x is even or odd, you'll see that we cannot answer whether this product is divisible by 12 with certainty in your examples above:

X=ODD
3(3+4)=21 Divisible by 12? NO
X=EVEN
6(4+4)=48 Divisible by 12? YES

Already we see that we have insufficiency to satisfy the stem.

Statement 2: If 3x is a multiple of two, we know that x MUST be even:

3 * X = 2, which means
Odd * X = Even, therefore
X must be even

While the question is literally asking if the product of these numbers is divisble by 12, we see now that it's really as simple as determining whether x is even or not. That's precisely what Statement 1 failed to do and what Statement 2 has done.

I hope this helps!

So is it a hard and fast rule that when the GMAT states "divisible by" it means divisible with remainder 0?

stevennu wrote:So is it a hard and fast rule that when the GMAT states "divisible by" it means divisible with remainder 0?

Yep. It will always be an integer (remainder of 0).