Yes, negative numbers can also be odd or even:

The odd numbers are: ... -5, -3, -1, 1, 3, 5, ....
The even numbers are: ... -4, -2, 0, 2, 4, ...

If you've learned rules for odd and even numbers (rules like: odd + odd = even), those rules apply to all odd and even numbers, regardless of whether they're positive or negative.

I glanced at that quora link, and almost none of the math in the first post there is right, so I'd try to forget you ever read that!

The DS question you posted is also bizarre. I don't know why the question even mentions J or K if the question itself doesn't ask about J or K, and if neither of the statements mentions J or K. And if a question asks "When is G*H*I > 12?", then that is a problem solving question, not a Data Sufficiency problem. For it to be a DS question, it would need to ask "Is G*H*I > 12?" If you've transcribed the question perfectly from your book, I'd be concerned about the quality of that book.

Hi David,

I agree that this prompt isn't written in proper GMAT "style", so I've tweaked it a bit:

G, H, and I are consecutive integers. Is the product of G, H and I greater than 12?

1. G ≥ 2
2. G is odd.

We're told that G, H and I are CONSECUTIVE integers (meaning they are 'in a row'). This is a YES/NO question. We can answer it by TESTing VALUES.

1. G ≥ 2

IF G=2, then H=3 and I=4... the product is (2)(3)(4) = 24 and the answer to the question is YES.
IF G=3, then H=4 and I=5... the product is (3)(4)(5) = 60 and the answer to the question is YES.
As you increase the value of G, then the values of H and I also increase and the product gets BIGGER. As such, the answer to the question is ALWAYS YES.
Fact 1 is SUFFICIENT.

2. G is odd.

IF G=3, then H=4 and I=5... the product is (3)(4)(5) = 60 and the answer to the question is YES.
IF G=1, then H=2 and I=3... the product is (1)(2)(3) = 6 and the answer to the question is NO.
Fact 2 is INSUFFICIENT.

In answer to your original questions - YES, you could use a negative value for G (and potentially H and I). Odd/Even and Positive/Negative are completely unrelated Number Properties. Since the prompt does NOT state that the integers are "positive", we don't have to assume that they are positive (and in certain DS questions, considering how 0 or negatives could impact the answer to the question is one of the necessary steps to properly solving the question).

Final Answer: A

GMAT assassins aren't born, they're made,
Rich