I'm not 100% sure I understand your question.

Everything comes down to whether or not a statement provides enough information to answer a target question with absolute certainty.

So, for example, if the target question is a YES/NO question, as in "Is k a prime number?", then we need to determine whether or not a statement provides enough information to state either "yes, k is definitely a prime number or "no, k is definitely not a prime number." If we can definitively answer the question (either yes or no), then the statement is sufficient.

If the target question is a VALUE question, as in "What is the value of k?", then we need to determine whether or not a statement provides enough information to state "the value of k must be ...... " If we can do this, then the statement is sufficient.

For more information about this, you might want to watch our free video that covers this particular question: https://www.gmatprepnow.com/module/gmat- ... cy?id=1098

Cheers,
Brent

A definitive YES or a definitive NO answer would each be sufficient. Only an answer of MAYBE (or "sometimes yes, sometimes no") would be insufficient.

However, "definitive NO is sufficient" is not a rule that the GMAT tests regularly. For most YES/NO questions, a statement that gives sufficient information will give a "yes" answer to the question.

Out of the DS problems in OG13 and the Quant Supplement 2nd Ed, only 1 that I can find has statements that give a definitive "no" answer:

DS #136 OG13
If @ represents one of the operations +, -, and x , is k @ (L + m) = (k @ L) + (k @ m) for all numbers k, L , and m ?

(1) k @ 1 is not equal to 1 @ k for some numbers k.

(2) @ represents subtraction.

(The actual problem used a circle, not an @ symbol, but I don't know how to recreate that here!)

We can rephrase the question as "does the operation @ represent multiplication?" as multiplication is the only operation for which k @ (L + m) = (k @ L) + (k @ m)

(1) k @ 1 is not equal to 1 @ k for some numbers k.

If these two are not equal, then @ must NOT represent multiplication, because k*1 = 1*k. Therefore, the answer to the question "is @ multiplication?" is "no, definitely not." Sufficient.

(2) @ represents subtraction.

Again, the answer to the question "is @ multiplication?" is "no, definitely not." Sufficient.

The answer is D.