If 8 < k < 8, is k < 2 ?

Not a good question.
If -8<k<8, is k<-2?

(1) k^2-7k-18>0 --> \((y+2)(y-9)>0\) --> \(y<-2\) or \(y>9\) --> as also given that \(-8<k<8\) then \(-8<k<-2\), so the answer to the question "is \(k<-2\)" will be YES. Sufficient.

(2) 1/k>1/2 --> you can directly tell that \(k\) must be positive in order this inequality to hold true, thus in any case \(k\) won't be less than -2, so the answer to the question "is \(k<-2\)" will be NO. Sufficient.

The exact range for \(k\) in order \(\frac{1}{k}>\frac{1}{2}\) to hold true will be \(0<k<2\): \(k\) must be positive and also it must be less than 2 so that LHS to be more than RHS OR rewrite as \(\frac{2-k}{2k}>0\) --> \(0<k<2\).

Now, technically answer would be D, as EACH statement ALONE is sufficient to answer the question.

But even though formal answer to the question is D (EACH statement ALONE is sufficient), this is not a realistic GMAT question, as: on the GMAT, two data sufficiency statements always provide TRUE information and these statements never contradict each other.

So we can not have answer YES from statement (1) and answer NO from statement (2), as in this case statements would contradict each other.

Guess statement (1) should read: k^2-7k-18<0. If it were so then \((y+2)(y-9)<0\) --> \(-2<y<9\) --> as also given that \(-8<k<8\) then \(-2<k<8\), so the answer to the question "is \(k<-2\)" will be NO. Sufficient.

So in this case answer would be D and statements wouldn't contradict each other.

Hope it's clear.