Since this is a yes or no question, sufficiency is determined if the statement(s) can definitively yield an unequivocal 'yes' or 'no'.

Stmt 1: Since 1/(k-1) > 0 then the denominator has to be positive. To make k-1 > 0, k>1. Since k>1 then we can check the stem of 'is 1/k > 0?' and know definitively that the answer is yes. Stmt 1 is sufficient.

Stmt 2: Since 1/(k+1) > 0, the denominator also must be positive. Therefore, we're evaluating k+1 > 0. We can solve for k, then as k>-1. If we take this truth to the stem of 1/k, then k>-1 could make 1/k positive or negative. Therefore Stmt 2 is insufficient.

Answer [A]

Hope this helps, good luck.

The question says that k cannot be 0,1 or -1 then :

According to stat(2) K+1>0 or K>-1 so k can only be above 1 which would make 1/k positive no matter what the value of k is right?? What am I missing here??

Remember that k does not only take on integer values. On the GMAT, you should always assume that variables are real, unless otherwise stated.

Knowing that k>-1 means that k could equal, for example, -1/2, so 1/k would be -2. Also, k could equal 1/3, so 1/k would 3. So statement (2) is insufficient.

Thanks rey!

Thanks!