This is a GMAT Prep Test question - Data Sufficency.

I thought the answer was E) Neither sufficient alone or together. The correct answer however is: A) Statement 1 is sufficient. Please explain how as my thoughts were:

If for example k = 2 or -2 (since it doesn't specify k is positive)

st1) 1/(2-1) > 0 yes, but 1/(-2-1) < 0 ----------Thus NS
st2) 1/(2+1) > 0 yes, but 1/(-2+1) < 0 -------------Thus NS

And together, I thought they weren't sufficient.

Statement 1 tells us that 1/(k-1) is greater than 0. Since the statements are absolute fact, any value of k that doesn't fit that inequality is not a valid possibility for k. Any negative number would leave us with a negative denominator, which doesn't work. Based on that and the values ruled out in the question itself, k must be positive, and 1 divided by a positive number is always positive. Sufficient.

For statement 2, we need to remember that k doesn't have to be an integer. If we plug in k=-.5, we get:

1/(-.5+1) > 0

1/.5 >0

2>0

So k=-.5 is valid. When we plug into the question, 1/-.5 is not greater than 0, which is a definitive no. For any positive value of k, we'd get a definitive yes, so, as a whole, we don't know. Insufficient.

Bill