1. 1/(k-1) > 0
Then k - 1 > 0
k >1
Then 1/k > 0.
Sufficient.

2. 1/(k+1)>0
k+1>0
k>-1

Choose k = -1/2, then 1/k = -2.
Choose k = 1/2, then 1/k = 2.

Insufficient.

Answer is A.

(A)

Always yes.

GMATQuantCoach wrote:1. 1/(k-1) > 0
Then k - 1 > 0
k >1
Then 1/k > 0.
Sufficient.

When you go from 1/(k-1) to (k-1), don't you change the inequality sign?

GMATQuantCoach wrote: 2. 1/(k+1)>0
k+1>0
k>-1

Choose k = -1/2, then 1/k = -2.
Choose k = 1/2, then 1/k = 2.

Insufficient.

When you go from 1/(k+1) to (k+1), don't you change the inequality sign?

GMATQuantCoach wrote: Answer is A.

the fact that the question is 1/(k-1) is only there to throw you off.....

What is 1/(k-1) > 0 saying?

It is saying that k - 1 > 0

The 1 on the top is insignificant because is has no bearing on whether it is negative or positive.
So A) can be rephrased to k - 1 > 0
B) rephrased to k + 1 > 0

So in A) k HAS to be greater than 1 (making 1/k positive)

B) k<-1, meaning that k can be negative or positive so insufficient.

Sorry

In B) k > -1

mike22629 wrote:the fact that the question is 1/(k-1) is only there to throw you off.....

What is 1/(k-1) > 0 saying?

It is saying that k - 1 > 0

The 1 on the top is insignificant because is has no bearing on whether it is negative or positive.
So A) can be rephrased to k - 1 > 0
B) rephrased to k + 1 > 0

So in A) k HAS to be greater than 1 (making 1/k positive)

B) k<-1, meaning that k can be negative or positive so insufficient.

Ahh... Thanks Mike22629.