Bunuel , excellent Q..

lets see what the Q is asking..

\(\frac{1}{(n−k)}>0\)..
since 1 is positive, we have to find if n-k>0 OR n>k..

lets see the statements--

(1)\(\frac{1}{k}<0\)
Nothing about n..
we know k<0..
Insuff

(2)\(\frac{1}{(n+2)}>0\)..
again nothing about k,
but n+2>0 or n>-2..
Insuff

combined..
we know n>-2, so least value of n is -1..
Statement I tells us that k<0..
so k's largest possible value could be -1..
but n ≠ k..
so if n is -1, k will not be -1.

so if n=-1, the largest value of k will be -2.. so n>k..
if n>-1, k can be -1 at the maximum, so again n>k..

our answer is YES
Suff
C
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Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

The first step of the VA (Variable Approach) method is to modify the original condition and the question, and then recheck the question.

The quesiton 1/(n-k) > 0 is equivalent to n-k>0 or n>k.

Since we have 2 variables (n and k) and 0 equations, C is most likely to be the answer. So, we should consider conditions 1) & 2) together first.

Conditions 1) & 2):
1/k < 0 ⇔ k < 0 ⇔ k ≤ -1
1/(n+2) > 0 ⇔ n+2 > 0 ⇔ n > -2 ⇔ n ≥ -1
Since n≠k, we have n > k.
Both conditions 1) & 2) are sufficient.

Since this is an integer question (one of the key question areas), we should also consider choices A and B by CMT(Common Mistake Type) 4(A).

Condition 1):
This condition provides us with no information about the variable n, so it is not sufficient.


Condition 2):
This condition provides us with no information about the variable k, so it is not sufficient.

Therefore, the answer is C.

Normally, in problems which require 2 equations, such as those in which the original conditions include 2 variables, or 3 variables and 1 equation, or 4 variables and 2 equations, each of conditions 1) and 2) provide an additional equation. In these problems, the two key possibilities are that C is the answer (with probability 70%), and E is the answer (with probability 25%). Thus, there is only a 5% chance that A, B or D is the answer. This occurs in common mistake types 3 and 4. Since C (both conditions together are sufficient) is the most likely answer, we save time by first checking whether conditions 1) and 2) are sufficient, when taken together. Obviously, there may be cases in which the answer is A, B, D or E, but if conditions 1) and 2) are NOT sufficient when taken together, the answer must be E.
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