Data Sufficiency

Hi prashanthichennupati,

This DS question has "conditional statements" in the ORIGINAL PROMPT, which almost never happens on the GMAT, so you don't have to "worry" about this showing up on Test Day. Using these conditions though, it's worth noting that Set K is an INFINITE set of numbers (you'd have to do some work to prove it though). Here's how you'd answer the question:

Is 12 in K? This is a Yes/NO Question, so we'll be looking to see if the answer is always yes, always no or inconsistent.

Fact 1 tells us 2 is in K.

From the first conditional statement, we know that -2 is also in K
From the second conditional statement, we know that since 2 and -2 are in K, then -4 is in K also.
Since, 2, -2 and -4 are there, so are 8 and -8, then so are 16, -16, 32 and -32, etc.
There's no way to know if 12 is there or not.
Fact 1 is INSUFFICIENT

Fact 2 tells us that 3 is in K

From the first conditional statement, we know that -3 is also in K
From the second conditional statement, we know that since 3 and -3 are in K, then -9 is in K also.
Since 3, -3 and -9 are there, so are 27 and -27, then so are 81 and -81, etc.
There's no way to know if 12 is there or not.
Fact 2 is INSUFFICIENT

Combining Facts, we know that 2 and 3 are in K
From the first conditional statement, we know that -2 and -3 are also in K
From the second conditional statement, we know that -4, -6 and -9 are also in K
Since -2 and -6 are in K, then we know that 12 is in K.
SUFFICIENT TOGETHER

Final Answer: C

GMAT assassins aren't born, they're made,
Rich