Hi Architj,
This question is at the "higher end" of the Algebra spectrum, but we can be strategic with it, use the answers to our advantage and TEST VALUES....
We're given that (X^2 -6X - 8)/(3X^2 + 14X + 16) < 0.
For this fraction to be negative, there are clearly some specific limitations to what's possible. I'm going to start with the simplest value possible:
IF....X = 0
we end up with: (-8)/(16) = -1/2
This fits the inequality, so X = 0 IS a possible solution.
Eliminate Answers D and E.
IF...X = 1
we end up with: (-13)/(33) = negative fraction
This fits with the inequality, so X = 1 IS a possible solution.
Eliminate Answer B.
With the two remaining answers, we have heavy "overlap", so we have to look for a value that appears in one of the options, but NOT in the other...
IF...X = -2
we end up with: (8)/(0) = undefined.
This DOES NOT fit with the inequality, so X = -2 is NOT a possible solution
Eliminate Answer A.
There's only one answer left...
Final Answer: C
GMAT assassins aren't born, they're made,
Rich
