IS (x+1)/(x-3) <0?
(1) -1<x<1
(2) X^2-4<0.
(1) -1<x<1
(2) X^2-4<0.
Hi abhasjha,
For this DS question, we can TEST Values and/or use Number Properties. Here's how using Number Properties can help you to make quick work of this question...
We're asked if (X+1)/(X-3) < 0. This is a YES/NO question.
*Note, the only way to get a "YES" answer is if the numerator and denominator are DIFFERENT signs (one positive, one negative).
Fact 1: -1 < X < 1
With this restriction, we can make some quick deductions about the numerator and denominator:
The numerator WILL be POSITIVE (0 < numerator < 2).
The denominator WILL be NEGATIVE (-4 < denominator < -2)
Under these conditions, we will ALWAYS end up with a negative fraction, so the answer to the question is ALWAYS YES.
Fact 1 is SUFFICIENT.
Fact 2: X^2 - 4 < 0
This gives us...
X^2 < 4
-2 < X < 2
Since this "range' of values includes the range from Fact 1, we know that we can get a YES answer.
IF....
-2 < X < -1 though, we end up with a NEGATIVE numerator AND a NEGATIVE denominator, which gives us a POSITIVE fraction. In this situation, the answer to the question is NO.
Fact 2 is INSUFFICIENT
Final Answer: A
GMAT assassins aren't born, they're made,
Rich
