NandishSS wrote:Is (x + 1)/(x - 3) < 0 ?
(1) -1 < x < 1
(2) x^2 - 4 < 0
The CRITICAL POINTS are x=-1 and x=3.
These are the only values where the left side is either 0 or undefined.
To determine where (x + 1)/(x - 3) < 0, test one value to the left of -1, one value between -1 and 3, and one value to the right of 3.
If x=-2, then (x+1)/(x-3) = (-2+1)/(-2-3) = 1/5.
If x=0, then (x+1)/(x-3) = (0+1)/(0-3) = -1/3.
If x=4, then (x+1)/(x-3) = (4+1)/(4-3) = 5.
Only the blue case -- which tests a value between -1 and 3 -- satisfies (x+1)/(x-3) < 0.
Implication:
(x+1)/(x-3) < 0 only if x is between -1 and 3.
Question stem, rephrased:
Is x between -1 and 3?
Statement 1: -1<x<1
Since -1<x<1, we know that x is between -1 and 3.
SUFFICIENT.
Statement 2: x² < 4
Case 1: x=0
In this case, x is between -1 and 3.
Case 2: x = -3/2
In this case, x is NOT between -1 and 3.
INSUFFICIENT.
The correct answer is
A.
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