utkalnayak wrote:Is x > 1?
1. (x+1)(|x|-1) > 0
2. |x| < 5
Statement 1: (x+1)(|x|-1) > 0
Determine the CRITICAL POINTS: the values where (x+1)(|x|-1) = 0.
(x+1)(|x|-1) = 0 when x=-1 or x=1.
To determine the ranges where (x+1)(|x|-1) > 0, test one value to the left and right of each critical point.
x<-1:
If we plug x=-2 into (x+1)(|x|-1) > 0, we get:
(-2+1)(|-2|-1) > 0
(-1)(1) > 0
-1 > 0.
Doesn't work.
Thus, x<-1 is not a valid range.
-1<x<1:
If we plug x=0 into (x+1)(|x|-1) > 0, we get:
(0+1)(|0|-1) > 0
(1)(-1) > 0
-1 > 0.
Doesn't work.
Thus, -1<x<1 is not a valid range.
x>1:
If we plug x=2 into (x+1)(|x|-1) > 0, we get:
(2+1)(|2|-1) > 0
(3)(1) > 0
3 > 0.
This works.
Thus, x>1 is a valid range.
Since x>1 is the only valid range, (x+1)(|x|-1) > 0 implies that x>1.
SUFFICIENT.
Statement 2: |x| < 5
It's possible that x=2, in which case x>1.
It's possible that x=0, in which case x<1.
INSUFFICIENT.
The correct answer is
A.
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