jainpiyushjain wrote:I am having difficulty understanding the official explanation, can you please help.
Is x > 1 ?
(1) (x + 1)(|x| - 1) > 0
(2) |x| < 5
OA A
Thank you
Statement 1: (x + 1)(|x| - 1) > 0
The CRITICAL POINTS are -1 and 1.
These are the only values where (x + 1)(|x| - 1) = 0.
To determine the ranges where (x + 1)(|x| - 1) > 0, test one value to the left and right of each critical point.
x < -1:
Plug x = -2 into (x + 1)(|x| - 1) > 0
(-2 + 1)(|-2| - 1) > 0
-1 * 1 > 0.
- 1 > 0.
Doesn't work.
x < -1 is NOT a valid range.
-1 < x < 1:
Plug x = 0 into (x + 1)(|x| - 1) > 0
(0 + 1)(|0| - 1) > 0
1 * -1 > 0.
- 1 > 0.
Doesn't work.
-1<x<1 is NOT a valid range.
x > 1:
Plug x = 2 into (x + 1)(|x| - 1) > 0:
(2 + 1)(|2| - 1) > 0
3 * 1 > 0.
3 > 0.
This works.
x > 1 is a valid range.
Since x>1 is the only valid range, SUFFICIENT.
Statement 2: |x| < 5
If x=4, then x>1.
If x=-4, then x<1.
INSUFFICIENT.
The correct answer is
A.
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