Is |X| <1 ?
1) |X+1| = 2|X-1|
2) |X-3| > 0.
Statement 1: |x+1| = 2|x-1|
Case 1:
x+1 = 2x-2
3 = x
Case 2:
x+1 = -(2x-2)
3x = 1
x = 1/3.
Confirm that both solutions are valid:
|3+1| = 2|3-1|
4=4.
|1/3 + 1| = 2|1/3 - 1|
4/3 = 4/3.
Since x=3 and x=1/3 are both valid solutions, we cannot determine whether |x|<1.
INSUFFICIENT.
Statement 2: |x-3| > 0
x can be any value other than 3.
INSUFFICIENT.
Statements 1 and 2 combined:
Since x=3 does not satisfy statement 2, both statements are satisfied only when x=1/3.
Thus, |x|<1.
SUFFICIENT.
The correct answer is
C.
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