jayanti wrote:Is �x�< 1?
(1) �x + 1� = 2�x - 1�
(2) �x - 3� ≠0
Statement 1: �x + 1� = 2�x - 1|.
Case 1:
x + 1 = 2(x-1)
x + 1 = 2x - 2
x=3.
Case 2:
x + 1 = -2(x-1)
x + 1 = -2x + 2
3x = 1
x = 1/3.
Since |3| > 1 and |1/3| < 1, insufficient.
Statement 2: �x - 3� ≠0.
Thus, x ≠3.
Since x can be any value other than 3, insufficient.
Statements 1 and 2 combined:
Since statement 2 indicates that x ≠3, the only value that satisfies both statements is x = 1/3.
Sufficient.
The correct answer is
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