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Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.
The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question.
The question can be modified as follows:
\((x-1)^3< (x-1)\)
\(=> (x-1)^3- (x-1) < 0\)
\(=> (x-1)((x-1)^2- 1) < 0\)
\(=> (x-1)((x-1)+1)((x-1)-1) < 0\)
\(=> x(x-1)(x-2) < 0\)
\(=> x < 0\) or \(1 < x < 2\)
So, the question asks whether \(x < 0\) or \(1 < x < 2\).
Condition 1)
Since the set of the question doesn’t include that of condition 1), it is not sufficient.
Condition 2)
Since the set of the question includes that of condition 2), it is sufficient.
Therefore, the answer is B.
Answer: B
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