Official Solution: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, and then recheck the question. In inequality questions, the law "Question is King" tells us that if the solution set of the question includes the solution set of the condition, then the condition is sufficient

Modifying the question:

\(x^2-x>0\)

\(x(x-1) > 0\)

\(x < 0\) or \(x > 1\) by the "LLGG" rule.

Condition 1): \(x > 0\)

Since the solution set of the question does not include the solution set of condition 1), condition 1) is not sufficient.

Condition 2):

\(x^3+x>0\)

\(x(x^2+1)>0\)

\(x>0\), since \(x^2+1 > 0\) is always true.

Condition 2) is equivalent to the condition 1), so it is not sufficient.

Conditions 1) & 2)

We have x >0 only from both conditions together.

Since the solution set of the question does not include the solution set of conditions 1) and 2) together, they are not sufficient.

Therefore, the answer is E.

Answer: E

If the original condition includes "1 variable", or "2 variables and 1 equation", or "3 variables and 2 equations" etc., one more equation is required to answer the question. If each of conditions 1) and 2) provide an additional equation, there is a 59% chance that D is the answer, a 38% chance that A or B is the answer, and a 3% chance that the answer is C or E. Thus, answer D (conditions 1) and 2), when applied separately, are sufficient to answer the question) is most likely, but there may be cases where the answer is A,B,C or E.

Answer: E

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