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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.

Condition 1)

\(x = |x|\)

\(=> x ≥ 0\)

In inequality questions, the law “Question is King” tells us that if the solution set of the question does not include the solution set of a condition, then the condition is not sufficient.

Condition 1 is not sufficient.

Condition 2)

\(x^2-x =0\)

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

\(=> x = 0\) or \(x = 1\)

If \(x = 0\), then the answer is “no”.

If \(x = 1\), then the answer is “yes”.

Since we don’t have a unique solution, condition 2) is not sufficient.

Conditions 1) & 2)

The two conditions give \(x = 0\) or \(x = 1\).

They are not sufficient, when taken together, by the argument above.

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.

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