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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, and then recheck the question.

\(y=px^2-4x+q\) has a minimum value when \(x = \frac{-(-4)}{2p} = \frac{2}{p}.\)

Thus, the question asks for the value of \(p\).

Since only condition 1) gives us information about p, only condition 1) is sufficient.

Therefore, A is the answer.

Answer: A

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