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Forget conventional ways of solving math questions. In DS, VA (Variable Approach) method is the easiest and quickest way to find the answer without actually solving the problem. Remember that equal number of variables and independent equations ensures a solution.

The first step of VA(Variable Approach) method is modifying the original condition and the question, and rechecking the number of variables and the number of equations.

To find the value of f(x), we can plug in 0 for the variables x and y.

Then we have \(f(0+0) = f(0) ∙ f(0) or f(0) = {f(0)}^2\)

\({f(0)}^2 - f(0) = 0\)

\(f(0) { f(0) – 1 } = 0\)

Then \(f(0) = 0 or f(0) = 1.\)

Then f(0) becomes an unknown variable and we have 1 variable. D is most likely to be the answer.

Condition 1)

Since f(0) > 0, we have f(0) = 1.

This is sufficient.

Condition 2)

Both 0 and 1 are integers, f(0) = 0 or f(0) = 1.

Thus, this is not sufficient.

Therefore, A is the answer.

Answer: A

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