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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.

When the question asks for a ratio, a fraction, a percent, a proportion or a rate, if one of conditions provides a ratio and the other condition provides a number, the condition with a ratio could be sufficient.

This question asks for a ratio.

Condition 1) provides a number and condition 2) provides the ratio, x/y = 2.

Thus, condition 2) is likely to be sufficient.

Condition 1) :

If \(x = 3\) and \(y = 1\), then \(\frac{(x+3y)}{(3x-y)}\) = \(\frac{6}{8}\) = \(\frac{3}{4}\)

If \(x = 5\) and \(y = 2\), then \(\frac{(x+3y)}{(3x-y)}\) = \(\frac{16}{13}\)

Since we do not obtain a unique answer, condition 1) is not sufficient.

Condition 2) :

Since \(x = 2y\), \(\frac{(x+3y)}{(3x-y)} = \frac{5y}{5y} = 1\).

Condition 2) is sufficient.

Therefore, B is the answer.

Answer: B

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