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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.

Modifying the question:

In order for \(4x^2 – y^2\) to be odd, \(y^2\) must be odd since \(4x^2\) is always even. This is equivalent to y being odd. So, the question asks if y is odd. Thus, the answer is B.

Condition 1)

If \(y\) is an odd number, then both \(2x + y\) and \(2x – y\) are odd numbers and \((2x+y)(2x-y)\) is an odd number.

If \(y\) is an even number, both \(2x + y\) and \(2x – y\) are even numbers and \((2x+y)(2x-y)\) is an even number.

Since the question does not have a unique answer, condition 1) is not sufficient.

Therefore, the answer is B.

Answer: B

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