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07 Apr 2023, 12:57
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Official Solution:
Does \(x = y\) ?
(1) \(\frac{xy}{x + y} = 0\)
To satisfy the above equation, the numerator must be zero. Hence, either \(x\) only or \(y\) only or both are equal to zero. If both \(x\) and \(y\) were equal to zero, so if \(x = y = 0\) were true, then \(x+y\) would also be zero. However, since division by zero is undefined, having \(x = y = 0\) would make \(\frac{xy}{x+y}\) undefined rather than equal to zero. Therefore, \(x\) cannot be equal to \(y\). Sufficient
(2) \(xy = 0\)
This implies that either \(x\) or \(y\) or both are equal to zero. Thus, it could be that \(x=y=0\). However, it's also possible that only one of them is zero and the other is any other number. Therefore, this statement alone is not sufficient to answer the question.
Answer: A
Does \(x = y\) ?
(1) \(\frac{xy}{x + y} = 0\)
To satisfy the above equation, the numerator must be zero. Hence, either \(x\) only or \(y\) only or both are equal to zero. If both \(x\) and \(y\) were equal to zero, so if \(x = y = 0\) were true, then \(x+y\) would also be zero. However, since division by zero is undefined, having \(x = y = 0\) would make \(\frac{xy}{x+y}\) undefined rather than equal to zero. Therefore, \(x\) cannot be equal to \(y\). Sufficient
(2) \(xy = 0\)
This implies that either \(x\) or \(y\) or both are equal to zero. Thus, it could be that \(x=y=0\). However, it's also possible that only one of them is zero and the other is any other number. Therefore, this statement alone is not sufficient to answer the question.
Answer: A
