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16 Sep 2014, 01:05
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What is \(y\) in terms of \(x\)?
(1) \(\frac{1}{\frac{x}{y} + \frac{y}{x}} = \frac{1}{2}\)
(2) \(\frac{x}{y} - \frac{y}{x} = 0\)
(1) \(\frac{1}{\frac{x}{y} + \frac{y}{x}} = \frac{1}{2}\)
(2) \(\frac{x}{y} - \frac{y}{x} = 0\)
16 Sep 2014, 01:05
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Official Solution:
Let \(z\) equal \(\frac{x}{y}\).
Statement (1) by itself is sufficient. S1 gives that \(\frac{1}{z + \frac{1}{z}} = \frac{1}{2}\) or \(z + \frac{1}{z} = 2\) or \(z^2 + 1 = 2z\) or \((z - 1)^2 = 0\) from where \(z = 1\) and \(y = x\).
Statement (2) by itself is insufficient. S2 gives that \(z - \frac{1}{z} = 0\) or \(z = \frac{1}{z}\) or \(z^2 = 1\). This means that either \(y = x\) or \(y = -x\).
Answer: A
Let \(z\) equal \(\frac{x}{y}\).
Statement (1) by itself is sufficient. S1 gives that \(\frac{1}{z + \frac{1}{z}} = \frac{1}{2}\) or \(z + \frac{1}{z} = 2\) or \(z^2 + 1 = 2z\) or \((z - 1)^2 = 0\) from where \(z = 1\) and \(y = x\).
Statement (2) by itself is insufficient. S2 gives that \(z - \frac{1}{z} = 0\) or \(z = \frac{1}{z}\) or \(z^2 = 1\). This means that either \(y = x\) or \(y = -x\).
Answer: A
18 Sep 2016, 13:27
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Hi Bunuel,
Can you provide some helpful tips/tricks of when we should know/recognize to use the "substitute for z" technique? It makes sense when you know to do this, but how do you recognize that this technique is a more efficient way of approaching the problem?
Can you provide some helpful tips/tricks of when we should know/recognize to use the "substitute for z" technique? It makes sense when you know to do this, but how do you recognize that this technique is a more efficient way of approaching the problem?
