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16 Sep 2014, 01:17
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If \(x\) and \(y\) are non-zero numbers, is \(\frac{x - y}{xy} > 0\) ?
(1) \(x < -1\) and \(y < -1\)
(2) \(xy > 1\)
(1) \(x < -1\) and \(y < -1\)
(2) \(xy > 1\)
16 Sep 2014, 01:17
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Official Solution:
If \(x\) and \(y\) are non-zero numbers, is \(\frac{x - y}{xy} > 0\) ?
(1) \(x < -1\) and \(y < -1\).
The above implies that both \(x\) and \(y\) are negative, and thus \(xy\) is positive. However, we still cannot determine the sign of \(x - y\). If \(x = -2\) and \(y = -3\), then \(x - y > 0\), and thus \(\frac{x - y}{xy} \) will be positive. However, if \(x = -3\) and \(y = -2\), then \(x - y < 0\), and thus \(\frac{x - y}{xy} \) will be negative. Not sufficient.
(2) \(xy > 1\)
As above, we know that \(xy\) is positive. However, as shown previously, this is not sufficient to determine an answer to the question.
(1)+(2) We have no new information. The examples we used in (1) satisfy (2) as well, so they are still valid when considering the statements together. Therefore, even taken together, the statements are still not sufficient.
Answer: E
If \(x\) and \(y\) are non-zero numbers, is \(\frac{x - y}{xy} > 0\) ?
(1) \(x < -1\) and \(y < -1\).
The above implies that both \(x\) and \(y\) are negative, and thus \(xy\) is positive. However, we still cannot determine the sign of \(x - y\). If \(x = -2\) and \(y = -3\), then \(x - y > 0\), and thus \(\frac{x - y}{xy} \) will be positive. However, if \(x = -3\) and \(y = -2\), then \(x - y < 0\), and thus \(\frac{x - y}{xy} \) will be negative. Not sufficient.
(2) \(xy > 1\)
As above, we know that \(xy\) is positive. However, as shown previously, this is not sufficient to determine an answer to the question.
(1)+(2) We have no new information. The examples we used in (1) satisfy (2) as well, so they are still valid when considering the statements together. Therefore, even taken together, the statements are still not sufficient.
Answer: E
26 Jan 2017, 11:42
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I have used a more algebraic approach, I hope it can help.
From the statement we can see that :
\(\frac{X-Y}{XY} > 0\) — Good shorcut to know
\(\frac{1}{X} - \frac{1}{Y} > 0\)
\(\frac{1}{X} > \frac{1}{Y}\)
To answer we need to compare X with Y, since neither Statement 1 nor Statement 2 gives us such information, the answer is E
From the statement we can see that :
\(\frac{X-Y}{XY} > 0\) — Good shorcut to know
\(\frac{1}{X} - \frac{1}{Y} > 0\)
\(\frac{1}{X} > \frac{1}{Y}\)
To answer we need to compare X with Y, since neither Statement 1 nor Statement 2 gives us such information, the answer is E
