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16 Sep 2014, 00:57
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If \(x^2 y^3 = 200\), what is the value of \(xy\)?
(1) \(y\) is an integer
(2) \(\frac{x}{y} = 2.5\)
(1) \(y\) is an integer
(2) \(\frac{x}{y} = 2.5\)
16 Sep 2014, 00:57
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Official Solution:
If \(x^2 y^3 = 200\), what is the value of \(xy\)?
(1) \(y\) is an integer.
\(y\) can be any positive integer, and for each value of \(y\), there will be two corresponding values of \(x\) to satisfy the equation \(x^2y^3=200\). For instance, if \(y=10\), then \(x^2y^3=x^2*1000=200\). This results in \(x=\frac{1}{\sqrt{5} }\) or \(x=-\frac{1}{\sqrt{5} }\). Consequently, there are infinite possible values for \(xy\). Not sufficient.
(2) \(\frac{x}{y}=2.5\).
Upon cross-multiplying, we get \(x=2.5y\). Plugging this into our original equation, we have \((2.5y)^2*y^3=6.25y^5=200\). Simplifying, we get \(y^5=32\), which implies \(y=2\). Then, \(x=2.5y=5\). Therefore, \(xy=10\). Sufficient.
Answer: B
If \(x^2 y^3 = 200\), what is the value of \(xy\)?
(1) \(y\) is an integer.
\(y\) can be any positive integer, and for each value of \(y\), there will be two corresponding values of \(x\) to satisfy the equation \(x^2y^3=200\). For instance, if \(y=10\), then \(x^2y^3=x^2*1000=200\). This results in \(x=\frac{1}{\sqrt{5} }\) or \(x=-\frac{1}{\sqrt{5} }\). Consequently, there are infinite possible values for \(xy\). Not sufficient.
(2) \(\frac{x}{y}=2.5\).
Upon cross-multiplying, we get \(x=2.5y\). Plugging this into our original equation, we have \((2.5y)^2*y^3=6.25y^5=200\). Simplifying, we get \(y^5=32\), which implies \(y=2\). Then, \(x=2.5y=5\). Therefore, \(xy=10\). Sufficient.
Answer: B
22 Aug 2016, 05:24
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I think this is a high-quality question and I agree with explanation.
