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09 Apr 2010, 20:14
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B
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Difficulty:
55%
(hard)
Question Stats:
60% (01:59) correct
40%
(02:03)
wrong
based on 719
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If \(x^2 y^3 = 200\), what is the value of \(xy\)?
(1) y is an integer
(2) x/y = 2.5
(1) y is an integer
(2) x/y = 2.5
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14 Apr 2010, 02:53
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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
(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
General Discussion
21 Aug 2011, 19:58
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x^2 * y^3 = 200
1. not sufficient
as different y will yield different x. hence different xy.
2. sufficient
x/y = 2.5
(2.5y)^2 * y ^3 = 200
25/4 y ^5 = 200 = >y =2
x =5
Answer is B.
1. not sufficient
as different y will yield different x. hence different xy.
2. sufficient
x/y = 2.5
(2.5y)^2 * y ^3 = 200
25/4 y ^5 = 200 = >y =2
x =5
Answer is B.
