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09 Apr 2010, 20:14
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60% (01:59) correct
40%
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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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Pure algebraic questions like this one are no longer part of the GMAT Data Sufficiency syllabus.
For relevant Data Sufficiency questions, please check the Data Sufficiency forum:
Data Sufficiency Forum
Data Sufficiency Forum
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
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.
21 Aug 2011, 22:44
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heyholetsgo
Even though, the solution has already been provided above, I want to point out something. The silver lining of DS questions is that you don't need to solve. If you know you will get a unique value, you are done.
Question stem: If \(x^2y^3=200\), what is xy?
Statement 1: y is an integer but x needn't be.
If y = 1, \(x = +-\sqrt{200}\)
If y = 2, x = +-5 etc
We do not know what xy is.
Statement 2:\(\frac{x}{y} = \frac{5}{2}\)
This means \(x = (\frac{5}{2})y\)
This value of x you can put above to get a unique value of y. (Since you will get y^5 = ... An odd power will give you only the positive solution here. )
Once you have the value of y, you get a unique value for x and hence you get a value for xy.
