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If xy^2 = 12 and xy = 4, then x = [#permalink]
20 May 2016, 17:35
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Question Stats:
87% (00:59) correct
12% (01:38) wrong based on 24 sessions
If \(xy^2 = 12\) and \(xy = 4\), then x = A. 1 B. 2 C. \(\sqrt{3}\) D. \(\frac{2}{3}\) E. \(\frac{4}{3}\) Practice Questions Question: 8 Page: 82
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Re: If xy^2 = 12 and xy = 4, then x = [#permalink]
20 May 2016, 17:37
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ExplanationFrom the given equations \(xy^2 = 12\) and \(xy= 4\), it follows that \(12 = xy^2 = (xy)y= 4y\), and so y = 3. Substituting y = 3 in the equation xy = 4 gives 3x = 4, or Thus the correct answer is Choice E.
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Re: If xy^2 = 12 and xy = 4, then x = [#permalink]
17 Mar 2017, 10:18
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sandy wrote: Explanation
From the given equations \(xy^2 = 12\) and \(xy= 4\), it follows that \(12 = xy^2 = (xy)y= 4y\), and so y = 3. Substituting y = 3 in the equation xy = 4 gives 3x = 4, or Thus the correct answer is Choice E. I dont understand why: \(12 = xy^2 = (xy)y= 4y\), Someone that can clarify this?



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Re: If xy^2 = 12 and xy = 4, then x = [#permalink]
17 Mar 2017, 13:09
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Hey it is given that \(xy = 4\) Now \(12 = xy^2\) can be rewritten as \(12 = (xy) \times y\) Put value of xy from the first equation \(12 = 4 \times y\) or \(y = 3\)
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Re: If xy^2 = 12 and xy = 4, then x = [#permalink]
18 Mar 2017, 02:25
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Thank you Sandy, this helps a lot!



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Re: If xy^2 = 12 and xy = 4, then x = [#permalink]
22 Jul 2017, 14:29
Great!



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Re: If xy^2 = 12 and xy = 4, then x = [#permalink]
11 Jun 2019, 11:28
The simplest way to solve is a fast substitution \(xy = 4\) and \(xy^2 = 12\) \(y^2 = \frac{12}{x} and y= \frac{4}{x}\) \(16x = 12x^2\) \(16x  12x^2=0\) \(4x3x^2=0\) \(x(43x)= 0\) \(x=0\) ans \(4=3x >>> x=\frac{4}{3}\) \(x=0\) is not among the solution bur \(x=\frac{4}{3}\) YES E is the answer
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Re: If xy^2 = 12 and xy = 4, then x = [#permalink]
11 Jun 2019, 11:35
sandy wrote: If \(xy^2 = 12\) and \(xy = 4\), then x = A. 1 B. 2 C. \(\sqrt{3}\) D. \(\frac{2}{3}\) E. \(\frac{4}{3}\) Practice Questions Question: 8 Page: 82
Another approach: If xy = 4, then: (xy)² = 4² Simplify: x²y² = 16The other given equation is: xy² = 12Divide the top equation by the bottom equation to get: x²y²/ xy² = 16/12Simplify: x = 16/12 = 4/3 Answer: E Cheers, Brent
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