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If xy^2 = 12 and xy = 4, then x =

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If xy^2 = 12 and xy = 4, then x = [#permalink] New post 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
[Reveal] Spoiler: OA

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Re: If xy^2 = 12 and xy = 4, then x = [#permalink] New post 20 May 2016, 17:37
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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.
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Re: If xy^2 = 12 and xy = 4, then x = [#permalink] New post 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] New post 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] New post 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] New post 22 Jul 2017, 14:29
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Re: If xy^2 = 12 and xy = 4, then x = [#permalink] New post 11 Jun 2019, 11:28
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The simplest way to solve is a fast substitution

\(xy = 4\) and \(xy^2 = 12\)

\(y^2 = \frac{12}{x} and y= \frac{4}{x}\)

\(16x = 12x^2\)

\(16x - 12x^2=0\)

\(4x-3x^2=0\)

\(x(4-3x)= 0\)

\(x=0\) 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] New post 11 Jun 2019, 11:35
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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 = 16

The other given equation is: xy² = 12

Divide the top equation by the bottom equation to get: x²y²/xy² = 16/12
Simplify: x = 16/12 = 4/3

Answer: E

Cheers,
Brent
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Re: If xy^2 = 12 and xy = 4, then x =   [#permalink] 11 Jun 2019, 11:35
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