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TAGS: GRE Prep Club Legend  Joined: 07 Jun 2014
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GRE 1: Q167 V156 WE: Business Development (Energy and Utilities)
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If xy^2 = 12 and xy = 4, then x = [#permalink]
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Expert's post 00:00

Question Stats: 89% (01:05) correct 10% (01:38) wrong based on 28 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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Sandy
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Try our free Online GRE Test GRE Prep Club Legend  Joined: 07 Jun 2014
Posts: 4809
GRE 1: Q167 V156 WE: Business Development (Energy and Utilities)
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Kudos [?]: 2083  , given: 397

Re: If xy^2 = 12 and xy = 4, then x = [#permalink]
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Expert's post
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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Sandy
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Re: If xy^2 = 12 and xy = 4, then x = [#permalink]
1
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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? GRE Prep Club Legend  Joined: 07 Jun 2014
Posts: 4809
GRE 1: Q167 V156 WE: Business Development (Energy and Utilities)
Followers: 135

Kudos [?]: 2083  , given: 397

Re: If xy^2 = 12 and xy = 4, then x = [#permalink]
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Expert's post
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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Sandy
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Re: If xy^2 = 12 and xy = 4, then x = [#permalink]
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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]
Great!
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Re: If xy^2 = 12 and xy = 4, then x = [#permalink]
Expert's post
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]
Expert's post
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

Cheers,
Brent
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Brent Hanneson – Creator of greenlighttestprep.com Sign up for my free GRE Question of the Day emails Re: If xy^2 = 12 and xy = 4, then x =   [#permalink] 11 Jun 2019, 11:35
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