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

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Math Expert
Joined: 02 Sep 2009
Posts: 56304
If xy^2 = 12 and xy = 4, then x =  [#permalink]

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01 May 2018, 05:23
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Question Stats:

84% (00:57) correct 16% (01:49) wrong based on 69 sessions

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

A. 1

B. 2

C. $$\sqrt{3}$$

D. $$\frac{2}{3}$$

E. $$\frac{4}{3}$$

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Manager
Joined: 05 Dec 2017
Posts: 53
Location: India
WE: Analyst (Commercial Banking)
Re: If xy^2 = 12 and xy = 4, then x =  [#permalink]

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01 May 2018, 05:46
Bunuel wrote:
If $$xy^2 = 12$$ and $$xy = 4$$, then x =

A. 1

B. 2

C. $$\sqrt{3}$$

D. $$\frac{2}{3}$$

E. $$\frac{4}{3}$$

$$xy^2 = 12$$ and $$xy = 4$$
now replace $$xy = 4$$ in $$y*xy$$ = 12
y = 3
Replacing y in $$xy$$= 12

X = $$\frac{4}{3}$$

Option E
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Re: If xy^2 = 12 and xy = 4, then x =  [#permalink]

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01 May 2018, 05:51
Bunuel wrote:
If $$xy^2 = 12$$ and $$xy = 4$$, then x =

A. 1

B. 2

C. $$\sqrt{3}$$

D. $$\frac{2}{3}$$

E. $$\frac{4}{3}$$

Given : $$xy^2 = 12$$ or $$xy*y = 12$$ -----(I)

&

$$xy = 4$$-----(II)

Using I and II

$$4y = 12$$

$$y = 3$$

Therefore , $$x (3)^2 = 12$$

$$x = \frac{12}{9}$$

$$x = \frac{4}{3}$$

(E)
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If xy^2 = 12 and xy = 4, then x =  [#permalink]

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02 May 2018, 08:13
Bunuel wrote:
If $$xy^2 = 12$$ and $$xy = 4$$, then x =

A. 1

B. 2

C. $$\sqrt{3}$$

D. $$\frac{2}{3}$$

E. $$\frac{4}{3}$$

$$xy^2 = 12$$ and $$xy=4$$

$$x*y*y = 12$$, i.e., $$(x*y)*y=12$$
$$4*y=12$$
$$y=3$$

$$x=?$$
$$xy=4$$, and $$y=3$$
$$x*3=4$$
$$x =\frac{4}{3}$$

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Re: If xy^2 = 12 and xy = 4, then x =  [#permalink]

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02 May 2018, 10:27
Bunuel wrote:
If $$xy^2 = 12$$ and $$xy = 4$$, then x =

A. 1

B. 2

C. $$\sqrt{3}$$

D. $$\frac{2}{3}$$

E. $$\frac{4}{3}$$

Let’s first establish that both x and y must be positive. Since xy^2 = 12, we see that x must be positive. And since xy = 4, we see that y must also be positive.

Dividing the first equation by the second, we have:

y = 3

Substituting y = 3 into the second equation, we have:

x(3) = 4

x = 4/3

Alternate Solution:

Let’s rewrite the first equation as:

x(xy) = 12

We are given that xy = 9, so we can substitute:

x(9) = 12

x = 12/9 = 4/3

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Re: If xy^2 = 12 and xy = 4, then x =  [#permalink]

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20 Aug 2018, 03:04
Bunuel wrote:
If $$xy^2 = 12$$ and $$xy = 4$$, then x =

A. 1

B. 2

C. $$\sqrt{3}$$

D. $$\frac{2}{3}$$

E. $$\frac{4}{3}$$

1.divide:
$$xy^2 = 12$$
/$$xy = 4$$
y=3
2. substitute:
x=4/3 => E
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Re: If xy^2 = 12 and xy = 4, then x =  [#permalink]

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20 Aug 2018, 06:55
Bunuel wrote:
If $$xy^2 = 12$$ and $$xy = 4$$, then x =

A. 1

B. 2

C. $$\sqrt{3}$$

D. $$\frac{2}{3}$$

E. $$\frac{4}{3}$$

$$y = \frac{xy^2}{xy}$$

So, $$y = \frac{12}{4}$$

Or, $$y = 3$$

We know that $$xy^2 = 12$$

Or, $$9x = 12$$

Or, $$x = \frac{4}{3}$$, Hence Answer must be (E)
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Manager
Joined: 20 Jul 2018
Posts: 87
GPA: 2.87
Re: If xy^2 = 12 and xy = 4, then x =  [#permalink]

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20 Aug 2018, 09:10
$$xy^2 = 12$$
$$xy*y = 12$$
$$4y = 12$$
$$y=3$$
so
$$3x=4$$
$$x=\frac{4}{3}$$
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Re: If xy^2 = 12 and xy = 4, then x =   [#permalink] 20 Aug 2018, 09:10
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