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Manager  Status: Current MBA Student
Joined: 19 Nov 2009
Posts: 96
Concentration: Finance, General Management
GMAT 1: 720 Q49 V40 If x does not equal to 0 and x = root(4xy - 4y^2), then in  [#permalink]

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3
15 00:00

Difficulty:   45% (medium)

Question Stats: 68% (01:59) correct 32% (02:50) wrong based on 393 sessions

### HideShow timer Statistics If x does not equal to 0 and $$x = \sqrt{4xy - 4 y^2}$$, then in terms of y, x = ?

A. 2y
B. y
C. y/2
D. 4y^2/(1-4y)
E. -2y
Retired Moderator Joined: 02 Sep 2010
Posts: 755
Location: London
Re: If x does not equal to 0 and x = root(4xy - 4y^2), then in  [#permalink]

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3
5
tonebeeze wrote:
If x does not = 0 and $$x = \sqrt{4xy-4y^2}$$ , then in terms of y, x =

a. 2y
b. y
c. $$y/2$$
d. $$-4^2/1-4y$$
e. -2y

$$x = \sqrt{4xy-4y^2}$$

Square both sides

$$x^2=4xy-4y^2$$
$$x^2+4y^2-4xy=0$$
$$(x-2y)^2=0$$
$$\Rightarrow x-2y=0$$
$$x=2y$$

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##### General Discussion
Senior Manager  Joined: 08 Nov 2010
Posts: 313
Re: If x does not equal to 0 and x = root(4xy - 4y^2), then in  [#permalink]

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is it possible to solve this one by plugging in numbers? any help will be appreciated.

thanks.
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Manager  Joined: 14 Feb 2011
Posts: 166
Re: If x does not equal to 0 and x = root(4xy - 4y^2), then in  [#permalink]

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Since the question and options both involve variables, plugging the numbers is probably going to make it more complicated. Better to solve it by squaring both sides and solving for x
Senior Manager  Joined: 08 Nov 2010
Posts: 313
Re: If x does not equal to 0 and x = root(4xy - 4y^2), then in  [#permalink]

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1
well, i kinda figured it out, and i think it will be good to know both systems to solve.
in order to make it more simpler i will plug in Y=1

so i will have

x^2=4x-4
x^2-4x+4=0
(x-2)^2=0
x=2.

if u look on the answers - and plug y=1, the only one that will give u x=2 is A.

therefore u have the answer very easy and quickly with almost no algebra.

what do u think?

thanks.
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Manager  Joined: 14 Feb 2011
Posts: 166
Re: If x does not equal to 0 and x = root(4xy - 4y^2), then in  [#permalink]

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1
Well - even after plugging you still need to square both sides and solve for x and then you need to plug it in four choices ( which is up to five extra steps - it just so happens that in this case, only one choice is suitable). Therefore, as a general rule, I would prefer to not plug in if both question and choices have variables.
Intern  Joined: 16 Nov 2013
Posts: 28
Location: United States
Concentration: Entrepreneurship, General Management
GPA: 3.49
If x does not equal to 0 and x = root(4xy - 4y^2), then in  [#permalink]

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1
If x does not equal to 0 and $$x = \sqrt{4xy - 4 y^2}$$, then in terms of y, x = ?

A. 2y
B. y
C. y/2
D. 4y^2/(1-4y)
E. -2y
Math Expert V
Joined: 02 Sep 2009
Posts: 56266
Re: If x does not equal to 0 and x = root(4xy - 4y^2), then in  [#permalink]

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2
registerincog wrote:
If x does not equal to 0 and $$x = \sqrt{4xy - 4 y^2}$$, then in terms of y, x = ?

A. 2y
B. y
C. y/2
D. 4y^2/(1-4y)
E. -2y

Square the expression: $$x^2 = 4xy - 4y^2$$ --> $$x^2-4xy+4y^2=(x-2y)^2=0$$ --> $$x=2y$$.

_________________
Math Expert V
Joined: 02 Sep 2009
Posts: 56266
Re: If x does not equal to 0 and x = root(4xy - 4y^2), then in  [#permalink]

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Bunuel wrote:
registerincog wrote:
If x does not equal to 0 and $$x = \sqrt{4xy - 4 y^2}$$, then in terms of y, x = ?

A. 2y
B. y
C. y/2
D. 4y^2/(1-4y)
E. -2y

Square the expression: $$x^2 = 4xy - 4y^2$$ --> $$x^2-4xy+4y^2=(x-2y)^2=0$$ --> $$x=2y$$.

Similar question to practice: if-x-0-and-x-root-8xy-16y-2-then-in-terms-of-y-x-140869.html
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Intern  Joined: 22 Dec 2014
Posts: 34
Re: If x does not equal to 0 and x = root(4xy - 4y^2), then in  [#permalink]

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tonebeeze wrote:
If x does not equal to 0 and $$x = \sqrt{4xy - 4 y^2}$$, then in terms of y, x = ?

A. 2y
B. y
C. y/2
D. 4y^2/(1-4y)
E. -2y

This is not a 700+ question!
Intern  Joined: 14 Oct 2014
Posts: 3
If x does not equal to 0 and x = root(4xy - 4y^2), then in  [#permalink]

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Bunuel wrote:
registerincog wrote:
If x does not equal to 0 and $$x = \sqrt{4xy - 4 y^2}$$, then in terms of y, x = ?

A. 2y
B. y
C. y/2
D. 4y^2/(1-4y)
E. -2y

Square the expression: $$x^2 = 4xy - 4y^2$$ --> $$x^2-4xy+4y^2=(x-2y)^2=0$$ --> $$x=2y$$.

Can you explain how you were able to get to (x-2y)^2? What is the strategy to know how to determine that quickly?
Math Expert V
Joined: 02 Sep 2009
Posts: 56266
Re: If x does not equal to 0 and x = root(4xy - 4y^2), then in  [#permalink]

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gmatczar wrote:
Bunuel wrote:
registerincog wrote:
If x does not equal to 0 and $$x = \sqrt{4xy - 4 y^2}$$, then in terms of y, x = ?

A. 2y
B. y
C. y/2
D. 4y^2/(1-4y)
E. -2y

Square the expression: $$x^2 = 4xy - 4y^2$$ --> $$x^2-4xy+4y^2=(x-2y)^2=0$$ --> $$x=2y$$.

Can you explain how you were able to get to (x-2y)^2? What is the strategy to know how to determine that quickly?

This is basic algebra.

$$a^2 - 2ab + b^2 = (a - b)^2$$.
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Status: Founder & CEO
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Posts: 6923
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Re: If x does not equal to 0 and x = root(4xy - 4y^2), then in  [#permalink]

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tonebeeze wrote:
If x does not equal to 0 and $$x = \sqrt{4xy - 4 y^2}$$, then in terms of y, x = ?

A. 2y
B. y
C. y/2
D. 4y^2/(1-4y)
E. -2y

We can square both sides of the given equation and obtain:

x^2 = 4xy - 4y^2

x^2 - 4xy + 4y^2 = 0

(x - 2y)(x - 2y) = 0

(x - 2y)^2 = 0

x - 2y = 0

x = 2y

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Re: If x does not equal to 0 and x = root(4xy - 4y^2), then in  [#permalink]

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_________________ Re: If x does not equal to 0 and x = root(4xy - 4y^2), then in   [#permalink] 28 Aug 2018, 15:04
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