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

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

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29 Oct 2010, 23:42
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Question Stats:

70% (01:35) correct 30% (02:31) wrong based on 334 sessions

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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
[Reveal] Spoiler: OA

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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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30 Oct 2010, 02:03
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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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Re: If x does not equal to 0 and x = root(4xy - 4y^2), then in [#permalink]

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19 Feb 2011, 04:11
is it possible to solve this one by plugging in numbers? any help will be appreciated.

thanks.
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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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19 Feb 2011, 06:49
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

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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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19 Feb 2011, 07:02
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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Re: If x does not equal to 0 and x = root(4xy - 4y^2), then in [#permalink]

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19 Feb 2011, 07:42
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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.

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

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21 Nov 2013, 02:06
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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

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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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21 Nov 2013, 02:15
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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: $$x^2 = 4xy - 4y^2$$ --> $$x^2-4xy+4y^2=(x-2y)^2=0$$ --> $$x=2y$$.

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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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21 Nov 2013, 02:16
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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Re: If x does not equal to 0 and x = root(4xy - 4y^2), then in [#permalink]

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19 Dec 2014, 19:14
Hello from the GMAT Club BumpBot!

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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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11 Jul 2015, 13:12
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!

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

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11 Dec 2015, 23:08
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?

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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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12 Dec 2015, 08:31
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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Re: If x does not equal to 0 and x = root(4xy - 4y^2), then in [#permalink]

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23 Aug 2017, 06:20
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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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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25 Aug 2017, 11:05
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] 25 Aug 2017, 11:05
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