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# If x≠0 and x = (4xy-4y^2)^1/2, then, in terms of y, x =

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Manager
Joined: 19 Oct 2010
Posts: 214
Location: India
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If x≠0 and x = (4xy-4y^2)^1/2, then, in terms of y, x =  [#permalink]

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26 Mar 2011, 07:34
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Difficulty:

45% (medium)

Question Stats:

66% (01:20) correct 34% (02:16) wrong based on 130 sessions

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If x≠0 and $$x = \sqrt{4xy-4y^2}$$, then, in terms of y, x =

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

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petrifiedbutstanding

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Joined: 20 Dec 2010
Posts: 1877
Re: If x≠0 and x = (4xy-4y^2)^1/2, then, in terms of y, x =  [#permalink]

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26 Mar 2011, 07:51
2
3
petrifiedbutstanding wrote:
If x≠0 and x = \sqrt{4xy-4y^2} , then, in
terms of y, x =

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

$$x = \sqrt{4xy-4y^2}$$
Square both sides;

$$x^2 = 4xy-4y^2$$
$$x^2+4y^2-4xy=0$$
$$(x-2y)^2=0$$ Note: $$(a-b)^2=a^2+b^2-2ab$$
$$(x-2y)^2=0$$
$$x-2y=0$$
$$x=2y$$

Ans: "A"
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##### General Discussion
Manager
Joined: 11 Feb 2011
Posts: 121
Re: If x≠0 and x = (4xy-4y^2)^1/2, then, in terms of y, x =  [#permalink]

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26 Mar 2011, 07:49
1
@petrifiedbutstanding:-

Well it means :
Squaring we get:
x^2 =4y(x-y)
Assume X^2=m >>>>>>>>>>>1
Than ,m=4y(m^1/2-y)
on solving:m-4y(m)^1/2+4y^2=0 >> quadratic in y s solve for y.
Y comes out to be =(m^1/2)/2

Hence,put m =x^2 from 1.

So x=2y

The answer shd be 2y. i.e A.

Pls confirm it .
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Manager
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Re: If x≠0 and x = (4xy-4y^2)^1/2, then, in terms of y, x =  [#permalink]

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26 Mar 2011, 07:53
If i am correct donot hesitate to kudo me .

Your support is required to bang GMAT.
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Manager
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Re: If x≠0 and x = (4xy-4y^2)^1/2, then, in terms of y, x =  [#permalink]

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26 Mar 2011, 07:57
Thnkss Flukee!!:)
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Re: If x≠0 and x = (4xy-4y^2)^1/2, then, in terms of y, x =  [#permalink]

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26 Mar 2011, 13:27
x^2 = 4xy-4(y^2) => (x-2y)^2 = 0

=> x = 2y

Retired Moderator
Joined: 16 Nov 2010
Posts: 1458
Location: United States (IN)
Concentration: Strategy, Technology
Re: If x≠0 and x = (4xy-4y^2)^1/2, then, in terms of y, x =  [#permalink]

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26 Mar 2011, 18:20
x = sqrt{4xy-4y^2}

Squaring both side :

=> x^2 = 4xy - 4y^2

Substituting answer choices, e.g., choice A :

=> (2y)^2 = 4*2y*y - 4y^2

=> 4y^2 - 8y^2 = - 4y^2

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

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

=> x = 2y

Note - I thought simplifying further would be faster and more accurate than plugging the answer choices in this case, but situations may vary.

Also, the OA seems to be wrong.
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Re: If x≠0 and x = (4xy-4y^2)^1/2, then, in terms of y, x =  [#permalink]

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14 Jul 2018, 19:11
petrifiedbutstanding wrote:
If x≠0 and $$x = \sqrt{4xy-4y^2}$$, then, in terms of y, x =

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

We first square both sides of the equation and then simplify. We have:

x^2 = 4xy - 4y^2

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

(2y - x)^2 = 0

2y - x = 0

2y = x

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Re: If x≠0 and x = (4xy-4y^2)^1/2, then, in terms of y, x = &nbs [#permalink] 14 Jul 2018, 19:11
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