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If xy ≠ 0 and x^2+4y^2=4xy, (x+y)/(x-y)=?

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If xy ≠ 0 and x^2+4y^2=4xy, (x+y)/(x-y)=?

by Max@Math Revolution » Tue Nov 13, 2018 3:32 am

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[Math Revolution GMAT math practice question]

If xy ≠ 0 and x^2+4y^2=4xy, (x+y)/(x-y)=?

A. 1
B. √2
C. √3
D. 2
E. 3
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by Brent@GMATPrepNow » Tue Nov 13, 2018 5:11 am
Max@Math Revolution wrote:[Math Revolution GMAT math practice question]

If xy ≠ 0 and x² + 4y² = 4xy, (x+y)/(x-y) = ?

A. 1
B. √2
C. √3
D. 2
E. 3
GIVEN: x² + 4y² = 4xy
Subtract 4xy from both sides to get: x² - 4xy + 4y² = 0
Factor left side to get: (x - 2y)(x - 2y) = 0
So, we can conclude that (x - 2y) = 0, which means x = 2y

Now take (x+y)/(x-y) and replace x with 2y to get:
(x + y)/(x - y) = (2y + y)/(2y - y)
= 3y/y
= 3

Answer: E

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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by Max@Math Revolution » Thu Nov 15, 2018 1:36 am
=>

x^2+4y^2=4xy
=> x^2-4xy+4y^2=0
=> (x-2y)^2=0
=> x=2y

Thus, (x+y)/(x-y) = (2y+y)/(2y-y) = 3y/y = 3.

Therefore, E is the answer.
Answer: E
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by fskilnik@GMATH » Thu Nov 15, 2018 8:37 am
Max@Math Revolution wrote:[Math Revolution GMAT math practice question]

If xy ≠ 0 and x^2+4y^2=4xy, (x+y)/(x-y)=?

A. 1
B. √2
C. √3
D. 2
E. 3
$$\left. \matrix{
x,y\,\, \ne 0 \hfill \cr
{x^2} + 4{y^2} = 4xy\,\,\,\left( * \right)\,\, \hfill \cr} \right\}\,\,\,\,\,\,\,;\,\,\,\,\,\,\,?\,\, = {{x + y} \over {x - y}}$$

Let´s do brutal street fighting (a.k.a. explore a particular case)!

$$x = 4\,\,\,\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\,\,{4^2} + 4{y^2} = {4^2}y\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,0 = 4 + {y^2} - 4y = {\left( {y - 2} \right)^2}\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,y = 2$$
$$\left( {x,y} \right) = \left( {4,2} \right)\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,? = {6 \over 2} = 3$$

This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
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