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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
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GMAT 1: 760 Q51 V42 GPA: 3.82

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Difficulty:   25% (medium)

Question Stats: 68% (01:23) correct 32% (02:09) wrong based on 140 sessions

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[Math Revolution GMAT math practice question]

If $$x^2+y^2=2xy,$$ then $$\frac{(x+y)}{(2x-y)}$$=?

$$A. -2$$
$$B. -1$$
$$C. 0$$
$$D. 1$$
$$E. 2$$

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Re: If x^2+y^2=2xy, then (x+y)/(2x-y)=?  [#permalink]

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(X-Y)^2 =0 => x=y
Substitute will result in 2

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Re: If x^2+y^2=2xy, then (x+y)/(2x-y)=?  [#permalink]

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MathRevolution wrote:
[Math Revolution GMAT math practice question]

If $$x^2+y^2=2xy,$$ then $$\frac{(x+y)}{(2x-y)}$$=?

$$A. -2$$
$$B. -1$$
$$C. 0$$
$$D. 1$$
$$E. 2$$

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

Sub in $$\frac{(x+y)}{(2x-y)}$$ ==> $$\frac{(x+x)}{(2x-x)}$$ => 2

Hence E
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Re: If x^2+y^2=2xy, then (x+y)/(2x-y)=?  [#permalink]

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$$? = \,\,{{x + y} \over {2x - y}}\,$$

$${x^2} + {y^2} = 2xy\,\,\,\left( * \right)$$

Important: x=0 (or y=0) implies (by (*)) that both x and y are equal to zero, what is impossible (because 2x-y is implicitly different from zero).

Conclusion: we may (and must) admit that x and y are nonzero to be able to find the correct solution (proceeding as shown in the posts above).

Regards,
Fabio.
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Re: If x^2+y^2=2xy, then (x+y)/(2x-y)=?  [#permalink]

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one more way to square this eq- (x+y)/(2x−y)
and upon solving we will get 2. (E)
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Re: If x^2+y^2=2xy, then (x+y)/(2x-y)=?  [#permalink]

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MathRevolution wrote:
[Math Revolution GMAT math practice question]

If $$x^2+y^2=2xy,$$ then $$\frac{(x+y)}{(2x-y)}$$=?

$$A. -2$$
$$B. -1$$
$$C. 0$$
$$D. 1$$
$$E. 2$$

Before looking at the question lets solve $$x^2+y^2=2xy$$

$$x^2+y^2=2xy$$
$$x^2+y^2-2xy=0$$
$$(x-y)^2= 0$$
which will give x=y

Now when you substitute this in the question
=$$\frac{(x+y)}{(2x-y)}$$

=$$\frac{(y+y)}{(2y-y)}$$

=$$\frac{(2y)}{(y)}$$

=2

Upon solving will give answer as E
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20 seconds approach: Simply pick smart numbers. X=Y=1. Plug these into the given equation. Final answer comes to be 2. Click option E and you are done! G
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Re: If x^2+y^2=2xy, then (x+y)/(2x-y)=?  [#permalink]

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I used the Test It strategy by assuming x = 1 and y = 1 which resulted in 2 as the right answer. Took less than 30 secs.

MathRevolution wrote:
[Math Revolution GMAT math practice question]

If $$x^2+y^2=2xy,$$ then $$\frac{(x+y)}{(2x-y)}$$=?

$$A. -2$$
$$B. -1$$
$$C. 0$$
$$D. 1$$
$$E. 2$$
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 7462
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: If x^2+y^2=2xy, then (x+y)/(2x-y)=?  [#permalink]

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=>

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

$$\frac{(x+y)}{(2x-y)}= \frac{(x+x)}{(2x-y)} = \frac{2x}{x} = 2$$, since $$x =y.$$

_________________ Re: If x^2+y^2=2xy, then (x+y)/(2x-y)=?   [#permalink] 30 Dec 2018, 18:31
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