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If x^2+y^2=2xy, then (x+y)/(2x-y)=?

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Math Revolution GMAT Instructor
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If x^2+y^2=2xy, then (x+y)/(2x-y)=?  [#permalink]

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New post 27 Dec 2018, 01:19
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A
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E

Difficulty:

  35% (medium)

Question Stats:

66% (01:07) correct 34% (01:55) wrong based on 87 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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New post 27 Dec 2018, 01:34
(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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New post 27 Dec 2018, 05:16
1
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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New post 27 Dec 2018, 06:26
\(? = \,\,{{x + y} \over {2x - y}}\,\)

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

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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New post 27 Dec 2018, 10:02
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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New post 27 Dec 2018, 10:13
1
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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If x^2+y^2=2xy, then (x+y)/(2x-y)=?  [#permalink]

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New post 27 Dec 2018, 18:29
1
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!
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Re: If x^2+y^2=2xy, then (x+y)/(2x-y)=?  [#permalink]

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New post 28 Dec 2018, 13:54
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
User avatar
V
Joined: 16 Aug 2015
Posts: 6815
GMAT 1: 760 Q51 V42
GPA: 3.82
Premium Member
Re: If x^2+y^2=2xy, then (x+y)/(2x-y)=?  [#permalink]

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New post 30 Dec 2018, 17:31
=>

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

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


Therefore, the answer is E.
Answer: E
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Re: If x^2+y^2=2xy, then (x+y)/(2x-y)=? &nbs [#permalink] 30 Dec 2018, 17:31
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