x^2 + 4 y^2 = 4 x y

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sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 amFollowed by: 80 members; Location: India; Thanked: 267 times; GMAT Score:760

by sanju09 » Mon Oct 18, 2010 5:57 am

If x^2 + 4 y^2 = 4 x y then (x + y)/ (x - y) is
(A) 2/3
(B) 2
(C) 3
(D) 10/3
(E) 4

[spoiler]???????????[/spoiler]

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Source: Beat The GMAT — Problem Solving | Mon Oct 18, 2010 5:57 am

shovan85: Community Manager; Posts: 991; Joined: Thu Sep 23, 2010 6:19 amFollowed by: 24 members; Location: Bangalore, India; Thanked: 146 times

by shovan85 » Mon Oct 18, 2010 6:01 am

IMO C

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

Apply Componendo Dividendo:

(x+y)/(x-y) = (2+1)/(2-1) = 3

FYI: https://en.wikipedia.org/wiki/Componendo_and_dividendo

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fskilnik@GMATH: GMAT Instructor; Posts: 1449; Joined: Sat Oct 09, 2010 2:16 pmFollowed by: 33 members; Thanked: 59 times

by fskilnik@GMATH » Mon Oct 18, 2010 6:20 am

shovan85 wrote: x^2 + 4y^2 - 4xy = 0
=> x^2 - 2 * x * 2y + (2y)^2 = 0
=> (x-2y)^2 = 0
=> x = 2y
=> x/y = 2

Apply Componendo Dividendo:

(x+y)/(x-y) = (2+1)/(2-1) = 3

FYI: https://en.wikipedia.org/wiki/Componendo_and_dividendo

Excellent, Shovan.

Please note that substituting x by 2y in the expression asked we find the exact same answer, for sure...

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English-speakers :: https://www.gmath.net
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shovan85: Community Manager; Posts: 991; Joined: Thu Sep 23, 2010 6:19 amFollowed by: 24 members; Location: Bangalore, India; Thanked: 146 times

by shovan85 » Mon Oct 18, 2010 6:26 am

fskilnik wrote:
shovan85 wrote: x^2 + 4y^2 - 4xy = 0
=> x^2 - 2 * x * 2y + (2y)^2 = 0
=> (x-2y)^2 = 0
=> x = 2y
=> x/y = 2

Apply Componendo Dividendo:

(x+y)/(x-y) = (2+1)/(2-1) = 3

FYI: https://en.wikipedia.org/wiki/Componendo_and_dividendo
Excellent, Shovan.

Please note that substituting x by 2y in the expression asked we find the exact same answer, for sure...

Thanks. I did that for cross verification but did not post it here

If the problem is Easy Respect it, if the problem is tough Attack it

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fskilnik@GMATH: GMAT Instructor; Posts: 1449; Joined: Sat Oct 09, 2010 2:16 pmFollowed by: 33 members; Thanked: 59 times

by fskilnik@GMATH » Mon Oct 18, 2010 6:41 am

shovan85 wrote: I did that for cross verification but did not post it here

Sure! I just mentioned it because someone could imagine that this (neat) tool/result you used was essential to get the answer, and of course it was not the case.

Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br

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sandeep800: Master | Next Rank: 500 Posts; Posts: 126; Joined: Tue Feb 09, 2010 6:37 pmFollowed by: 4 members

by sandeep800 » Wed Oct 20, 2010 11:27 pm

although at first look i would have tried to solve it by using componendo and dividendo but yeah substitution works well here... !!

A body of clay, a mind full of play, a moment's life - that is me!!!

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AtifS: Senior | Next Rank: 100 Posts; Posts: 43; Joined: Sat Jan 23, 2010 12:18 amFollowed by: 1 member; Thanked: 1 times

by AtifS » Thu Oct 21, 2010 1:21 am

My explanation:
x^2 + 4y^2 = 4xy
=> x^2 + 4 y^2 - 4xy = 0
=> x^2 - 4 xy + 4 y^2 = 0
=> (x - 2y)^2 = 0
=> x - 2y = 0
=> x = 2y
=> x/2 = y

Now put the value of x/2 into (x + y)/(x - y)

(x + y)/(x - y)
= (x + x/2)/(x - x/2)
= {(2x+x)/2}/{(2x-x)/2}
= (3x/2)/(x/2)
= (3x/2) * (2/x)
= 3x/2 * 2/x ---> 2 will be canceled and x as well (because they are reciprocals of each other)
= 3 --> Answer
So, "C" is the answer for me, which is "3"

I am not perfect

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bacchewar_prashant: Senior | Next Rank: 100 Posts; Posts: 39; Joined: Tue Sep 28, 2010 11:34 pm; Thanked: 1 times

by bacchewar_prashant » Thu Oct 21, 2010 1:35 am

C for me

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frank1: Legendary Member; Posts: 537; Joined: Fri Jan 22, 2010 10:06 pmFollowed by: 1 member; Thanked: 14 times

by frank1 » Thu Oct 21, 2010 7:27 am

sanju09 wrote:If x^2 + 4 y^2 = 4 x y then (x + y)/ (x - y) is
(A) 2/3
(B) 2
(C) 3
(D) 10/3
(E) 4

[spoiler]???????????[/spoiler]

x^2 + 4 y^2 = 4 x y
x^2 + 4 y^2 - 4 x y=0(it is in form a^2+2ab+b^2 where a=x and b=2y)
so
(x-2y)^2=0
x=2y
now actual question is x+y / x -y =?
substitute x=2y

2y+y / 2y-y =3y/y =3

So C
thanks

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pkit: Junior | Next Rank: 30 Posts; Posts: 29; Joined: Thu Jul 29, 2010 8:28 amFollowed by: 1 member; Thanked: 5 times

by pkit » Fri Oct 22, 2010 2:48 am

Very nice solution, thanks

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