I've attached a pic of the problem at the solution. Sorry for not being able to black out the solution part. The suggested solution by manhattan gmat certainly makes sense but it involves a lot of manipulation that I couldn't really think of on the spot.
When I was doing the problem, I just crossed multiplied and started canceling things out and ended up with the equation [1/(x-y) = 2].
How do I manipulate x/y from [1/(x-y) = 2]? Thanks.
please help with this difficult problem
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Well, I got x/y=9 by doing the following:
We have:
sqrt(x)+sqrt(y)/x-y=2sqrt(x)+2sqrt(y)/x+2sqrt(xy)+y
We can rewrite the above equation as:
sqrt(x)+sqrt(y)/x-y=2(sqrt(x)=sqrt(y))/(sqrt(x)+sqrt(y))^(2)
Now cross multiply:
(sqrt(x)+sqrt(y))^(3)=2(sqrt(x)+sqrt(y))(x-y)
One of the sqrt(x)+sqrt(y)'s cancel and you're left with
(sqrt(x)+sqrt(y))^(2)=2x-2y
x+2sqrt(xy)+y=2x-2y
2sqrt(xy)+3y=x
x-2sqrt(xy)-3y=0
Now factor:
(sqrt(x)-3sqrt(y))(sqrt(x)+sqrt(y))=0
sqrt(x)-3sqrt(y)=0
sqrt(x)=3sqrt(y)
Square both sides:
x=9y
x/y=9
This problem was very time consuming. I really don't think a problem like this would be on the GMAT.
1=2x-2y. That's as far as you can get.
We have:
sqrt(x)+sqrt(y)/x-y=2sqrt(x)+2sqrt(y)/x+2sqrt(xy)+y
We can rewrite the above equation as:
sqrt(x)+sqrt(y)/x-y=2(sqrt(x)=sqrt(y))/(sqrt(x)+sqrt(y))^(2)
Now cross multiply:
(sqrt(x)+sqrt(y))^(3)=2(sqrt(x)+sqrt(y))(x-y)
One of the sqrt(x)+sqrt(y)'s cancel and you're left with
(sqrt(x)+sqrt(y))^(2)=2x-2y
x+2sqrt(xy)+y=2x-2y
2sqrt(xy)+3y=x
x-2sqrt(xy)-3y=0
Now factor:
(sqrt(x)-3sqrt(y))(sqrt(x)+sqrt(y))=0
sqrt(x)-3sqrt(y)=0
sqrt(x)=3sqrt(y)
Square both sides:
x=9y
x/y=9
This problem was very time consuming. I really don't think a problem like this would be on the GMAT.
There's no way you can get x/y from 1/(x-y)=2How do I manipulate x/y from [1/(x-y) = 2]? Thanks.
1=2x-2y. That's as far as you can get.
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