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Difficulty: 505-555 Level,    Algebra,                         
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Re: If (x + y)/(xy) = 1, then y = [#permalink]
Bunuel wrote:
SOLUTION

If (x + y)/(xy) = 1, then y =

(A) x/(x - 1)
(B) x/(x + 1)
(C) (x - 1)/x
(D) (x + 1)/x
(E) x

\(\frac{x + y}{xy} = 1\);

\(x + y = xy\);

\(x = xy-y\);

\(x = y(x-1)\);

\(y=\frac{x}{x-1}\).

Answer: A.



Could you please explain the last step ? i.e. how you got from x= y(x-1) to your solution?!

Yo divided x by y and then you got x/y=(x-1) and how do you get the x over now ?
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Re: If (x + y)/(xy) = 1, then y = [#permalink]
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sauberheine1 wrote:
Bunuel wrote:
SOLUTION

If (x + y)/(xy) = 1, then y =

(A) x/(x - 1)
(B) x/(x + 1)
(C) (x - 1)/x
(D) (x + 1)/x
(E) x

\(\frac{x + y}{xy} = 1\);

\(x + y = xy\);

\(x = xy-y\);

\(x = y(x-1)\);

\(y=\frac{x}{x-1}\).

Answer: A.



Could you please explain the last step ? i.e. how you got from x= y(x-1) to your solution?!

Yo divided x by y and then you got x/y=(x-1) and how do you get the x over now ?


Divide both parts of \(x = y(x-1)\) by x-1 to get \(\frac{x}{x-1}=y\).
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Re: If (x + y)/(xy) = 1, then y = [#permalink]
I had a very strange way of solving this. Might not always work.

I plugged in numbers and already wasted enough time trying to figure out which numbers to plug in that I didn't want to go back and solve algebraically.

So what numbers added to each other and divided by the product of each other equals 1? The only ones I could think of included 0 making the solution undefined. X=1 Y=0 ...... Answer A is also Undefined while all the others give some sort of solution.

Warning: I suck at math so take my advice with a grain of salt.
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Re: If (x + y)/(xy) = 1, then y = [#permalink]
Expert Reply
Hi DJ1986,

This question is a type of 'in terms of' question - the prompt gives you an equation and asks you to isolate one of the variables 'in terms of' the other variable(s) in the equation. These types of questions are typically best solved with Algebra (TESTing VALUES can get complicated and you might not easily find values that 'fit' the given equation.

To answer your question though, X=2, Y=2 gives us (2+2)/(2)(2) = 1. Using those values would lead us to 2 answers though (Answers A and E).

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Re: If (x + y)/(xy) = 1, then y = [#permalink]
Expert Reply
Quote:

If (x + y)/(xy) = 1, then y =

(A) x/(x - 1)
(B) x/(x + 1)
(C) (x - 1)/x
(D) (x + 1)/x
(E) x


We can simplify the given equation:

(x + y)/(xy) = 1

x + y = xy

x = xy - y

x = y(x - 1)

x/(x - 1) = y

Answer: A
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Re: If (x + y)/(xy) = 1, then y = [#permalink]
ScottTargetTestPrep wrote:
Quote:

If (x + y)/(xy) = 1, then y =

(A) x/(x - 1)
(B) x/(x + 1)
(C) (x - 1)/x
(D) (x + 1)/x
(E) x


We can simplify the given equation:

(x + y)/(xy) = 1

x + y = xy

x = xy - y

x = y(x - 1)

x/(x - 1) = y

Answer: A


Thanks ScottTargetTestPrep, to clarify at this stage x + y = xy, y = xy-x , y = x(y-1) would have been correct too right if it's in the answer choice? Thanks
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Re: If (x + y)/(xy) = 1, then y = [#permalink]
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Re: If (x + y)/(xy) = 1, then y = [#permalink]
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