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

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If (x + y)/(xy) = 1, then y =  [#permalink]

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New post 05 Mar 2014, 02:09
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A
B
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E

Difficulty:

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Question Stats:

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The Official Guide For GMAT® Quantitative Review, 2ND Edition

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

Problem Solving
Question: 128
Category: Algebra First-degree equations
Page: 78
Difficulty: 600


GMAT Club is introducing a new project: The Official Guide For GMAT® Quantitative Review, 2ND Edition - Quantitative Questions Project

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

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New post 05 Mar 2014, 02:09
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Re: If (x + y)/(xy) = 1, then y =  [#permalink]

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New post 05 Mar 2014, 19:34
1
\(Answer = A = \frac{x}{(x - 1)}\)

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

x + y = xy

xy - y = x

y(x-1) = x

\(y = \frac{x}{(x-1)}\)
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Re: If (x + y)/(xy) = 1, then y =  [#permalink]

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New post 05 Mar 2014, 21:08
(x + y)/(xy) = 1
(x/xy) + (y/xy) = 1
1/y + 1/x = 1
1/y = 1 - 1/x
1/y = (x-1)/x
=> y = x/(x-1)

Ans is (A).
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Re: If (x + y)/(xy) = 1, then y =  [#permalink]

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New post 10 Feb 2015, 02:02
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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New post 10 Feb 2015, 05:55
1
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]

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New post 11 Feb 2015, 07:15
Thanks a lot - after 5/6 hours i sometimes get a little bit confused with the easiest calculations.

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

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New post 22 Nov 2015, 10:54
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]

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New post 25 Nov 2015, 15:45
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]

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New post 22 May 2017, 18:39
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]

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New post 10 Oct 2017, 08:03
I was wondering if you guys could help me with my timing issue. I've attached a picture of how I approach the simplification of this problem. A

s you can see, I only got it right from the 3rd time. The first 2 attempts, in which I tried to immediately isolate y on the RHS, wasted quite a bit of my time. I'm wondering is there an approach that I'm missing? Is there a way I can see from the problem that I shouldn't be isolating y straight away?

Thank you for your help!
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WhatsApp Image 2017-10-10 at 16.57.32.jpeg
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Re: If (x + y)/(xy) = 1, then y =  [#permalink]

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New post 27 Feb 2018, 09:40
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.


Bunuel - how did you get "1" here \(x = y(x-1)\); :?


Also i wonder why my solution is not correct, pls see below

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

x+y =xy

xy=x+y

x = \(\frac{x+y}{x}\)
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Re: If (x + y)/(xy) = 1, then y =  [#permalink]

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New post 27 Feb 2018, 10:34
1
dave13 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.


Bunuel - how did you get "1" here \(x = y(x-1)\); :?


Also i wonder why my solution is not correct, pls see below

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

x+y =xy

xy=x+y

x = \(\frac{x+y}{x}\)


\(x = xy-y\);

Factor pout y from xy - y and you'll get \(x = y(x-1)\).

As for your question: the question asks to find the value of y in terms of x. Your solution does not give y in terms of x.
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Re: If (x + y)/(xy) = 1, then y =  [#permalink]

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New post 28 Feb 2018, 01:37
Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

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

Problem Solving
Question: 128
Category: Algebra First-degree equations
Page: 78
Difficulty: 600


GMAT Club is introducing a new project: The Official Guide For GMAT® Quantitative Review, 2ND Edition - Quantitative Questions Project

Each week we'll be posting several questions from The Official Guide For GMAT® Quantitative Review, 2ND Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution.

We'll be glad if you participate in development of this project:
1. Please provide your solutions to the questions;
2. Please vote for the best solutions by pressing Kudos button;
3. Please vote for the questions themselves by pressing Kudos button;
4. Please share your views on difficulty level of the questions, so that we have most precise evaluation.

Thank you!

IMO A I am not so good in algebra so going through plugin we can write x+y=xy this can be possible through x=2 and y=2 or x=0 and y=0 so A ill give me the required result.
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Re: If (x + y)/(xy) = 1, then y =  [#permalink]

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New post 20 May 2019, 21:10
Bunuel
Approach 1:
(X+Y)/XY=1
or, X+Y=XY
or, Y=XY-X
So, Y=X(Y-1)
Approach 2:
(X+Y)/XY=1
or, XY=X+Y
So, Y=(X+Y)/X
Why these two approaches are not leading me to the solutions? Please tell me, what is wrong with my approaches or what mistake I have made.

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

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New post 20 May 2019, 21:12
msu6800 wrote:
Bunuel
Approach 1:
(X+Y)/XY=1
or, X+Y=XY
or, Y=XY-X
So, Y=X(Y-1)
Approach 2:
(X+Y)/XY=1
or, XY=X+Y
So, Y=(X+Y)/X
Why these two approaches are not leading me to the solutions? Please tell me, what is wrong with my approaches or what mistake I have made.

Posted from my mobile device


The question asks to find the value of y in terms of x. Your solution does not give y in terms of x.
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Re: If (x + y)/(xy) = 1, then y =  [#permalink]

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New post 20 May 2019, 21:17
Bunuel, I gussed it. Your comments have made me more confident. Answer options give a clue to express y in terms of x.
Thanks

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

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New post 15 Sep 2019, 09:42
Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

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

Problem Solving
Question: 128
Category: Algebra First-degree equations
Page: 78
Difficulty: 600


GMAT Club is introducing a new project: The Official Guide For GMAT® Quantitative Review, 2ND Edition - Quantitative Questions Project

Each week we'll be posting several questions from The Official Guide For GMAT® Quantitative Review, 2ND Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution.

We'll be glad if you participate in development of this project:
1. Please provide your solutions to the questions;
2. Please vote for the best solutions by pressing Kudos button;
3. Please vote for the questions themselves by pressing Kudos button;
4. Please share your views on difficulty level of the questions, so that we have most precise evaluation.

Thank you!


Given: (x + y)/(xy) = 1

Asked: y = ?

(x + y)/(xy) = 1
x+y = xy
x = xy-y = (x-1)y
y = x/(x-1)

IMO A
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Re: If (x + y)/(xy) = 1, then y =   [#permalink] 15 Sep 2019, 09:42
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