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Math Expert V
Joined: 02 Sep 2009
Posts: 58367
If (x + y)/(xy) = 1, then y =  [#permalink]

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12 00:00

Difficulty:   15% (low)

Question Stats: 77% (01:15) correct 23% (02:04) wrong based on 630 sessions

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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

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.

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Math Expert V
Joined: 02 Sep 2009
Posts: 58367
Re: If (x + y)/(xy) = 1, then y =  [#permalink]

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3
5
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

$$\frac{x + y}{xy} = 1$$;

$$x + y = xy$$;

$$x = xy-y$$;

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

$$y=\frac{x}{x-1}$$.

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

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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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GMAT 1: 590 Q45 V27 Re: If (x + y)/(xy) = 1, then y =  [#permalink]

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(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).
Intern  Joined: 26 Jan 2015
Posts: 9
Re: If (x + y)/(xy) = 1, then y =  [#permalink]

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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

$$\frac{x + y}{xy} = 1$$;

$$x + y = xy$$;

$$x = xy-y$$;

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

$$y=\frac{x}{x-1}$$.

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 ?
Math Expert V
Joined: 02 Sep 2009
Posts: 58367
Re: If (x + y)/(xy) = 1, then y =  [#permalink]

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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

$$\frac{x + y}{xy} = 1$$;

$$x + y = xy$$;

$$x = xy-y$$;

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

$$y=\frac{x}{x-1}$$.

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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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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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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GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: If (x + y)/(xy) = 1, then y =  [#permalink]

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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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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

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Intern  B
Joined: 12 Aug 2016
Posts: 7
Re: If (x + y)/(xy) = 1, then y =  [#permalink]

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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!
Attachments WhatsApp Image 2017-10-10 at 16.57.32.jpeg [ 61.41 KiB | Viewed 31750 times ]

VP  D
Joined: 09 Mar 2016
Posts: 1230
Re: If (x + y)/(xy) = 1, then y =  [#permalink]

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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

$$\frac{x + y}{xy} = 1$$;

$$x + y = xy$$;

$$x = xy-y$$;

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

$$y=\frac{x}{x-1}$$.

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 = $$\frac{x+y}{x}$$
Math Expert V
Joined: 02 Sep 2009
Posts: 58367
Re: If (x + y)/(xy) = 1, then y =  [#permalink]

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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

$$\frac{x + y}{xy} = 1$$;

$$x + y = xy$$;

$$x = xy-y$$;

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

$$y=\frac{x}{x-1}$$.

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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Posts: 233
Re: If (x + y)/(xy) = 1, then y =  [#permalink]

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

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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
Math Expert V
Joined: 02 Sep 2009
Posts: 58367
Re: If (x + y)/(xy) = 1, then y =  [#permalink]

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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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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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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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E-mail : kinshook.chaturvedi@gmail.com Re: If (x + y)/(xy) = 1, then y =   [#permalink] 15 Sep 2019, 09:42
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