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

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Math Expert
Joined: 02 Sep 2009
Posts: 42652

Kudos [?]: 135978 [0], given: 12719

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

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05 Mar 2014, 01:09
Expert's post
10
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Difficulty:

15% (low)

Question Stats:

75% (00:55) correct 25% (01:23) wrong based on 541 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

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Kudos [?]: 135978 [0], given: 12719

Math Expert
Joined: 02 Sep 2009
Posts: 42652

Kudos [?]: 135978 [0], given: 12719

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

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05 Mar 2014, 01:09
Expert's post
5
This post was
BOOKMARKED
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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05 Mar 2014, 18:34
1
KUDOS
$$Answer = A = \frac{x}{(x - 1)}$$

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

x + y = xy

xy - y = x

y(x-1) = x

$$y = \frac{x}{(x-1)}$$
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Kudos [?]: 2794 [1], given: 193

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

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05 Mar 2014, 20:08
(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).

Kudos [?]: 108 [0], given: 104

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

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10 Feb 2015, 01:02
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

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

$$x + y = xy$$;

$$x = xy-y$$;

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

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

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 ?

Kudos [?]: 2 [0], given: 6

Math Expert
Joined: 02 Sep 2009
Posts: 42652

Kudos [?]: 135978 [1], given: 12719

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

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10 Feb 2015, 04:55
1
KUDOS
Expert's post
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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Kudos [?]: 135978 [1], given: 12719

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

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11 Feb 2015, 06:15
Thanks a lot - after 5/6 hours i sometimes get a little bit confused with the easiest calculations.

Sorry

Kudos [?]: 2 [0], given: 6

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GMAT 1: 600 Q33 V40
GPA: 3.3
Re: If (x + y)/(xy) = 1, then y = [#permalink]

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22 Nov 2015, 09:54
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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25 Nov 2015, 14:45
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.

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

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22 May 2017, 17:39
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

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

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10 Oct 2017, 07:03
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?

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WhatsApp Image 2017-10-10 at 16.57.32.jpeg [ 61.41 KiB | Viewed 4305 times ]

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Re: If (x + y)/(xy) = 1, then y =   [#permalink] 10 Oct 2017, 07:03
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