Last visit was: 23 May 2024, 08:35 It is currently 23 May 2024, 08:35
Toolkit
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

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

SORT BY:
Tags:
Show Tags
Hide Tags
Math Expert
Joined: 02 Sep 2009
Posts: 93419
Own Kudos [?]: 626056 [43]
Given Kudos: 81940
Math Expert
Joined: 02 Sep 2009
Posts: 93419
Own Kudos [?]: 626056 [15]
Given Kudos: 81940
General Discussion
SVP
Joined: 27 Dec 2012
Status:The Best Or Nothing
Posts: 1559
Own Kudos [?]: 7238 [1]
Given Kudos: 193
Location: India
Concentration: General Management, Technology
WE:Information Technology (Computer Software)
Intern
Joined: 26 Jan 2015
Posts: 7
Own Kudos [?]: 8 [0]
Given Kudos: 6
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

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

$$x + y = xy$$;

$$x = xy-y$$;

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

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

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
Joined: 02 Sep 2009
Posts: 93419
Own Kudos [?]: 626056 [1]
Given Kudos: 81940
Re: If (x + y)/(xy) = 1, then y = [#permalink]
1
Kudos
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 $$\frac{x}{x-1}=y$$.
Manager
Joined: 05 Jul 2015
Posts: 53
Own Kudos [?]: 187 [0]
Given Kudos: 3
GMAT 1: 600 Q33 V40
GPA: 3.3
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.
GMAT Club Legend
Joined: 19 Dec 2014
Status:GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Posts: 21843
Own Kudos [?]: 11693 [0]
Given Kudos: 450
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: If (x + y)/(xy) = 1, then y = [#permalink]
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.

GMAT assassins aren't born, they're made
Rich
Target Test Prep Representative
Joined: 14 Oct 2015
Status:Founder & CEO
Affiliations: Target Test Prep
Posts: 18893
Own Kudos [?]: 22304 [0]
Given Kudos: 285
Location: United States (CA)
Re: If (x + y)/(xy) = 1, then y = [#permalink]
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

Senior Manager
Joined: 16 Nov 2021
Posts: 473
Own Kudos [?]: 28 [0]
Given Kudos: 5900
Location: United Kingdom
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

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
Non-Human User
Joined: 09 Sep 2013
Posts: 33150
Own Kudos [?]: 829 [0]
Given Kudos: 0
Re: If (x + y)/(xy) = 1, then y = [#permalink]
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
Re: If (x + y)/(xy) = 1, then y = [#permalink]
Moderator:
Math Expert
93418 posts