GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 13 Oct 2019, 23:11 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)/(x − y) = 1/2, then (xy + x^2)/(xy − x^2) =

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

Hide Tags

Math Expert V
Joined: 02 Sep 2009
Posts: 58335
If (x + y)/(x − y) = 1/2, then (xy + x^2)/(xy − x^2) =  [#permalink]

Show Tags

1
2 00:00

Difficulty:   5% (low)

Question Stats: 96% (01:30) correct 4% (02:08) wrong based on 109 sessions

HideShow timer Statistics

If $$\frac{x + y}{x − y} = \frac{1}{2}$$, then $$\frac{xy + x^2}{xy − x^2}=$$

(A) –4.2

(B) –1/2

(C) 1.1

(D) 3

(E) 5.3

Source: Nova GMAT
Difficulty Level: 500

_________________
Senior SC Moderator V
Joined: 22 May 2016
Posts: 3536
Re: If (x + y)/(x − y) = 1/2, then (xy + x^2)/(xy − x^2) =  [#permalink]

Show Tags

1
1
Bunuel wrote:
If $$\frac{x + y}{x − y} = \frac{1}{2}$$, then $$\frac{xy + x^2}{xy − x^2}=$$

(A) –4.2

(B) –1/2

(C) 1.1

(D) 3

(E) 5.3

Method I - Algebra

$$\frac{xy + x^2}{xy − x^2}$$ =

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

$$\frac{(y + x)}{(y - x)}$$

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

- $$\frac{(x + y)}{(x - y)}$$

Given $$\frac{x + y}{x − y} = \frac{1}{2}$$, then

- $$\frac{(x + y)}{(x - y)}$$ = - $$\frac{1}{2}$$

Method II - assign values derived from first equation, plug into second equation

$$\frac{x + y}{x − y}$$ = $$\frac{1}{2}$$ Cross multiply:
$$2 (x + y) = (x - y)$$
$$2x + 2y = x - y$$
$$x = -3y$$

Let x = -6 and y = 2, plug into second equation $$\frac{xy + x^2}{xy − x^2}=$$

$$\frac{-12 + 36}{- 12 - 36}$$

= - $$\frac{24}{48}$$ or - $$\frac{1}{2}$$

_________________
SC Butler has resumed! Get two SC questions to practice, whose links you can find by date, here.

Choose life.

Originally posted by generis on 01 Jun 2017, 14:26.
Last edited by generis on 29 Apr 2019, 15:00, edited 3 times in total.
Director  V
Joined: 04 Dec 2015
Posts: 745
Location: India
Concentration: Technology, Strategy
WE: Information Technology (Consulting)
Re: If (x + y)/(x − y) = 1/2, then (xy + x^2)/(xy − x^2) =  [#permalink]

Show Tags

1
1
Bunuel wrote:
If $$\frac{x + y}{x − y} = \frac{1}{2}$$, then $$\frac{xy + x^2}{xy − x^2}=$$

(A) –4.2

(B) –1/2

(C) 1.1

(D) 3

(E) 5.3

Taking x as common from the fraction; $$\frac{xy + x^2}{xy − x^2}$$
$$\frac{x(y + x)}{x(y - x)}$$
Cancelling out "x" we get = $$\frac{x+y}{-(x-y)}$$

Given; $$\frac{x + y}{x − y} = \frac{1}{2}$$
Therefore ; $$\frac{x+y}{-(x-y)}$$ = - $$\frac{1}{2}$$
Current Student B
Joined: 09 Dec 2015
Posts: 112
Location: India
Concentration: General Management, Operations
Schools: IIMC (A)
GMAT 1: 700 Q49 V36 GPA: 3.5
WE: Engineering (Consumer Products)
Re: If (x + y)/(x − y) = 1/2, then (xy + x^2)/(xy − x^2) =  [#permalink]

Show Tags

(xy + x^2)/(xy-x^2)
= x(y+x)/x(y-x)
= (y+x)/(y-x)
= -(x+y)/(x-y) = -1/2

Option B should be the correct answer.
Intern  B
Joined: 26 Jul 2016
Posts: 41
Location: India
Re: If (x + y)/(x − y) = 1/2, then (xy + x^2)/(xy − x^2) =  [#permalink]

Show Tags

(xy+x^2)/(xy-x^2)= (y+x)/(y-x)= -((x+y)/(x-y))= -1/2
Target Test Prep Representative G
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2817
Re: If (x + y)/(x − y) = 1/2, then (xy + x^2)/(xy − x^2) =  [#permalink]

Show Tags

Bunuel wrote:
If $$\frac{x + y}{x − y} = \frac{1}{2}$$, then $$\frac{xy + x^2}{xy − x^2}=$$

(A) –4.2

(B) –1/2

(C) 1.1

(D) 3

(E) 5.3

Let’s simplify (xy + x^2)/(xy - x^2):

x(y + x)/[x(y - x)]

We know x cannot equal zero (because (x + y)/(x - y) will not equal 1/2); therefore we can cancel the x:

(x + y)/(y - x)

(x + y)/(x - y) * -1

½ * -1 = -½

_________________

Jeffrey Miller

Head of GMAT Instruction

Jeff@TargetTestPrep.com

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Manager  B
Joined: 19 Jul 2017
Posts: 84
Location: India
Concentration: General Management, Strategy
GPA: 3.5
Re: If (x + y)/(x − y) = 1/2, then (xy + x^2)/(xy − x^2) =  [#permalink]

Show Tags

Take the x from the numerator and denominator and -1 from the denominator to get the given condition.

-1*(x+y)/(x-y)= -1/2

Hence Ans:B
Non-Human User Joined: 09 Sep 2013
Posts: 13080
Re: If (x + y)/(x − y) = 1/2, then (xy + x^2)/(xy − x^2) =  [#permalink]

Show Tags

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)/(x − y) = 1/2, then (xy + x^2)/(xy − x^2) =   [#permalink] 09 Feb 2019, 14:29
Display posts from previous: Sort by

If (x + y)/(x − y) = 1/2, then (xy + x^2)/(xy − x^2) =

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne  