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

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Expert Post
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V
Joined: 02 Sep 2009
Posts: 41890

Kudos [?]: 128966 [0], given: 12185

If (x + y)/(x − y) = 1/2, then (xy + x^2)/(xy − x^2) = [#permalink]

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New post 01 Jun 2017, 12:04
00:00
A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

95% (01:06) correct 5% (01:32) wrong based on 68 sessions

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Kudos [?]: 128966 [0], given: 12185

Director
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P
Joined: 22 May 2016
Posts: 815

Kudos [?]: 265 [0], given: 552

If (x + y)/(x − y) = 1/2, then (xy + x^2)/(xy − x^2) = [#permalink]

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New post 01 Jun 2017, 14:26
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

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

\(2 (x + y) = (x - y)\) ==> \(2x + 2y = x - y\) ==>

\(x = -3y\)

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 - \(\frac{1}{2}\)

[Reveal] Spoiler:
Answer B

Last edited by genxer123 on 01 Jun 2017, 14:32, edited 1 time in total.

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Director
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Re: If (x + y)/(x − y) = 1/2, then (xy + x^2)/(xy − x^2) = [#permalink]

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New post 01 Jun 2017, 14:29
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KUDOS
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 ; \(\frac{x+y}{-(x-y)}\) = - \(\frac{1}{2}\)
Answer B...

Kudos [?]: 302 [1], given: 261

Manager
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B
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Posts: 113

Kudos [?]: 18 [0], given: 48

Location: India
Concentration: General Management, Operations
GMAT 1: 700 Q49 V36
GPA: 3.5
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Re: If (x + y)/(x − y) = 1/2, then (xy + x^2)/(xy − x^2) = [#permalink]

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New post 07 Jun 2017, 04:43
(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.

Kudos [?]: 18 [0], given: 48

Intern
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Joined: 26 Jul 2016
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Re: If (x + y)/(x − y) = 1/2, then (xy + x^2)/(xy − x^2) = [#permalink]

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New post 07 Jun 2017, 09:27
(xy+x^2)/(xy-x^2)= (y+x)/(y-x)= -((x+y)/(x-y))= -1/2
Answer- B

Kudos [?]: 1 [0], given: 16

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Re: If (x + y)/(x − y) = 1/2, then (xy + x^2)/(xy − x^2) = [#permalink]

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New post 10 Jun 2017, 07:30
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

Answer: B
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Kudos [?]: 836 [0], given: 5

Manager
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Re: If (x + y)/(x − y) = 1/2, then (xy + x^2)/(xy − x^2) = [#permalink]

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New post 27 Aug 2017, 23:46
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

Kudos [?]: 10 [0], given: 85

Re: If (x + y)/(x − y) = 1/2, then (xy + x^2)/(xy − x^2) =   [#permalink] 27 Aug 2017, 23:46
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