It is currently 24 Feb 2018, 10:19

### 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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# If (4 - x)/(2 + x) = x, what is the value of x^2 + 3x -4 ?

Author Message
TAGS:

### Hide Tags

Manager
Joined: 02 Dec 2012
Posts: 178
If (4 - x)/(2 + x) = x, what is the value of x^2 + 3x -4 ? [#permalink]

### Show Tags

17 Dec 2012, 08:12
7
This post was
BOOKMARKED
00:00

Difficulty:

5% (low)

Question Stats:

79% (00:52) correct 21% (01:19) wrong based on 888 sessions

### HideShow timer Statistics

If (4 - x)/(2 + x) = x, what is the value of x^2 + 3x -4 ?

(A) -4
(B) -1
(C) 0
(D) 1
(E) 2
[Reveal] Spoiler: OA
Math Expert
Joined: 02 Sep 2009
Posts: 43896
Re: If (4 - x)/(2 + x) = x, what is the value of x^2 + 3x -4 ? [#permalink]

### Show Tags

17 Dec 2012, 08:14
2
KUDOS
Expert's post
2
This post was
BOOKMARKED
If (4 - x)/(2 + x) = x, what is the value of x^2 + 3x -4 ?

(A) -4
(B) -1
(C) 0
(D) 1
(E) 2

$$\frac{4-x}{2+x}=x$$ --> $$4-x=x*(2+x)$$ --> $$4-x=2x+x^2$$ --> $$x^2+3x-4=0$$. As you can see there is no need to solve for x to answer the question.

_________________
Intern
Joined: 26 May 2012
Posts: 21
Concentration: Marketing, Technology
GMAT Date: 09-17-2012
Re: If (4 - x)/(2 + x) = x, what is the value of x^2 + 3x -4 ? [#permalink]

### Show Tags

17 Dec 2012, 08:21
Simplify by keeping all the terms on side.
The equation becomes:

(4-x) = x*(2+x)

Now, expand the RHS of the equation:
(4-x) = 2x+x^2

Now, you see you already have a prt of the solution, a +ve x^2, so now, you need to move the LHS of the equation to the RHS and equate to 0:

0 = 2x+x^2-4+x

Simplify this further by adding 2x and x and voila!

x^2+3x-4 = 0

Non-Human User
Joined: 09 Sep 2013
Posts: 13764
Re: If (4 - x)/(2 + x) = x, what is the value of x^2 + 3x -4 ? [#permalink]

### Show Tags

12 Jul 2014, 21:46
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.
_________________
Non-Human User
Joined: 09 Sep 2013
Posts: 13764
Re: If (4 - x)/(2 + x) = x, what is the value of x^2 + 3x -4 ? [#permalink]

### Show Tags

29 Aug 2015, 02:06
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.
_________________
Non-Human User
Joined: 09 Sep 2013
Posts: 13764
Re: If (4 - x)/(2 + x) = x, what is the value of x^2 + 3x -4 ? [#permalink]

### Show Tags

23 May 2017, 04:16
1
KUDOS
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.
_________________
Board of Directors
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 3326
Location: India
GPA: 3.5
Re: If (4 - x)/(2 + x) = x, what is the value of x^2 + 3x -4 ? [#permalink]

### Show Tags

23 May 2017, 08:04
If (4 - x)/(2 + x) = x, what is the value of x^2 + 3x -4 ?

(A) -4
(B) -1
(C) 0
(D) 1
(E) 2

$$\frac{(4 - x)}{(2 + x)} = x$$

Or, $$4 - x = 2x +x^2$$

Or, $$x^2 + 3x - 4 = 0$$

Thus, the answer must be (C) 0
_________________

Thanks and Regards

Abhishek....

PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS

How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only )

Target Test Prep Representative
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2016
Re: If (4 - x)/(2 + x) = x, what is the value of x^2 + 3x -4 ? [#permalink]

### Show Tags

25 May 2017, 14:46
If (4 - x)/(2 + x) = x, what is the value of x^2 + 3x -4 ?

(A) -4
(B) -1
(C) 0
(D) 1
(E) 2

We can simplify the given equation by first multiplying each side of the equation by (2 + x).

(4 - x)/(2 + x) = x

4 - x = x(2 + x)

4 - x = x^2 + 2x

x^2 + 3x - 4 = 0

_________________

Jeffery Miller

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Re: If (4 - x)/(2 + x) = x, what is the value of x^2 + 3x -4 ?   [#permalink] 25 May 2017, 14:46
Display posts from previous: Sort by