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

 It is currently 18 Oct 2019, 22:28 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 (4 - x)/(2 + x) = x, what is the value of x^2 + 3x -4 ?

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

Hide Tags

Manager  Joined: 02 Dec 2012
Posts: 173
If (4 - x)/(2 + x) = x, what is the value of x^2 + 3x -4 ?  [#permalink]

Show Tags

2
13 00:00

Difficulty:   5% (low)

Question Stats: 82% (01:08) correct 18% (01:45) wrong based on 775 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
Math Expert V
Joined: 02 Sep 2009
Posts: 58453
If (4 - x)/(2 + x) = x, what is the value of x^2 + 3x -4 ?  [#permalink]

Show Tags

4
1
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.

_________________
General Discussion
Intern  Joined: 26 May 2012
Posts: 16
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

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

The answer is option C.
Board of Directors D
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 4772
Location: India
GPA: 3.5
WE: Business Development (Commercial Banking)
Re: If (4 - x)/(2 + x) = x, what is the value of x^2 + 3x -4 ?  [#permalink]

Show Tags

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 G
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2815
Re: If (4 - x)/(2 + x) = x, what is the value of x^2 + 3x -4 ?  [#permalink]

Show Tags

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

_________________

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.

VP  D
Joined: 09 Mar 2016
Posts: 1230
Re: If (4 - x)/(2 + x) = x, what is the value of x^2 + 3x -4 ?  [#permalink]

Show Tags

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

guys by we already see from question that it is quadratic x^2 + 3x -4 and it always equals zero no ? Senior PS Moderator D
Status: It always seems impossible until it's done.
Joined: 16 Sep 2016
Posts: 737
GMAT 1: 740 Q50 V40 GMAT 2: 770 Q51 V42 Re: If (4 - x)/(2 + x) = x, what is the value of x^2 + 3x -4 ?  [#permalink]

Show Tags

dave13 wrote:
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

guys by we already see from question that it is quadratic x^2 + 3x -4 and it always equals zero no ? Not quite.

On solving the given equation ,

$$(4-x)/(2+x) = x$$
$$4-x = x*(2+x)$$
$$4-x = x^2 + 2x$$
$$0 = x^2 + 3x - 4$$

Hence 0.
_________________
Regards,

“Do. Or do not. There is no try.” - Yoda (The Empire Strikes Back)
VP  D
Joined: 09 Mar 2016
Posts: 1230
Re: If (4 - x)/(2 + x) = x, what is the value of x^2 + 3x -4 ?  [#permalink]

Show Tags

dave13 wrote:
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

guys by we already see from question that it is quadratic x^2 + 3x -4 and it always equals zero no ? Not quite.

On solving the given equation ,

$$(4-x)/(2+x) = x$$
$$4-x = x*(2+x)$$
$$4-x = x^2 + 2x$$
$$0 = x^2 + 3x - 4$$

Hence 0.

hey Gladiator59 thanks ! What do mean by "Not quite." do you mean that it is not always that quadratics equal ZERO ? Senior PS Moderator D
Status: It always seems impossible until it's done.
Joined: 16 Sep 2016
Posts: 737
GMAT 1: 740 Q50 V40 GMAT 2: 770 Q51 V42 Re: If (4 - x)/(2 + x) = x, what is the value of x^2 + 3x -4 ?  [#permalink]

Show Tags

1
dave13 wrote:

hey Gladiator59 thanks ! What do mean by "Not quite." do you mean that it is not always that quadratics equal ZERO ? Yeah dave13,

Precisely so. "Quadratics" may or may not equal 0. What does always equal zero is a "Quadratic equation".

So for example.

$$x^2 +3x - 4 = 0$$ could be re-written as
$$x^2 + 3x -3 = 1$$ ( adding 1 to both RHS and LHS )

Here the LHS is a "quadratic" expression that equals 1 (RHS)

More generally speaking .. quadratic expressions are parabolas and where the intersect the x-axis they equal zero.

Best,
_________________
Regards,

“Do. Or do not. There is no try.” - Yoda (The Empire Strikes Back)
SVP  P
Joined: 03 Jun 2019
Posts: 1723
Location: India
Re: If (4 - x)/(2 + x) = x, what is the value of x^2 + 3x -4 ?  [#permalink]

Show Tags

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

4-x = 2x + x^2
x^2+3x-4=0

IMO C

Posted from my mobile device
_________________
"Success is not final; failure is not fatal: It is the courage to continue that counts."

Please provide kudos if you like my post. Kudos encourage active discussions.

My GMAT Resources: -

Efficient Learning
All you need to know about GMAT quant

Tele: +91-11-40396815
Mobile : +91-9910661622
E-mail : kinshook.chaturvedi@gmail.com Re: If (4 - x)/(2 + x) = x, what is the value of x^2 + 3x -4 ?   [#permalink] 15 Sep 2019, 06:37
Display posts from previous: Sort by

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

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne  