Last visit was: 29 Apr 2024, 09:00 It is currently 29 Apr 2024, 09:00
Decision Tracker
My Rewards
New comers' posts
New posts
Unanswered

Close

GRE Prep 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
Your Progress

every week, we’ll send you an estimated GRE 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.

Go to My Error Log Learn more
Close

Request Expert Reply

Confirm Cancel
PREVIOUS TOPIC
NEXT TOPIC

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

Tags :
Find Similar Topics  About  Add a Tag

Show Tags
Hide Tags

User avatar
D
Carcass
Verbal Expert
Joined: 18 Apr 2015
Posts: 28668
Own Kudos [?]: 33165 [2]
Given Kudos: 25180
Send PM
If (4-x)/(2+x)=x, what is the value of x^2+3x-4? [#permalink] New post   16 Jun 2020, 03:28
Expert Reply
2
Bookmarks
00:00

Question Stats:

62% (01:05) correct 38% (01:37) wrong based on 50 sessions

Hide Show 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
ShowHide Answer
Official Answer
C
User avatar
D
Carcass
Verbal Expert
Joined: 18 Apr 2015
Posts: 28668
Own Kudos [?]: 33165 [0]
Given Kudos: 25180
Send PM
Re: If (4-x)/(2+x)=x, what is the value of x^2+3x-4? [#permalink] New post   16 Jun 2020, 03:28
Expert Reply
Post A Detailed Correct Solution For The Above Questions And Get A Kudos.
Question From Our New Project: GRE Quant Challenge Questions Daily - NEW EDITION!
User avatar
P
GreenlightTestPrep
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Own Kudos [?]: 11694 [2]
Given Kudos: 136
Send PM

Top Member of the Month
Re: If (4-x)/(2+x)=x, what is the value of x^2+3x-4? [#permalink] New post   16 Jun 2020, 05:22
1
1
Bookmarks
Carcass 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


Given: (4 - x)/(2 + x) = x
Eliminate the fraction by multiplying both sides by (2 + x) to get: (4 - x) = (x)(2 + x)
Expand: 4 - x = 2x + x²
Add x to both sides: 4 = x² + 3x
Subtract 4 from both sides: 0 = x² + 3x - 4

PERFECT! The question asks us to find the value of x² + 3x - 4, and we just showed that the expression equals 0

Answer: C

Cheers,
Brent
User avatar
Farina
Senior Manager
Senior Manager
Joined: 10 Feb 2020
Posts: 496
Own Kudos [?]: 335 [0]
Given Kudos: 299
Send PM
Re: If (4-x)/(2+x)=x, what is the value of x^2+3x-4? [#permalink] New post   Updated on: 17 Jun 2020, 18:27
I am confused about question. Don't we have to find roots? we won't apply quadratic equation formula?
GreenlightTestPrep wrote:
The question asks us to find the value of x² + 3x - 4
Notice that this in a algebraic EXPRESSION and not an algebraic EQUATION.

Most algebraic EXPRESSIONS can have infinitely many values.

For example, if x = 0, then x² + 3x - 4 = 0² + 3(0) - 4 = -4
If x = 2, then x² + 3x - 4 = 2² + 3(2) - 4 = 6
If x = 10, then x² + 3x - 4 = 10² + 3(10) - 4 = 126
If x = -5, then x² + 3x - 4 = (-5)² + 3(-5) - 4 = 6
etc

So, on it's own, the algebraic EXPRESSION x² + 3x - 4 has no particular value. In fact, the value of x² + 3x - 4 depends exclusively on the value of x.


The EQUATION x² + 3x - 4 = 0 is different.
When we're asked to solve this equation, we're looking for a value(s) of x such that the algebraic EXPRESSION x² + 3x - 4 has the value of 0.

Cheers,
Brent

Originally posted by Farina on 16 Jun 2020, 17:44.
Last edited by Farina on 17 Jun 2020, 18:27, edited 1 time in total.
avatar
jgastelor
Manager
Manager
Joined: 15 May 2020
Posts: 91
Own Kudos [?]: 73 [0]
Given Kudos: 0
Send PM
Re: If (4-x)/(2+x)=x, what is the value of x^2+3x-4? [#permalink] New post   17 Jun 2020, 17:28
1
(4-x)/)(2+x) = x

4 - x = 2x + x^2

2x + x^2 = 4 - x

x^2 + 3x - 4 = 0

And this is the question.
avatar
B
Ashgre
Retired Moderator
Joined: 18 Oct 2018
Posts: 148
Own Kudos [?]: 179 [0]
Given Kudos: 27
Send PM
Re: If (4-x)/(2+x)=x, what is the value of x^2+3x-4? [#permalink] New post   05 Nov 2020, 17:31
1
Carcass 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


(4-x)/(2+x)=x --> 4-x = 2x+x^2 --> 4 = x^2 + 3x.

If we substitute x^2 + 3 as 4 we get 4-4 = 0.

Hence option C is the answer.
avatar
anasp99
Intern
Intern
Joined: 21 Aug 2020
Posts: 39
Own Kudos [?]: 29 [0]
Given Kudos: 0
Send PM
Re: If (4-x)/(2+x)=x, what is the value of x^2+3x-4? [#permalink] New post   06 Nov 2020, 17:06
1
Another way you could figure this out fairly quickly without having to use much brain power is plugging in the answer choices into the first equation and seeing which of the values you plug in for X hold true.
For example:
The first equation is: (4-x) / (2+x) = x.
A) -4
Let's plug in -4 to start with...
(4+4) / (2-4) = -4 ?
8 / -2 = -4 Which is correct.
So now you know your x-value.
Be careful because the question asks for the value for x^2 + 3x - 4, NOT the value of x!
Plugging in x = -4 to the equation gets us x^2 + 3x - 4 = 0 which is the answer (C).

Saves a good bit of time if you're quick to utilize tricks like this and don't really know how to work it out using algebra or don't want to use the algebra.
User avatar
bumpbot
GRE Prep Club Legend
GRE Prep Club Legend
Joined: 07 Jan 2021
Posts: 4447
Own Kudos [?]: 68 [0]
Given Kudos: 0
Send PM
Re: If (4-x)/(2+x)=x, what is the value of x^2+3x-4? [#permalink] New post   13 Apr 2024, 01:26
Hello from the GRE Prep Club BumpBot!

Thanks to another GRE Prep 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.
Prep Club for GRE Bot
gmatclubot
[#permalink]
Moderators:
BrushMyQuant
Moderator
1085 posts
VibhuAnurag
GRE Instructor
218 posts

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

Main navigation

Partners

GRE Resources

www.ets.org/gre | About | Terms and Conditions and Privacy Policy | Prep Club for GRE Rules | Contact