Bạn đang xem: x^4+4
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 đồ sộ Daily Prep Questions via tin nhắn.
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 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 đồ sộ your email? No problem, unsubscribe here.
Hello Guest!
It appears that you are browsing the GMAT Club diễn đàn unregistered!
Signing up is free, quick, and confidential.
Join 700,000+ members and get the full benefits of GMAT Club
Registration gives you:

Tests
Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan Prep. All are không tính phí for GMAT Club members.

Applicant Stats
View detailed applicant stats such as GPA, GMAT score, work experience, location, application status, and more

Books/Downloads
Download thousands of study notes, question collections, GMAT Club’s Grammar and Math books. All are free!
and many more benefits!
Jan 10
770 on the GMAT? It's a goal that many students aspire đồ sộ achieve, but only 1% of all test takers receive it. Watch this interview đồ sộ learn how Mantavya scored a remarkable 770 GMAT with just 2 months of preparation in first attempt.
Jan 11
1. GMAT Club Tests Are Focus Ready: Now Featuring 5 Full Length Focus Tests: 2. Why You Should Use LSAT Tests for GMAT RC & CR: 3. From 650 on GMAT Classic đồ sộ 695 (98th Percentile) on GMAT Focus: and more.
Jan 13
Do you want đồ sộ ace the GMAT Focus? Join Piyush Beriwala in this webinar as he guides you through a smart study plan đồ sộ achieve the 99th %ile on the GMAT Focus. Learn the best strategies and tips đồ sộ master the test and boost your score.
Jan 13
Attend this session đồ sộ learn how đồ sộ Deconstruct arguments, PreThink Author’s Assumptions, and apply Negation Test.
Jan 13
Attend this không tính phí GMAT Algebra Webinar and learn how đồ sộ master the most challenging Inequalities and Absolute Value problems with ease.
Jan 13
2000+ không tính phí GMAT videos  20+ tiện ích help videos  15+ interview prep videos
Jan 15
András Domschitz recently scored 735 (99.5%) on the GMAT Focus Edition. In this Clip, we discuss his GMAT Focus study plan and techniques and how TTP’s selfstudy course helped him achieve an incredible 735 score on the GMAT Edition
Jan 15
Video explanations + diagnosis of 10 weakest areas + oneweek access đồ sộ 10 SC ebooks and 200 short videos!
Jan 16
Join Giorgio and many other students who have used Target Test Prep đồ sộ score high on the GMAT Focus Edition. Start your 5day trial of the TTP GMAT Course today for FREE.
Intern
Joined: 09 Apr 2012
Posts: 48
When is x  4 = 4  x? [#permalink] 03 May 2012, 10:38
Question Stats:
59% (01:07) correct 41% (01:01) wrong based on 2821 sessions
Hide Show timer Statistics
When is x  4 = 4  x?
A. x = 4
B. x = 0
C. x > 4
D. x <= 4
E. x < 0
Re: When is x  4 = 4  x? [#permalink] 03 May 2012, 11:04
nkimidi7y wrote:
When is x4 = 4x?
A. x=4
B. x=0
C. x>4
D. x<=4
E. x< 0
I could answer this question by plugging in some numbers.
But how tự i prove this using algebra?
Absolute value properties:
When \(x\leq{0}\) then \(x=x\), or more generally when \(some \ expression\leq{0}\) then \(some \ expression={(some \ expression)}\). For example: \(5=5=(5)\);
When \(x\geq{0}\) then \(x=x\), or more generally when \(some \ expression\geq{0}\) then \(some \ expression={some \ expression}\). For example: \(5=5\);
So, \(x4=4x=(x4)\) đồ sộ be true should be that \(x4\leq{0}\) > \(x\leq{4}\).
Answer: D.
Hope it's clear.
_________________
Re: When is x  4 = 4  x? [#permalink] 08 May 2012, 09:57
nkimidi7y wrote:
4x is always >=0.
So x is always <=4.
Is this what you have meant?
x4 = 4x
1) x4 is ALWAYS none negative.
so , 4x must be also more or equal đồ sộ zero
4x>=0
x<=4
2) if x<4 , then 4x=4x
if x>=4 x4=4x x=4
so x <= 4
_________________
Happy are those who dream dreams and are ready đồ sộ pay the price đồ sộ make them come true
I am still on all gmat forums. msg u if you want đồ sộ ask u smth
Intern
Joined: 09 Apr 2012
Posts: 48
Re: When is x  4 = 4  x? [#permalink] 03 May 2012, 14:00
4x is always >=0.
So x is always <=4.
Is this what you have meant?
Intern
Joined: 12 Dec 2011
Posts: 7
Location: Italy
Concentration: Finance, Entrepreneurship
GMAT Date: 04092013
GPA: 4
WE:Management Consulting (Consulting)
Re: When is x  4 = 4  x? [#permalink] 28 Oct 2012, 01:56
Bunuel wrote:
nkimidi7y wrote:
When is x4 = 4x?
A. x=4
B. x=0
C. x>4
D. x<=4
E. x< 0
I could answer this question by plugging in some numbers.
But how tự i prove this using algebra?
Absolute value properties:
When \(x\leq{0}\) then \(x=x\), or more generally when \(some \ expression\leq{0}\) then \(some \ expression\leq{(some \ expression)}\). For example: \(5=5=(5)\);
When \(x\geq{0}\) then \(x=x\), or more generally when \(some \ expression\geq{0}\) then \(some \ expression\leq{some \ expression}\). For example: \(5=5\);
So, \(x4=4x=(x4)\) đồ sộ be true should be that \(x4\leq{0}\) > \(x\leq{4}\).
Answer: D.
Hope it's clear.
Hi Bunuel
I am trying đồ sộ understand theese two properties, but how is it possible đồ sộ have X=X, in order that absolute value has đồ sộ be always positive?
Could you please provide u an explaination in more details?
Thanks in advance
Re: When is x  4 = 4  x? [#permalink] 29 Oct 2012, 01:56
mario1987 wrote:
Bunuel wrote:
nkimidi7y wrote:
When is x4 = 4x?
A. x=4
B. x=0
C. x>4
D. x<=4
E. x< 0
I could answer this question by plugging in some numbers.
But how tự i prove this using algebra?
Absolute value properties:
When \(x\leq{0}\) then \(x=x\), or more generally when \(some \ expression\leq{0}\) then \(some \ expression\leq{(some \ expression)}\). For example: \(5=5=(5)\);
When \(x\geq{0}\) then \(x=x\), or more generally when \(some \ expression\geq{0}\) then \(some \ expression\leq{some \ expression}\). For example: \(5=5\);
So, \(x4=4x=(x4)\) đồ sộ be true should be that \(x4\leq{0}\) > \(x\leq{4}\).
Answer: D.
Hope it's clear.
Hi Bunuel
I am trying đồ sộ understand theese two properties, but how is it possible đồ sộ have X=X, in order that absolute value has đồ sộ be always positive?
Could you please provide u an explaination in more details?
Thanks in advance
When \(x\leq{0}\), for example when \(x=5\), then \(5=5=(5)\) sánh \(x=x\) (negative =(negative)=positive).
For more kiểm tra Absolute Value chapter of Math book:
mathabsolutevaluemodulus86462.html
Hope it helps.
_________________
Senior Manager
Joined: 13 Aug 2012
Posts: 337
Concentration: Marketing, Finance
GPA: 3.23
Re: When is x  4 = 4  x? [#permalink] 05 Dec 2012, 03:51
x4 = 4x
Absolute values are always positive or greater kêu ca 0.
So, 4x >= 0 ==> x <= 4
Answer: D
There is no need đồ sộ test values.
Intern
Joined: 27 Nov 2012
Status:Need some help
Posts: 8
Location: United States
Concentration: General Management, Human Resources
GPA: 3.56
WE:Sales (Internet and New Media)
Re: When is x  4 = 4  x? [#permalink] 06 Jan 2013, 13:26
Hi brunel,
You said some expression when it is > = 0 then l some espression l <= some expression.
In this case how tự i know X4 is >= 0
Thanks!
Re: When is x  4 = 4  x? [#permalink] 07 Jan 2013, 02:37
LiquidGrave wrote:
Hi brunel,
You said some expression when it is > = 0 then l some espression l <= some expression.
In this case how tự i know X4 is >= 0
Thanks!
We have that \(x4=4x=(x4)\). So, \(some \ expression\leq{(some \ expression)}\), thus \(x4\leq{0}\) > \(x\leq{4}\).
Hope it's clear.
_________________
Intern
Joined: 08 Feb 2013
Posts: 1
Re: When is x  4 = 4  x? [#permalink] 10 Feb 2013, 05:14
Why not E?
If i am not mistaken when x<0, then x1 = x1?
Re: When is x  4 = 4  x? [#permalink] 10 Feb 2013, 05:21
Victorlp89 wrote:
Why not E?
If i am not mistaken when x<0, then x1 = x1?
First of all we have x4 = 4x not x1 = x1.
Next, x1 = x1 for \(x\geq{1}\).
If \(x\leq{1}\), then \(x1=(x1)=1x\)
_________________
Intern
Joined: 05 Mar 2013
Posts: 13
Re: When is x  4 = 4  x? [#permalink] 13 Mar 2013, 13:45
how come all of a sudden the answer has inequalities when the question only had equal signs? that's the part i dont understand
Manager
Joined: 24 Sep 2012
Posts: 68
Location: United States
Concentration: Entrepreneurship, International Business
GPA: 3.2
WE:Education (Education)
Re: When is x  4 = 4  x? [#permalink] 14 Mar 2013, 12:19
Absolute value of any number or expression must be positive.
If (x4) is positive then x4 is also positive
What if x4 is negative? Since the absolute value must be positive, x4 would be equal đồ sộ (x4)=4x.
Right?
We know that x4 would have đồ sộ be negative for the equation in question đồ sộ be true. This would imply that x would have đồ sộ be a small positive number smaller kêu ca 4 or a negative number. You can take examples đồ sộ test that.
x=14 (x4)=ve
x=1, x4=3 ve
x=4, implies x4=0 and 4x=0. Thus, the equation is satisfied.
Hence, d is the answer.
Coming đồ sộ your question, if a question đơn hàng with equality it also indirectly đơn hàng with inequality. If you say the equation is satisfied when x=0,x=4,x=5 and sánh on, it also implies that the equation is true for all values of x less kêu ca or equal đồ sộ 4.
An equation exists only at certain points. We have đồ sộ find those points and if those points range over a large space, the easiest way would be express it as inequality.
Note: An equality question can have answers which might be expressed as inequalities. There is nothing wrong with it.
Hope it helps! Let u know if I can help you any further.
dhlee922 wrote:
how come all of a sudden the answer has inequalities when the question only had equal signs? that's the part i dont understand
Intern
Joined: 05 Mar 2013
Posts: 13
Re: When is x  4 = 4  x? [#permalink] 14 Mar 2013, 16:34
thanks Kris. that does help. i guess my follow up question would be, is there a way đồ sộ solve it algebraically rather kêu ca plugging in numbers?
Kris01 wrote:
Absolute value of any number or expression must be positive.
If (x4) is positive then x4 is also positive
What if x4 is negative? Since the absolute value must be positive, x4 would be equal đồ sộ (x4)=4x.
Right?
We know that x4 would have đồ sộ be negative for the equation in question đồ sộ be true. This would imply that x would have đồ sộ be a small positive number smaller kêu ca 4 or a negative number. You can take examples đồ sộ test that.
x=14 (x4)=ve
x=1, x4=3 ve
x=4, implies x4=0 and 4x=0. Thus, the equation is satisfied.
Hence, d is the answer.
Coming đồ sộ your question, if a question đơn hàng with equality it also indirectly đơn hàng with inequality. If you say the equation is satisfied when x=0,x=4,x=5 and sánh on, it also implies that the equation is true for all values of x less kêu ca or equal đồ sộ 4.
An equation exists only at certain points. We have đồ sộ find those points and if those points range over a large space, the easiest way would be express it as inequality.
Note: An equality question can have answers which might be expressed as inequalities. There is nothing wrong with it.
Hope it helps! Let u know if I can help you any further.
dhlee922 wrote:
how come all of a sudden the answer has inequalities when the question only had equal signs? that's the part i dont understand
Manager
Joined: 24 Jan 2013
Posts: 62
Re: When is x  4 = 4  x? [#permalink] 14 Mar 2013, 17:19
When is x4 = 4x?
Critical Values method:
The Critical Value here is x=4 (we make the absolute value term equal đồ sộ zero), sánh we have this conditions đồ sộ check:
1) x<4: (x4)=4x > x4=x4 > true for all values of x, but only when x<4 the initial condition is satisfied > true always that x<4
2) x=4: 0=0 > this is true always that x=4
3) x>4: x4=4x > 2x=8 > x=4 > initial condition of x>4 is not met
Therefore, there is a solution only when: x<=4
Solution D
Manager
Joined: 24 Sep 2012
Posts: 68
Location: United States
Concentration: Entrepreneurship, International Business
GPA: 3.2
WE:Education (Education)
Re: When is x  4 = 4  x? [#permalink] 15 Mar 2013, 10:26
As Johnwesley said, for x4=4x, s4 should be negative or equal đồ sộ 0.
i.e. x4<=0
Hence, x<=4
[quote="dhlee922"]thanks Kris. that does help. i guess my follow up question would be, is there a way đồ sộ solve it algebraically rather kêu ca plugging in numbers?
Intern
Joined: 01 Sep 2012
Status:Joining Cranfield Sep 2014
Posts: 42
Concentration: Technology, General Management
GMAT 1: 530 Q50 V14
GMAT 2: 630 Q48 V29
WE:Engineering (Energy and Utilities)
Re: When is x  4 = 4  x? [#permalink] 09 Aug 2013, 21:24
I solved it in this way.
When is x4 = 4x?
Choice A: X=4, it is true but X cannot be always 4
Choice B: X=0, it is also true, but X cannot be always 0
Choice C: X>4, it is false, for e.g. X=6, then one side of equation is 2 and the other side is 2
Choice D: X<=4, this choice encapsulate Choice A, Choice B and for all other conditions and is true for above said equation. Hence the answer choice is D.
It took only 1min đồ sộ solve this problem with above method.
A. x=4
B. x=0
C. x>4
D. x<=4
E. x< 0
VP
Joined: 06 Sep 2013
Posts: 1355
Concentration: Finance
Re: When is x  4 = 4  x? [#permalink] 19 Dec 2013, 04:14
Bunuel wrote:
Victorlp89 wrote:
Why not E?
If i am not mistaken when x<0, then x1 = x1?
First of all we have x4 = 4x not x1 = x1.
Next, x1 = x1 for \(x\geq{1}\).
If \(x\leq{1}\), then \(x1=(x1)=1x\)
Hi Bunuel,
Sinetunes you can manipulate say x4=(x+4)=4x is what you'll kết thúc up with.
So then how tự you solve when you have 4x = 4x?
Is this property correct or what are its limitations?
Thanks
J
Re: When is x  4 = 4  x? [#permalink] 19 Dec 2013, 04:32
jlgdr wrote:
Bunuel wrote:
Victorlp89 wrote:
Why not E?
If i am not mistaken when x<0, then x1 = x1?
First of all we have x4 = 4x not x1 = x1.
Next, x1 = x1 for \(x\geq{1}\).
If \(x\leq{1}\), then \(x1=(x1)=1x\)
Hi Bunuel,
Sinetunes you can manipulate say x4=(x+4)=4x is what you'll kết thúc up with.
So then how tự you solve when you have 4x = 4x?
Is this property correct or what are its limitations?
Thanks
J
\(4x = 4x\) > \(4x\geq{0}\) > \(x\leq{4}\).
_________________
Re: When is x  4 = 4  x? [#permalink] 19 Dec 2013, 05:54
Silly u, thats correct
Thanks
Cheers
J:)
Posted from my mobile device
Re: When is x  4 = 4  x? [#permalink]
19 Dec 2013, 05:54
Bình luận