Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 09 Apr 2012
Posts: 59

When is x  4 = 4  x?
[#permalink]
Show Tags
03 May 2012, 11:38
Question Stats:
57% (00:46) correct 43% (00:41) wrong based on 1933 sessions
HideShow timer Statistics
When is x  4 = 4  x? A. x = 4 B. x = 0 C. x > 4 D. x <= 4 E. x < 0
Official Answer and Stats are available only to registered users. Register/ Login.




Math Expert
Joined: 02 Sep 2009
Posts: 48037

Re: When is x  4 = 4  x?
[#permalink]
Show Tags
03 May 2012, 12:04




Senior Manager
Joined: 23 Oct 2010
Posts: 361
Location: Azerbaijan
Concentration: Finance

Re: When is x  4 = 4  x?
[#permalink]
Show Tags
08 May 2012, 10:57
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 to 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 to pay the price to make them come true
I am still on all gmat forums. msg me if you want to ask me smth




Manager
Joined: 09 Apr 2012
Posts: 59

Re: When is x  4 = 4  x?
[#permalink]
Show Tags
03 May 2012, 15:00
4x is always >=0. So x is always <=4.
Is this what you have meant?



Intern
Joined: 12 Dec 2011
Posts: 9
Location: Italy
Concentration: Finance, Entrepreneurship
GMAT Date: 04092013
GPA: 4
WE: Management Consulting (Consulting)

Re: When is x  4 = 4  x?
[#permalink]
Show Tags
28 Oct 2012, 02:56
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 do 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, \(x4=4x=(x4)\) to be true should be that \(x4\leq{0}\) > \(x\leq{4}\). Answer: D. Hope it's clear. Hi Bunuel I am trying to understand theese two properties, but how is it possible to have X=X, in order that absolute value has to be always positive? Could you please provide me an explaination in more details? Thanks in advance



Math Expert
Joined: 02 Sep 2009
Posts: 48037

Re: When is x  4 = 4  x?
[#permalink]
Show Tags
29 Oct 2012, 02:56
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 do 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, \(x4=4x=(x4)\) to be true should be that \(x4\leq{0}\) > \(x\leq{4}\). Answer: D. Hope it's clear. Hi Bunuel I am trying to understand theese two properties, but how is it possible to have X=X, in order that absolute value has to be always positive? Could you please provide me an explaination in more details? Thanks in advance When \(x\leq{0}\), for example when \(x=5\), then \(5=5=(5)\) so \(x=x\) (negative =(negative)=positive). For more check Absolute Value chapter of Math book: mathabsolutevaluemodulus86462.htmlHope it helps.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Senior Manager
Joined: 13 Aug 2012
Posts: 441
Concentration: Marketing, Finance
GPA: 3.23

Re: When is x  4 = 4  x?
[#permalink]
Show Tags
05 Dec 2012, 04:51
x4 = 4x Absolute values are always positive or greater than 0. So, 4x >= 0 ==> x <= 4 Answer: D There is no need to test values.
_________________
Impossible is nothing to God.



Intern
Status: Need some help
Joined: 27 Nov 2012
Posts: 8
Location: United States
Concentration: General Management, Human Resources
Schools: HBS '16, Wharton Exec '17, Kellogg 1YR '15, Sloan '16, Tuck '16, Yale '16, Duke Fuqua, Anderson FEMBA '17, Marshall '16, Cambridge, Booth, CBS, Cornell Tech '15, Berkeley Haas
GPA: 3.56
WE: Sales (Internet and New Media)

Re: When is x  4 = 4  x?
[#permalink]
Show Tags
06 Jan 2013, 14:26
Hi brunel,
You said some expression when it is > = 0 then l some espression l <= some expression.
In this case how do i know X4 is >= 0
Thanks!



Math Expert
Joined: 02 Sep 2009
Posts: 48037

Re: When is x  4 = 4  x?
[#permalink]
Show Tags
07 Jan 2013, 03:37



Intern
Joined: 08 Feb 2013
Posts: 2

Re: When is x  4 = 4  x?
[#permalink]
Show Tags
10 Feb 2013, 06:14
Why not E?
If i am not mistaken when x<0, then x1 = x1?



Math Expert
Joined: 02 Sep 2009
Posts: 48037

Re: When is x  4 = 4  x?
[#permalink]
Show Tags
10 Feb 2013, 06:21



Intern
Joined: 05 Mar 2013
Posts: 13

Re: When is x  4 = 4  x?
[#permalink]
Show Tags
13 Mar 2013, 14:45
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: 85
Location: United States
Concentration: Entrepreneurship, International Business
GPA: 3.2
WE: Education (Education)

Re: When is x  4 = 4  x?
[#permalink]
Show Tags
14 Mar 2013, 13:19
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 to (x4)=4x. Right? We know that x4 would have to be negative for the equation in question to be true. This would imply that x would have to be a small positive number smaller than 4 or a negative number. You can take examples to 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 to your question, if a question deals with equality it also indirectly deals with inequality. If you say the equation is satisfied when x=0,x=4,x=5 and so on, it also implies that the equation is true for all values of x less than or equal to 4. An equation exists only at certain points. We have to 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 me 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]
Show Tags
14 Mar 2013, 17:34
thanks Kris. that does help. i guess my follow up question would be, is there a way to solve it algebraically rather than 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 to (x4)=4x. Right? We know that x4 would have to be negative for the equation in question to be true. This would imply that x would have to be a small positive number smaller than 4 or a negative number. You can take examples to 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 to your question, if a question deals with equality it also indirectly deals with inequality. If you say the equation is satisfied when x=0,x=4,x=5 and so on, it also implies that the equation is true for all values of x less than or equal to 4. An equation exists only at certain points. We have to 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 me 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: 72

Re: When is x  4 = 4  x?
[#permalink]
Show Tags
14 Mar 2013, 18:19
When is x4 = 4x?
Critical Values method:
The Critical Value here is x=4 (we make the absolute value term equal to zero), so we have this conditions to 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: 85
Location: United States
Concentration: Entrepreneurship, International Business
GPA: 3.2
WE: Education (Education)

Re: When is x  4 = 4  x?
[#permalink]
Show Tags
15 Mar 2013, 11:26
As Johnwesley said, for x4=4x, s4 should be negative or equal to 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 to solve it algebraically rather than plugging in numbers?



Manager
Status: Joining Cranfield Sep 2014
Joined: 01 Sep 2012
Posts: 59
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]
Show Tags
09 Aug 2013, 22:24
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 to solve this problem with above method.
A. x=4 B. x=0 C. x>4 D. x<=4 E. x< 0



SVP
Joined: 06 Sep 2013
Posts: 1850
Concentration: Finance

Re: When is x  4 = 4  x?
[#permalink]
Show Tags
19 Dec 2013, 05:14
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 end up with. So then how do you solve when you have 4x = 4x? Is this property correct or what are its limitations? Thanks J



Math Expert
Joined: 02 Sep 2009
Posts: 48037

Re: When is x  4 = 4  x?
[#permalink]
Show Tags
19 Dec 2013, 05:32



SVP
Joined: 06 Sep 2013
Posts: 1850
Concentration: Finance

Re: When is x  4 = 4  x?
[#permalink]
Show Tags
19 Dec 2013, 06:54
Silly me, thats correct Thanks Cheers J:)
Posted from my mobile device




Re: When is x  4 = 4  x? &nbs
[#permalink]
19 Dec 2013, 06:54



Go to page
1 2
Next
[ 36 posts ]



