Author 
Message 
TAGS:

Hide Tags

Current Student
Joined: 06 Sep 2013
Posts: 1997
Concentration: Finance

Re: When is x4 = 4x? [#permalink]
Show Tags
19 Dec 2013, 06:54
Silly me, thats correct Thanks Cheers J:)
Posted from my mobile device



Intern
Joined: 19 Jan 2014
Posts: 31

Re: When is x4 = 4x? [#permalink]
Show Tags
22 Jan 2014, 00:30
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 \(some \ expression={(some \ expression)}\). 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, \(x4=4x=(x4)\) to be true should be that \(x4\leq{0}\) > \(x\leq{4}\). Answer: D. Hope it's clear. This might sound silly but i just started preparing for GMAT, and I have a question. Why is it then in some cases we take x<0 or x>0 and in this problem we have x<=0 and x>=0 Thank you.



Math Expert
Joined: 02 Sep 2009
Posts: 39723

Re: When is x4 = 4x? [#permalink]
Show Tags
23 Jan 2014, 03:50
bytatia 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 \(some \ expression={(some \ expression)}\). 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, \(x4=4x=(x4)\) to be true should be that \(x4\leq{0}\) > \(x\leq{4}\). Answer: D. Hope it's clear. This might sound silly but i just started preparing for GMAT, and I have a question. Why is it then in some cases we take x<0 or x>0 and in this problem we have x<=0 and x>=0 Thank you. Well, it all depends on the problem at hand. For this problem, we need = sign because x=4 also satisfies x4 = 4x. Below posts might help to brush up fundamentals on modulus:
_________________
New to the Math Forum? Please read this: 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



Manager
Joined: 04 Oct 2013
Posts: 162
Location: India
GMAT Date: 05232015
GPA: 3.45

Re: When is x4 = 4x? [#permalink]
Show Tags
24 Jan 2014, 01:03
When is x4 = 4x?
A. x=4 B. x=0 C. x>4 D. x<=4 E. x< 0
\(x4 = 4x\)
Or, \(\frac{x4}{x4}=1\)
=> \((x4) < 0\) or \(x = 0\)
Or, \(x <= 4\)
Answer: (D)



Director
Joined: 23 Jan 2013
Posts: 586

Re: When is x4 = 4x? [#permalink]
Show Tags
29 Nov 2014, 00:23
1
This post received KUDOS
Question asks when distance between x and 4 expressed as x4 is equal to 4x
until x is left to 4 or equal to 4 we get the equation right so x4=4x
Number line is
x4>
if x goes righter we get
4x>
x4 will continue to be positive, but 4x will be negative
Algebraically:
x4=4x 2x=8, x=4
(x4)=4x x+4=4x 0=0, so infinitely many solutions when x<4
x<=4
D



Manager
Joined: 13 Dec 2013
Posts: 55
GPA: 2.71

When is x4 = 4x? [#permalink]
Show Tags
10 Dec 2014, 00:29
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 \(some \ expression={(some \ expression)}\). 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, \(x4=4x=(x4)\) to be true should be that \(x4\leq{0}\) > \(x\leq{4}\). Answer: D. Hope it's clear. I am still new to modulus so please do bare with me if I sound stupid. This problem can be solved easily by picking numbers but to understand the concepts I tried to solve it using the books I read. So according to the book, I need to take into account when the modulus is positive and negative when solving \(x4>0, x>4\) x4=4x x=4 (not sure if this value has to be rejected or not. Please help) and when \(x+4<0, x<=4\) (x+4)=4x x4=4x Just lost here. My question is why do we chose X<=4 why do we chose one condition over the other.



Math Expert
Joined: 02 Sep 2009
Posts: 39723

When is x4 = 4x? [#permalink]
Show Tags
10 Dec 2014, 04:34
saadis87 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 \(some \ expression={(some \ expression)}\). 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, \(x4=4x=(x4)\) to be true should be that \(x4\leq{0}\) > \(x\leq{4}\). Answer: D. Hope it's clear. I am still new to modulus so please do bare with me if I sound stupid. This problem can be solved easily by picking numbers but to understand the concepts I tried to solve it using the books I read. So according to the book, I need to take into account when the modulus is positive and negative when solving \(x4>0, x>4\) x4=4x x=4 (not sure if this value has to be rejected or not. Please help) and when \(x+4<0, x<=4\) (x+4)=4x x4=4x Just lost here. My question is why do we chose X<=4 why do we chose one condition over the other. For the second case, when x  4 < 0 (x < 4), x  4 becomes (x  4), so we'd have (x  4) = 4  x, which gives 4 = 4. Since 4 = 4 is true, then it means that for x < 4, x4 = 4x holds true. Combining x = 4 from the first case and x < 4 from the second, we'll have x <= 4. Hope it's clear.
_________________
New to the Math Forum? Please read this: 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



Manager
Joined: 13 Dec 2013
Posts: 55
GPA: 2.71

Re: When is x4 = 4x? [#permalink]
Show Tags
10 Dec 2014, 05:28
Bunuel wrote: saadis87 wrote: I am still new to modulus so please do bare with me if I sound stupid.
This problem can be solved easily by picking numbers but to understand the concepts I tried to solve it using the books I read. So according to the book, I need to take into account when the modulus is positive and negative when solving
\(x4>0, x>4\)
x4=4x x=4 (not sure if this value has to be rejected or not. Please help)
and when \(x+4<0, x<=4\) (x+4)=4x x4=4x Just lost here.
My question is why do we chose X<=4 why do we chose one condition over the other.
For the second case, when x + 4 < 0 (x < 4), x  4 becomes (x  4), so we'd have (x  4) = 4  x, which gives 4 = 4. Since 4 = 4 is true, then it means that for x < 4, x4 = 4x holds true. Combining x = 4 from the first case and x < 4 from the second, we'll have x <= 4. Hope it's clear. Makes a lot more sense, Thankyou



Intern
Joined: 27 Jan 2015
Posts: 7

Re: When is x4 = 4x? [#permalink]
Show Tags
24 Mar 2015, 04:12
The equation holds true for every x value < 0. IMO answer choice E satisfies the equation as well. How can we cross out E?



Math Expert
Joined: 02 Sep 2009
Posts: 39723

Re: When is x4 = 4x? [#permalink]
Show Tags
24 Mar 2015, 04:18



GMAT Club Legend
Joined: 09 Sep 2013
Posts: 16009

Re: When is x4 = 4x? [#permalink]
Show Tags
28 Mar 2016, 05:05
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.
_________________
GMAT Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources



Verbal Forum Moderator
Joined: 02 Aug 2009
Posts: 4571

Re: When is x4 = 4x? [#permalink]
Show Tags
15 Apr 2016, 20:59
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 \(some \ expression={(some \ expression)}\). 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, \(x4=4x=(x4)\) to be true should be that \(x4\leq{0}\) > \(x\leq{4}\). Answer: D. Hope it's clear. Hi Bunuel, I feel the way Q is asked, even x= 4, x=0 or x<0 may fit in.. the Q asks " When is x4 = 4x? ofcourse when x=4, ans is yes.. when x= 0... ans is yes.. yes x<=4 gives the entire range, BUT the Q does not ask that..Had the Q been. when all is x4 = 4x? for which all values is x4 = 4x? OR What is the range of x for x4 = 4x?Would in ACTUAL GMAT, the wordings of this kind MEAN what we are inferring here?
_________________
Absolute modulus :http://gmatclub.com/forum/absolutemodulusabetterunderstanding210849.html#p1622372 Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html



Math Expert
Joined: 02 Sep 2009
Posts: 39723

Re: When is x4 = 4x? [#permalink]
Show Tags
16 Apr 2016, 10:14
chetan2u 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 \(some \ expression={(some \ expression)}\). 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, \(x4=4x=(x4)\) to be true should be that \(x4\leq{0}\) > \(x\leq{4}\). Answer: D. Hope it's clear. Hi Bunuel, I feel the way Q is asked, even x= 4, x=0 or x<0 may fit in.. the Q asks " When is x4 = 4x? ofcourse when x=4, ans is yes.. when x= 0... ans is yes.. yes x<=4 gives the entire range, BUT the Q does not ask that..Had the Q been. when all is x4 = 4x? for which all values is x4 = 4x? OR What is the range of x for x4 = 4x?Would in ACTUAL GMAT, the wordings of this kind MEAN what we are inferring here?You are right the wording of the question is poor.
_________________
New to the Math Forum? Please read this: 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



Manager
Joined: 10 Apr 2016
Posts: 56
Concentration: Strategy, Entrepreneurship
GPA: 3.01

Re: When is x4 = 4x? [#permalink]
Show Tags
17 Apr 2016, 04:54
For those struggling to understand how this works with the equal / lesser signs X=4 x4=4x > 44=44 X=3 x4=4x > 1=1 X=2 24=42 > 2=2 X=1 X=0 And so on .
_________________
Took the Gmat and got a 520 after studying for 3 weeks with a fulltime job. Now taking it again, but with 6 weeks of prep time and a part time job. Studying every day is key, try to do at least 5 exercises a day.



Director
Joined: 04 Jun 2016
Posts: 650

Re: When is x4 = 4x? [#permalink]
Show Tags
25 Jul 2016, 03:52
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? x4 = 4x? Since a Mod always returns +ve value x4 can be seen as >0 for all mathematical purposes so our equation becomes 0<4x 4x >0 x<4 Answer is D {more or less; there seems to be a sign problem in either in option or in the original question}
_________________
Posting an answer without an explanation is "GOD COMPLEX". The world doesn't need any more gods. Please explain you answers properly. FINAL GOODBYE : 17th SEPTEMBER 2016. .. 16 March 2017  I am back but for all purposes please consider me semiretired.




Re: When is x4 = 4x?
[#permalink]
25 Jul 2016, 03:52



Go to page
Previous
1 2
[ 35 posts ]




