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Re: When is x  4 = 4  x?
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21 Jan 2014, 23:30
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.



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Re: When is x  4 = 4  x?
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23 Jan 2014, 02:50
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:
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Re: When is x  4 = 4  x?
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24 Jan 2014, 00:03
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)



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Re: When is x  4 = 4  x?
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28 Nov 2014, 23:23
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



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Re: When is x  4 = 4  x?
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09 Dec 2014, 23:29
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.



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Re: When is x  4 = 4  x?
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10 Dec 2014, 03:34
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.
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Re: When is x  4 = 4  x?
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10 Dec 2014, 04:28
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



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Re: When is x  4 = 4  x?
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24 Mar 2015, 03:12
The equation holds true for every x value < 0. IMO answer choice E satisfies the equation as well. How can we cross out E?



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Re: When is x  4 = 4  x?
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24 Mar 2015, 03:18



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Re: When is x  4 = 4  x?
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15 Apr 2016, 19:59
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?
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1) Absolute modulus : http://gmatclub.com/forum/absolutemodulusabetterunderstanding210849.html#p1622372 2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html 3) effects of arithmetic operations : https://gmatclub.com/forum/effectsofarithmeticoperationsonfractions269413.html
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Re: When is x  4 = 4  x?
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16 Apr 2016, 09:14
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.
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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.
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Re: When is x  4 = 4  x?
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17 Apr 2016, 03:54
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 .
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Re: When is x  4 = 4  x?
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25 Jul 2016, 02:52
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}
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Re: When is x  4 = 4  x?
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06 Aug 2017, 01:55
Well let us begin with knowing  a = a when a<= 0 Therefore, x4 = 4x when x4 <=0 Hence, D



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Re: When is x  4 = 4  x?
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13 Nov 2017, 13:00
a  b = b  a ; when a<b or a=b (includes 0)
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Re: When is x  4 = 4  x?
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26 Nov 2017, 03:56
nkimidi7y wrote: When is x  4 = 4  x?
A. x = 4 B. x = 0 C. x > 4 D. x <= 4 E. x < 0 Why not just A? i was confused b/w A and D but I agree with D but why not A?



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Re: When is x  4 = 4  x?
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13 Sep 2018, 02:52
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, This is a good quality question and bit tricky. I selected A as an answer. After looking at answer choice, i can understand solution perfectly. As per my thought process, whenever the question has equal to sign then we get either 2 values or one value (x=4). But how can i avoid mistake on this type of question? Which triggering point forces you to think on nonnegative value?
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