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# M20-22

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Math Expert
Joined: 02 Sep 2009
Posts: 46167

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16 Sep 2014, 01:08
1
2
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Difficulty:

35% (medium)

Question Stats:

59% (00:35) correct 41% (00:40) wrong based on 160 sessions

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If set $$S$$ consists of all different solutions of equation $$|x - 4| = x$$, what is the range of set $$S$$ ?

A. 0
B. 2
C. 4
D. 6
E. 8

_________________
Math Expert
Joined: 02 Sep 2009
Posts: 46167

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16 Sep 2014, 01:08
1
2
Official Solution:

If set $$S$$ consists of all different solutions of equation $$|x - 4| = x$$, what is the range of set $$S$$ ?

A. 0
B. 2
C. 4
D. 6
E. 8

If $$x$$ is greater than or equal to 4, equation $$|x - 4| = x$$ turns into $$x - 4 = x$$. The last one has no solutions. If $$x$$ is less than 4, equation $$|x - 4| = x$$ turns into $$4 - x = x$$ or $$x = 2$$.

Thus, set $$S$$ has only one element: 2. The range of any one-element set is 0.

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Intern
Joined: 03 Jul 2014
Posts: 16

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24 Jan 2015, 05:06
Hi ,

I got the answer as 0 only .
But my approach was different .

|x-4| = x

Case I

So if x >4
then we have
x-4= x , hence no solution .

Case II

If x < 4
x is -ve

-x + 4 = -x
Again no solution .

I think if we substitute on one side , will it not effect the other X on the RHS as well.

Another doubt is Whats the Range of a Null Set?
Brief me properties of Null set.

Regards.
Math Expert
Joined: 02 Sep 2009
Posts: 46167

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24 Jan 2015, 05:15
hanschris5 wrote:
Hi ,

I got the answer as 0 only .
But my approach was different .

|x-4| = x

Case I

So if x >4
then we have
x-4= x , hence no solution .

Case II

If x < 4
x is -ve

-x + 4 = -x
Again no solution .

I think if we substitute on one side , will it not effect the other X on the RHS as well.

Another doubt is Whats the Range of a Null Set?
Brief me properties of Null set.

Regards.

Why did you substitute x by -x? When x is less than 4, equation |x - 4| = x turns into 4 - x = x or x = 2.
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Intern
Joined: 30 Mar 2015
Posts: 10

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08 Sep 2017, 13:24
1
please what doest it mean rage of set that has one element is 0 what if there two element ???
Director
Joined: 29 Jun 2017
Posts: 500
GPA: 4
WE: Engineering (Transportation)

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08 Sep 2017, 14:46
If x>4
X-4=x
No soln

0<x<4
4-x=x
X=2

If x<0
4-x=-x
No soln

So x=2 is only solution

So S =[2]
Range =0

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Director
Joined: 29 Jun 2017
Posts: 500
GPA: 4
WE: Engineering (Transportation)

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08 Sep 2017, 14:49
1
hichem wrote:
please what doest it mean rage of set that has one element is 0 what if there two element ???

If there are 2 elements

Let 2 numbers be -1 and 5
Then range is 5-(-1) =6
Let 2 numbers -1 and -2
Range will be -1-(-2) = 2-1=1
If there are 2,2 then range is 0
Range is always >=0
Never negative.

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Manager
Joined: 26 Mar 2016
Posts: 60
Location: India
Concentration: Strategy, General Management
GMAT 1: 720 Q50 V36
GRE 1: 313 Q166 V147
GPA: 3.3
WE: Other (Consulting)

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12 Oct 2017, 06:14
Bunuel wrote:
Official Solution:

If set $$S$$ consists of all different solutions of equation $$|x - 4| = x$$, what is the range of set $$S$$ ?

A. 0
B. 2
C. 4
D. 6
E. 8

If $$x$$ is greater than or equal to 4, equation $$|x - 4| = x$$ turns into $$x - 4 = x$$. The last one has no solutions. If $$x$$ is less than 4, equation $$|x - 4| = x$$ turns into $$4 - x = x$$ or $$x = 2$$.

Thus, set $$S$$ has only one element: 2. The range of any one-element set is 0.

Point noted.
simple logic. But would have costed more on the exam
Thankfully, I learned it now itself
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Manager
Joined: 04 Jul 2017
Posts: 60
Location: India
Concentration: Marketing, General Management
GPA: 1
WE: Analyst (Consulting)

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12 Oct 2017, 10:39
Bunuel wrote:
If set $$S$$ consists of all different solutions of equation $$|x - 4| = x$$, what is the range of set $$S$$ ?

A. 0
B. 2
C. 4
D. 6
E. 8

Hi Bunuel, Can you please provide me a like to more similar types of problems? Thanks in advance.
Math Expert
Joined: 02 Sep 2009
Posts: 46167

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12 Oct 2017, 10:45
aashishagarwal2 wrote:
Bunuel wrote:
If set $$S$$ consists of all different solutions of equation $$|x - 4| = x$$, what is the range of set $$S$$ ?

A. 0
B. 2
C. 4
D. 6
E. 8

Hi Bunuel, Can you please provide me a like to more similar types of problems? Thanks in advance.

Statistics + Absolute Value
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Re: M20-22   [#permalink] 12 Oct 2017, 10:45
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# M20-22

Moderators: chetan2u, Bunuel

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