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M20-22

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New post 16 Sep 2014, 01:08
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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.


Answer: A
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New post 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 .

Please correct my misconception.

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.

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Re: M20-22 [#permalink]

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New post 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 .

Please correct my misconception.

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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Re: M20-22 [#permalink]

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please what doest it mean rage of set that has one element is 0 what if there two element ???

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Re: M20-22 [#permalink]

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New post 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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Re: M20-22 [#permalink]

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New post 08 Sep 2017, 14:49
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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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Re: M20-22 [#permalink]

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New post 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.


Answer: A



Point noted.
simple logic. But would have costed more on the exam :)
Thankfully, I learned it now itself
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Re: M20-22 [#permalink]

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New post 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.

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Re: M20-22 [#permalink]

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New post 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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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?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 128463 [0], given: 12173

Re: M20-22   [#permalink] 12 Oct 2017, 10:45
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