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Wavy Line Method Application - Exercise Question #5

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Wavy Line Method Application - Exercise Question #5 [#permalink]

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New post 26 Aug 2016, 02:43
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Wavy Line Method Application - Exercise Question #5


Find the range of values of x that satisfy the inequality \(\frac{(x^2-4)}{(x-5)(x^2-9)} < 0\)




Wavy Line Method Application has been explained in detail in the following post:: http://gmatclub.com/forum/wavy-line-method-application-complex-algebraic-inequalities-224319.html


Detailed solution will be posted soon.
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Re: Wavy Line Method Application - Exercise Question #5 [#permalink]

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New post 26 Aug 2016, 10:10
EgmatQuantExpert wrote:
Wavy Line Method Application - Exercise Question #5


Find the range of values of x that satisfy the inequality \(\frac{(x^2-4)}{(x-5)(x^2-9)} < 0\)




Wavy Line Method Application has been explained in detail in the following post:: http://gmatclub.com/forum/wavy-line-method-application-complex-algebraic-inequalities-224319.html


Detailed solution will be posted soon.


Inequality is \(\frac{(x^2-4)}{(x-5)(x^2-9)} < 0\)

it can be written as \(\frac{(x-2)(x+2)}{(x-5)(x-3)(x+3)} < 0\)

So, we have the Zero pints of x as -3,-2,2,3 and 5

But We cannot have x = -3,3 or 5.

So, when drawing these values on the number line, we will get the range of x as

(-infinity,-3)U(-2,2)U(3,5)

Please correct me if I am missing anything.
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Re: Wavy Line Method Application - Exercise Question #5 [#permalink]

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New post 18 Nov 2016, 03:22
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Solution:

Hey Everyone,

Please find below the solution of the given problem.

Rewriting the inequality to easily identify the zero points

We know that \((x^2 – 4) = (x+2)(x-2)\)

And similarly, \((x^2-9) = (x+3)(x-3)\)

So, the given inequality can be written as:

\((x+2)(x-2)/(x – 5)(x+3)(x-3)<0\)

Plotting the zero points and drawing the wavy line:

Image

Required Range:

x < -3 or -2 < x < 2 or 3 < x < 5

Correct Answer: Option D
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Re: Wavy Line Method Application - Exercise Question #5 [#permalink]

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New post 09 Apr 2017, 23:52
What are answer choices ? I cannot see any of them

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Re: Wavy Line Method Application - Exercise Question #5 [#permalink]

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New post 09 Apr 2017, 23:56

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Wavy Line Method Application - Exercise Question #5 [#permalink]

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New post 10 Apr 2017, 00:40
Here is what i did in this question==>

Critical points => Equate the numerator and denominator terms to zero and obtain the critical points.

In here => x^2-4=0 => x=2 and x=-2
Also x-5=0 => x=5
And finally x^2-9=0=> x=3 and x=-3

Critical points => -3,-2,2,3,5

Now mark these on the number line and pick up a number in each boundary.
If the value makes the original inequality true => Pick that boundary else discard

=> x=> (-∞,-3)U(-2,2)U(3,5)


Personal Opinion-> This question might be good for practise but is most certainly not a GMAT like Question.


The wavy figure that is attached above makes it look scary.In reality we don't need that crazy figure.
Just plug in numbers in a simple plain straight line by marking the critical points.

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Re: Wavy Line Method Application - Exercise Question #5 [#permalink]

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New post 31 Jul 2017, 02:42
Does the range include 2 and -2 because the points are not circled on the number line like other points?
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Re: Wavy Line Method Application - Exercise Question #5 [#permalink]

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New post 05 Aug 2017, 09:35
Shiv2016 wrote:
Does the range include 2 and -2 because the points are not circled on the number line like other points?


The range would have included any of the critical points -3, -2, 2, 3 and 5 if the equation read \(\frac{(x^2-4)}{(x-5)(x^2-9)} <= 0\) (notice the equal sign at the right)

So, to answer your question, it doesn't include 2 and -2.

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Re: Wavy Line Method Application - Exercise Question #5   [#permalink] 05 Aug 2017, 09:35
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