GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 06 Dec 2019, 10:50

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Find the range of values of x that satisfy the inequality (x^2-4)(x-5)

Author Message
TAGS:

### Hide Tags

e-GMAT Representative
Joined: 04 Jan 2015
Posts: 3158
Find the range of values of x that satisfy the inequality (x^2-4)(x-5)  [#permalink]

### Show Tags

Updated on: 23 Dec 2018, 03:48
00:00

Difficulty:

5% (low)

Question Stats:

77% (01:40) correct 23% (01:57) wrong based on 159 sessions

### HideShow timer Statistics

Wavy Line Method Application - Exercise Question #5

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

A. x < -3 or 3 < x < 5

B. x < -3 or -2 < x < 2

C. -2 < x < 2 or 3 < x < 5

D. x < -3 or -2 < x < 2 or 3 < x < 5

E. x < -3

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.

_________________

Originally posted by EgmatQuantExpert on 26 Aug 2016, 02:43.
Last edited by Bunuel on 23 Dec 2018, 03:48, edited 5 times in total.
Board of Directors
Status: Stepping into my 10 years long dream
Joined: 18 Jul 2015
Posts: 3564
Re: Find the range of values of x that satisfy the inequality (x^2-4)(x-5)  [#permalink]

### Show Tags

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.
_________________
My GMAT Story: From V21 to V40
My MBA Journey: My 10 years long MBA Dream
My Secret Hacks: Best way to use GMATClub | Importance of an Error Log!
Verbal Resources: All SC Resources at one place | All CR Resources at one place

GMAT Club Inbuilt Error Log Functionality - View More.
New Visa Forum - Ask all your Visa Related Questions - here.
New! Best Reply Functionality on GMAT Club!
Find a bug in the new email templates and get rewarded with 2 weeks of GMATClub Tests for free
Check our new About Us Page here.
e-GMAT Representative
Joined: 04 Jan 2015
Posts: 3158
Re: Find the range of values of x that satisfy the inequality (x^2-4)(x-5)  [#permalink]

### Show Tags

Updated on: 07 Aug 2018, 06:46
1
1
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:

Required Range:

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

_________________

Originally posted by EgmatQuantExpert on 18 Nov 2016, 03:22.
Last edited by EgmatQuantExpert on 07 Aug 2018, 06:46, edited 3 times in total.
Current Student
Joined: 12 Aug 2015
Posts: 2548
Schools: Boston U '20 (M)
GRE 1: Q169 V154
Re: Find the range of values of x that satisfy the inequality (x^2-4)(x-5)  [#permalink]

### Show Tags

10 Apr 2017, 00:40
2
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.

_________________
Director
Joined: 02 Sep 2016
Posts: 641
Re: Find the range of values of x that satisfy the inequality (x^2-4)(x-5)  [#permalink]

### Show Tags

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?
Manager
Joined: 20 Aug 2015
Posts: 89
Location: India
Schools: ISB '21 (A)
GMAT 1: 710 Q50 V36
GPA: 3
Re: Find the range of values of x that satisfy the inequality (x^2-4)(x-5)  [#permalink]

### Show Tags

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)

Intern
Joined: 11 Oct 2018
Posts: 21
Location: Germany
Re: Find the range of values of x that satisfy the inequality (x^2-4)(x-5)  [#permalink]

### Show Tags

17 Mar 2019, 10:40
EgmatQuantExpert wrote:
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:

Required Range:

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

Hi, since we have 5 zero points and no number with an even power, can we deduce that the must be 3 or 4 intervals for x? Since there is no answer with 4 intervals and only one with 3 intervals, this must be the right answer, true?
Manager
Joined: 27 Oct 2017
Posts: 72
Re: Find the range of values of x that satisfy the inequality (x^2-4)(x-5)  [#permalink]

### Show Tags

19 Mar 2019, 12:23
EgmatQuantExpert wrote:
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:

Required Range:

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

Can you please explain, how we have come to the required range?
Intern
Joined: 11 Oct 2018
Posts: 21
Location: Germany
Find the range of values of x that satisfy the inequality (x^2-4)(x-5)  [#permalink]

### Show Tags

19 Mar 2019, 12:40
arorni wrote:
Can you please explain, how we have come to the required range?

This is exactly what she did I think you have to specify your question a bit. Which part did you not understand?
Manager
Joined: 27 Oct 2017
Posts: 72
Find the range of values of x that satisfy the inequality (x^2-4)(x-5)  [#permalink]

### Show Tags

19 Mar 2019, 12:56
mtambiev wrote:
arorni wrote:
Can you please explain, how we have come to the required range?

This is exactly what she did I think you have to specify your question a bit. Which part did you not understand?

I saw Payal's other post on wavy line https://gmatclub.com/forum/wavy-line-me ... 24319.html. It indeed cleared my doubt about this question, but I am a little confused about drawing wavy lines. Do we always have to start drawing the wavy line from the -ve region (ie Is it the upper right corner)? How the wavy line of (x-1)^2 will look, I got the idea that for even powers the line will remain in the same region but why we have started drawing from the -ve region?
Intern
Joined: 11 Oct 2018
Posts: 21
Location: Germany
Find the range of values of x that satisfy the inequality (x^2-4)(x-5)  [#permalink]

### Show Tags

19 Mar 2019, 13:11
arorni wrote:
mtambiev wrote:
arorni wrote:
Can you please explain, how we have come to the required range?

This is exactly what she did I think you have to specify your question a bit. Which part did you not understand?

I saw Payal's other post on wavy line https://gmatclub.com/forum/wavy-line-me ... 24319.html. It indeed cleared my doubt about this question, but I am a little confused about drawing wavy lines. Do we always have to start drawing the wavy line from the -ve region (ie Is it the upper right corner)? How the wavy line of (x-1)^2 will look, I got the idea that for even powers the line will remain in the same region but why we have started drawing from the -ve region?

Ok i got you. As you can see in her approach, the largest zero point for x is 5 (from all the others:-3,-2,2,3,5). So its easy to check if the equation gives a positive or negative result, if you plug in numbers that are less than the smallest zero point (here: -3) or greater the largest zero point (5).

So let's try all number greater the largest zero point, which is 5. For example, plug in $$x=10$$. Then all terms in the brackets will be positive, so for all $$x>5$$ the equation is $$>0$$.

Remember:
$$+*+=+$$
$$-*+=-$$
$$-*-=+$$

Further on, for even powers, the line will not cross the axis, but bounces back, for odd powers it does cross the axis.
Find the range of values of x that satisfy the inequality (x^2-4)(x-5)   [#permalink] 19 Mar 2019, 13:11
Display posts from previous: Sort by