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

 It is currently 16 Jul 2018, 20:46

### 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

# Wavy Line Method Application - Exercise Question #5

Author Message
TAGS:

### Hide Tags

e-GMAT Representative
Joined: 04 Jan 2015
Posts: 1755
Wavy Line Method Application - Exercise Question #5 [#permalink]

### Show Tags

26 Aug 2016, 02:43
00:00

Difficulty:

(N/A)

Question Stats:

100% (01:10) correct 0% (00:00) wrong based on 19 sessions

### HideShow timer Statistics

Wavy Line Method Application - Exercise Question #5

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

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.
_________________

Ace GMAT quant
Articles and Question to reach Q51 | Question of the week

Number Properties – Even Odd | LCM GCD
Word Problems – Percentage 1 | Percentage 2 | Time and Work 1 | Time and Work 2 | Time, Speed and Distance 1 | Time, Speed and Distance 2
Advanced Topics- Permutation and Combination 1 | Permutation and Combination 2 | Permutation and Combination 3 | Probability
Geometry- Triangles 1 | Triangles 2 | Triangles 3 | Common Mistakes in Geometry
Algebra- Wavy line

Practice Questions
Number Properties 1 | Number Properties 2 | Algebra 1 | Geometry | Prime Numbers | Absolute value equations | Sets

| '4 out of Top 5' Instructors on gmatclub | 70 point improvement guarantee | www.e-gmat.com

Board of Directors
Status: Stepping into my 10 years long dream
Joined: 18 Jul 2015
Posts: 3686
Re: Wavy Line Method Application - Exercise Question #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.

Find a bug in the new email templates and get rewarded with 2 weeks of GMATClub Tests for free

e-GMAT Representative
Joined: 04 Jan 2015
Posts: 1755
Re: Wavy Line Method Application - Exercise Question #5 [#permalink]

### Show Tags

18 Nov 2016, 03:22
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

_________________

Ace GMAT quant
Articles and Question to reach Q51 | Question of the week

Number Properties – Even Odd | LCM GCD
Word Problems – Percentage 1 | Percentage 2 | Time and Work 1 | Time and Work 2 | Time, Speed and Distance 1 | Time, Speed and Distance 2
Advanced Topics- Permutation and Combination 1 | Permutation and Combination 2 | Permutation and Combination 3 | Probability
Geometry- Triangles 1 | Triangles 2 | Triangles 3 | Common Mistakes in Geometry
Algebra- Wavy line

Practice Questions
Number Properties 1 | Number Properties 2 | Algebra 1 | Geometry | Prime Numbers | Absolute value equations | Sets

| '4 out of Top 5' Instructors on gmatclub | 70 point improvement guarantee | www.e-gmat.com

Manager
Joined: 16 Oct 2015
Posts: 73
Location: India
Concentration: Technology, General Management
Schools: ISB '19, IIMA , IIMB, IIMC
GMAT 1: 520 Q44 V17
GMAT 2: 530 Q44 V20
GMAT 3: 710 Q48 V40
GPA: 3.45
WE: Research (Energy and Utilities)
Re: Wavy Line Method Application - Exercise Question #5 [#permalink]

### Show Tags

09 Apr 2017, 23:52
What are answer choices ? I cannot see any of them
Math Expert
Joined: 02 Sep 2009
Posts: 47020
Re: Wavy Line Method Application - Exercise Question #5 [#permalink]

### Show Tags

09 Apr 2017, 23:56
What are answer choices ? I cannot see any of them

As you can see answer choices were not provided for this question.
_________________
BSchool Forum Moderator
Joined: 12 Aug 2015
Posts: 2646
GRE 1: Q169 V154
Wavy Line Method Application - Exercise Question #5 [#permalink]

### Show Tags

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.

_________________

MBA Financing:- INDIAN PUBLIC BANKS vs PRODIGY FINANCE!

Getting into HOLLYWOOD with an MBA!

The MOST AFFORDABLE MBA programs!

STONECOLD's BRUTAL Mock Tests for GMAT-Quant(700+)

AVERAGE GRE Scores At The Top Business Schools!

Director
Joined: 02 Sep 2016
Posts: 742
Re: Wavy Line Method Application - Exercise Question #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?
_________________

Help me make my explanation better by providing a logical feedback.

If you liked the post, HIT KUDOS !!

Don't quit.............Do it.

Manager
Joined: 20 Aug 2015
Posts: 96
Location: India
GMAT 1: 710 Q50 V36
GPA: 3
Re: Wavy Line Method Application - Exercise Question #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)

Re: Wavy Line Method Application - Exercise Question #5   [#permalink] 05 Aug 2017, 09:35
Display posts from previous: Sort by

# Events & Promotions

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.