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

 It is currently 16 Jan 2019, 04:24

### 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

## Events & Promotions

###### Events & Promotions in January
PrevNext
SuMoTuWeThFrSa
303112345
6789101112
13141516171819
20212223242526
272829303112
Open Detailed Calendar
• ### The winning strategy for a high GRE score

January 17, 2019

January 17, 2019

08:00 AM PST

09:00 AM PST

Learn the winning strategy for a high GRE score — what do people who reach a high score do differently? We're going to share insights, tips and strategies from data we've collected from over 50,000 students who used examPAL.
• ### Free GMAT Strategy Webinar

January 19, 2019

January 19, 2019

07:00 AM PST

09:00 AM PST

Aiming to score 760+? Attend this FREE session to learn how to Define your GMAT Strategy, Create your Study Plan and Master the Core Skills to excel on the GMAT.

# Find the range of values of x that satisfy the inequality (x - 3)^2

Author Message
TAGS:

### Hide Tags

e-GMAT Representative
Joined: 04 Jan 2015
Posts: 2438
Find the range of values of x that satisfy the inequality (x - 3)^2  [#permalink]

### Show Tags

Updated on: 23 Dec 2018, 02:51
4
4
00:00

Difficulty:

(N/A)

Question Stats:

88% (01:14) correct 13% (04:18) wrong based on 43 sessions

### HideShow timer Statistics

Wavy Line Method Application - Exercise Question #2

Find the range of values of x that satisfy the inequality $$(x - 3)^2 (x + 1)^5 (x^2 - 9) < 0$$

A. x > 1
B. x > -3
C. -1 < x < 3
D. x < -3 or -1 < x < 3
E. x < -3

Wavy Line Method Application has been explained in detail in the following post:: Wavy Line Method Application - Complex Algebraic Inequalities

Detailed solution will be posted soon.

_________________

Number Properties | Algebra |Quant Workshop

Success Stories
Guillermo's Success Story | Carrie's Success Story

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

Number Properties – Even Odd | LCM GCD | Statistics-1 | Statistics-2 | Remainders-1 | Remainders-2
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 | Inequalities

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

Originally posted by EgmatQuantExpert on 26 Aug 2016, 01:32.
Last edited by Bunuel on 23 Dec 2018, 02:51, edited 3 times in total.
Board of Directors
Status: Stepping into my 10 years long dream
Joined: 18 Jul 2015
Posts: 3629
Re: Find the range of values of x that satisfy the inequality (x - 3)^2  [#permalink]

### Show Tags

26 Aug 2016, 08:55
3
EgmatQuantExpert wrote:
Wavy Line Method Application - Exercise Question #2

Find the range of values of x that satisfy the inequality $$(x - 3)^2 (x + 1)^5 (x^2 - 9) < 0$$

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.

Solving the inequality, we will get (x-3)^2(x+1)^5(x+3)(x-3) < 0

or (x-3)^3 (x+1)^5 (x+3) < 0.

Solving on the number line, we will get the points -3,-1 and 3.

Since the power of each is ODD. hence, the range of x will be (-infinity, -3) U (-1,3).

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.

Manager
Joined: 20 Apr 2014
Posts: 89
Re: Find the range of values of x that satisfy the inequality (x - 3)^2  [#permalink]

### Show Tags

17 Nov 2016, 07:40
I guess the final answer is : -1< X <3 & x <-3
since the zero points are 3 , -1 , -3
if we try each number within the range , the inequality will hold true, using the detailed equation :
(x-3)(x-3)(x+1)(x+3)(x-3)<0
But I propose to ignore the even powered expression like the case of (x-3) since the product of such expression must be positive.
e-GMAT Representative
Joined: 04 Jan 2015
Posts: 2438
Re: Find the range of values of x that satisfy the inequality (x - 3)^2  [#permalink]

### Show Tags

Updated on: 07 Aug 2018, 05:46
1
1
Solution:

Hey Everyone,

Please find below, the solution of the given problem.

Rewriting the inequality to easily identify the zero points

$$(x-3)^2 (x+1)^5 (x^2-9)<0$$

Since

$$(x^2-9)=(x+3)*(x-3)$$

The given inequality can be written as

$$(x-3)^3 (x+1)^5 (x+3)<0$$

Plotting the zero points and drawing the wavy line:

Required Range: x < -3 or -1 < x < 3

_________________

Number Properties | Algebra |Quant Workshop

Success Stories
Guillermo's Success Story | Carrie's Success Story

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

Number Properties – Even Odd | LCM GCD | Statistics-1 | Statistics-2 | Remainders-1 | Remainders-2
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 | Inequalities

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

Originally posted by EgmatQuantExpert on 18 Nov 2016, 01:36.
Last edited by EgmatQuantExpert on 07 Aug 2018, 05:46, edited 1 time in total.
Director
Joined: 02 Sep 2016
Posts: 679
Re: Find the range of values of x that satisfy the inequality (x - 3)^2  [#permalink]

### Show Tags

30 Jul 2017, 23:45
@e-gmat team

Is it by any chance possible that all the powers are even and hence the wavy line bounces back for all the points?
_________________

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

If you liked the post, HIT KUDOS !!

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

Intern
Joined: 06 Oct 2015
Posts: 10
Re: Find the range of values of x that satisfy the inequality (x - 3)^2  [#permalink]

### Show Tags

30 Aug 2018, 05:39
1
Shiv2016 wrote:
@e-gmat team

Is it by any chance possible that all the powers are even and hence the wavy line bounces back for all the points?

If all the powers are zero then the equation never becomes less than zero.
e.x: (x-3)^4(x+6)^6(x-1)^2<0
here the minimum value of the inequality is 0, for no value of x the equation becomes less than zero.
no solution is the answer in such case.
Re: Find the range of values of x that satisfy the inequality (x - 3)^2 &nbs [#permalink] 30 Aug 2018, 05:39
Display posts from previous: Sort by