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

 It is currently 10 Dec 2019, 12:31 ### 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

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # Find the range of values of x that satisfy the inequality (x-10)^3 (x+

Author Message
TAGS:

### Hide Tags

e-GMAT Representative V
Joined: 04 Jan 2015
Posts: 3158
Find the range of values of x that satisfy the inequality (x-10)^3 (x+  [#permalink]

### Show Tags 00:00

Difficulty:   5% (low)

Question Stats: 81% (01:30) correct 19% (02:01) wrong based on 162 sessions

### HideShow timer Statistics

Wavy Line Method Application - Exercise Question #6

Find the range of values of x that satisfy the inequality $$\frac{(x-10)^3 (x+7)^5}{(x-5)^5 (x-6)^4} > 0$$

A. -7 < x < 5 or x > 10
B. -7 < x < 5
C. x > 10
D. -6 < x < 5 or x > 11
E. -7 < x < 4 or x > 12

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, 02:47.
Last edited by Bunuel on 23 Dec 2018, 03:55, edited 1 time in total.
Edited the question.
Board of Directors V
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-10)^3 (x+  [#permalink]

### Show Tags

1
EgmatQuantExpert wrote:
Wavy Line Method Application - Exercise Question #6

Find the range of values of x that satisfy the inequality $$\frac{(x-10)^3 (x+7)^5}{(x-5)^5 (x-6)^4} > 0$$

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 given is $$\frac{(x-10)^3 (x+7)^5}{(x-5)^5 (x-6)^4} > 0$$

We will have the Zero points as -7,5,6 and 10.
Since the power of (x-6)^4 is EVEN, we will not move the curve from 6 to the upside of the line.

So, the range of x will be (-7,5) U (10,infinity)

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 V
Joined: 04 Jan 2015
Posts: 3158
Re: Find the range of values of x that satisfy the inequality (x-10)^3 (x+  [#permalink]

### Show Tags

1
2
Solution

Hey Everyone,

Please find below the solution of the given problem.

We see that each factor has a power greater than 1.

We just need to keep in mind that the process is exactly the same: The wavy line passes through the zero point if the power of the corresponding factor is odd. The wavy line bounces back from the zero point if the power of the corresponding factor is even.

(x-6) is the only factor with an even power in the given expression and so the wavy line should bounce back at x = 6.

Plotting the zero points and drawing the wavy line: Required Range:

-7 < x < 5 or x > 10

_________________
Intern  B
Joined: 20 Oct 2017
Posts: 27
Re: Find the range of values of x that satisfy the inequality (x-10)^3 (x+  [#permalink]

### Show Tags

EgmatQuantExpert wrote:
Solution

Hey Everyone,

Please find below the solution of the given problem.

We see that each factor has a power greater than 1.

We just need to keep in mind that the process is exactly the same: The wavy line passes through the zero point if the power of the corresponding factor is odd. The wavy line bounces back from the zero point if the power of the corresponding factor is even.

(x-6) is the only factor with an even power in the given expression and so the wavy line should bounce back at x = 6.

Plotting the zero points and drawing the wavy line: Required Range:

-7 < x < 5 or x > 10

For x=6 the answer is zero. Sho should the correct answer then be split into:
1) 6 < x < 10
2) 5 < x < 6
3) x < -7
Senior Manager  G
Joined: 29 Dec 2017
Posts: 374
Location: United States
Concentration: Marketing, Technology
GMAT 1: 630 Q44 V33 GMAT 2: 690 Q47 V37 GMAT 3: 710 Q50 V37 GPA: 3.25
WE: Marketing (Telecommunications)
Re: Find the range of values of x that satisfy the inequality (x-10)^3 (x+  [#permalink]

### Show Tags

kritikalal wrote:
EgmatQuantExpert wrote:
Solution

Hey Everyone,

Please find below the solution of the given problem.

We see that each factor has a power greater than 1.

We just need to keep in mind that the process is exactly the same: The wavy line passes through the zero point if the power of the corresponding factor is odd. The wavy line bounces back from the zero point if the power of the corresponding factor is even.

(x-6) is the only factor with an even power in the given expression and so the wavy line should bounce back at x = 6.

Plotting the zero points and drawing the wavy line: Required Range:

-7 < x < 5 or x > 10

For x=6 the answer is zero. Sho should the correct answer then be split into:
1) 6 < x < 10
2) 5 < x < 6
3) x < -7

We have to find (+) not (-), in this case x = 6 has no meaning for us, since range -7 < x < 5 or x > 10 doesn't include x=6.
Intern  B
Joined: 29 May 2016
Posts: 5
Re: Find the range of values of x that satisfy the inequality (x-10)^3 (x+  [#permalink]

### Show Tags

EgmatQuantExpert wrote:
Solution

Hey Everyone,

Please find below the solution of the given problem.

We see that each factor has a power greater than 1.

We just need to keep in mind that the process is exactly the same: The wavy line passes through the zero point if the power of the corresponding factor is odd. The wavy line bounces back from the zero point if the power of the corresponding factor is even.

(x-6) is the only factor with an even power in the given expression and so the wavy line should bounce back at x = 6.

Plotting the zero points and drawing the wavy line:

Required Range:

-7 < x < 5 or x > 10

Hi Payal,

Can you please explain why the exclusion holes are marked at 10 and -7 instead of 5 and 6(following the same strategy as in question 4 and in concepts for wavy line)?

TIA

Thanks,
Sakshi
e-GMAT Representative V
Joined: 04 Jan 2015
Posts: 3158
Re: Find the range of values of x that satisfy the inequality (x-10)^3 (x+  [#permalink]

### Show Tags

1
Hey sakshi.2sep,

We have explained this in detail in our article.
We suggest you go through it once.

Here is the link for the article:
Wavy Line Method Application: http://gmatclub.com/forum/wavy-line-met ... 24319.html

If you still have any doubt, please let us know.
We will be more than happy to resolve your doubt.

Regards,
Ashutosh
e-GMAT
_________________
Intern  B
Joined: 29 May 2016
Posts: 5
Re: Find the range of values of x that satisfy the inequality (x-10)^3 (x+  [#permalink]

### Show Tags

Hi Ashuhtosh,

After going through the article once more, I understand why -7 and 10 are excluded from the solution set but still doubtful if 5 and 6 should also be excluded as they are in the denominator and we should never consider cases where the denominator becomes zero. Please explain why did we not exclude 5 and 6?

Thanks and regards,
Sakshi
e-GMAT Representative V
Joined: 04 Jan 2015
Posts: 3158
Re: Find the range of values of x that satisfy the inequality (x-10)^3 (x+  [#permalink]

### Show Tags

Hey sakshi.2sep,

I have 1 question.

Can we multiply both sides of the inequality by $$(x-5)^10(x-6)^8$$ in the above fraction?
If you do this then inequality will become $${(x-10)^3 (x+7)^5}{(x-5)^5 (x-6)^4} > 0$$

Now, you can solve the inequality.
Hope this helps you.

Regards,
Ashutosh
_________________
Intern  B
Joined: 29 May 2016
Posts: 5
Re: Find the range of values of x that satisfy the inequality (x-10)^3 (x+  [#permalink]

### Show Tags

Hey Ashutosh,

Thank you. I do get this question in both the forms: denominator and multiplying by square. Just got confused with the holes (exclusions) marked for 2 points(-7,10) of the solution set and NOT marked for other 2 points (5,6) of the solution set in the wavy line representation. However, the answer mentioned as Required Range: -7 < x < 5 or x > 10 has no doubt.

Regards,
Sakshi
Intern  S
Joined: 18 Jun 2017
Posts: 48
Re: Find the range of values of x that satisfy the inequality (x-10)^3 (x+  [#permalink]

### Show Tags

hey EgmatQuantExpert,

You have given great explanation and practice problems.
but I am getting totally confused with starting points of drawing curve.
for above problem, I drew curve starting from top left.
and considered positive parts. where answer is different.

this must be something obvious. but pls help me to get there.
e-GMAT Representative V
Joined: 04 Jan 2015
Posts: 3158
Re: Find the range of values of x that satisfy the inequality (x-10)^3 (x+  [#permalink]

### Show Tags

manasveek wrote:
hey EgmatQuantExpert,

You have given great explanation and practice problems.
but I am getting totally confused with starting points of drawing curve.
for above problem, I drew curve starting from top left.
and considered positive parts. where answer is different.

this must be something obvious. but pls help me to get there.

Hey manasveek,
you need to start drawing the curve from the top right portion.
I am quoting a part of the article that explains the method:

Quote:
How to draw the wavy line?

1. How to start: Once you draw the number line and mark the zero points on the number line, it’s time to draw the wavy line. Start from the top right most portion. Be ready to alternate (or not alternate) the region of the wave based on how many times a point is root to the given expression.

2. How to alternate:
if the power of a term is odd, then the wave simply passes through the corresponding point (root) into the other region (to –ve region if the wave is currently in the positive region and to the +ve region if the wave is currently in the negative region).

I will suggest you go through the whole article: Wavy Line Method Application - Complex Algebraic Inequalities

Also, read our new article about solving inequalities: Solving inequalities- Number Line Method

_________________
Intern  S
Joined: 18 Jun 2017
Posts: 48
Re: Find the range of values of x that satisfy the inequality (x-10)^3 (x+  [#permalink]

### Show Tags

thank you EgmatQuantExpert for such a quick reply.
I tried going through new article and totally understood concept and why is that we start drawing curve from top right.
a very useful article as always by E-gmat.
Thank you very much!

Regards,
Manasvee.
Intern  B
Joined: 10 Apr 2016
Posts: 2
Location: Singapore
GMAT 1: 640 Q49 V28 Re: Find the range of values of x that satisfy the inequality (x-10)^3 (x+  [#permalink]

### Show Tags

EgmatQuantExpert wrote:
Solution

Hey Everyone,

Please find below the solution of the given problem.

We see that each factor has a power greater than 1.

We just need to keep in mind that the process is exactly the same: The wavy line passes through the zero point if the power of the corresponding factor is odd. The wavy line bounces back from the zero point if the power of the corresponding factor is even.

(x-6) is the only factor with an even power in the given expression and so the wavy line should bounce back at x = 6.

Plotting the zero points and drawing the wavy line: Required Range:

-7 < x < 5 or x > 10

Dear Ms. Tandon,

Thank you for all your replies. I've gone through them, but yet I have one question about the inclusion and exclusion of '6' in the solution if the question was presented differently.

$$\frac{(x-10)^3 (x+7)^5 (x-6)^4}{(x-5)^5} > 0$$
$$\frac{(x-10)^3 (x+7)^5 (x-6)^4}{(x-5)^5} >= 0$$

May I know if x=6 will be included in both of the scenarios? Re: Find the range of values of x that satisfy the inequality (x-10)^3 (x+   [#permalink] 26 Jul 2019, 12:17
Display posts from previous: Sort by

# Find the range of values of x that satisfy the inequality (x-10)^3 (x+  