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

It is currently 19 Oct 2019, 08:50

Close

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
Your Progress

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.

Close

Request Expert Reply

Confirm Cancel

List the negative integral values of x that render the algebraic expre

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Find Similar Topics 
e-GMAT Representative
User avatar
V
Joined: 04 Jan 2015
Posts: 3074
List the negative integral values of x that render the algebraic expre  [#permalink]

Show Tags

New post 26 Aug 2016, 02:36
1
4
00:00
A
B
C
D
E

Difficulty:

(N/A)

Question Stats:

97% (01:09) correct 3% (02:23) wrong based on 152 sessions

HideShow timer Statistics

Wavy Line Method Application - Exercise Question #3


List the negative integral values of x that render the algebraic expression \((x – 5)^8 (x – 2)^3\) positive.


A. -4, -5
B. -3, -4
C. -2, -5
D. -1
E. no negative integral value exists for x



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.

_________________
Board of Directors
User avatar
V
Status: Stepping into my 10 years long dream
Joined: 18 Jul 2015
Posts: 3580
Reviews Badge
Re: List the negative integral values of x that render the algebraic expre  [#permalink]

Show Tags

New post 26 Aug 2016, 09:58
1
EgmatQuantExpert wrote:
Wavy Line Method Application - Exercise Question #3


List the negative integral values of x that render the algebraic expression \((x – 5)^8 (x – 2)^3\) positive.




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.


Question States we need to find out the value of negative integral values of x such that \((x – 5)^8 (x – 2)^3\) >0

Since the power of (x-5) is EVEN, we don't need to consider the negative values between 2 and 5.

Substituting the values of x as 2 and 5 on number line, we will get the range of x as (-infinity, 2).

Please correct me if I am missing anything.
_________________
My LinkedIn abhimahna.
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
Blog: Subscribe to Question of the Day Blog
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.
Intern
Intern
avatar
B
Joined: 08 Nov 2015
Posts: 12
Re: List the negative integral values of x that render the algebraic expre  [#permalink]

Show Tags

New post 04 Sep 2016, 23:54
4
Hi Abhimahna,

For x=1, the expression is negative whereas we want the resultant expression to be positive.

In my opinion, there are no negative integral solutions for this expression to result in a positive number.

Please cross-check by plugging in negative values (x=-1,-2 and so on)
Board of Directors
User avatar
V
Status: Stepping into my 10 years long dream
Joined: 18 Jul 2015
Posts: 3580
Reviews Badge
Re: List the negative integral values of x that render the algebraic expre  [#permalink]

Show Tags

New post 04 Sep 2016, 23:59
Jurassic wrote:
Hi Abhimahna,

For x=1, the expression is negative whereas we want the resultant expression to be positive.

In my opinion, there are no negative integral solutions for this expression to result in a positive number.

Please cross-check by plugging in negative values (x=-1,-2 and so on)


Yes, you are correct. I missed such a simple thing. Thanks Jurassic Park :-D

Your 1st Kudo will be given by me. :)
_________________
My LinkedIn abhimahna.
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
Blog: Subscribe to Question of the Day Blog
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
Manager
avatar
B
Joined: 31 Oct 2011
Posts: 50
Location: India
GMAT 1: 660 Q48 V32
GPA: 3.56
WE: Programming (Computer Software)
Reviews Badge
Re: List the negative integral values of x that render the algebraic expre  [#permalink]

Show Tags

New post 06 Sep 2016, 19:34
Zero points are 2 and 5. Plot them on the number line.

Start from x=5 (top right). Power of (x-5) is even. So, the wavy line should bounce back at x=5.

From the graph, for any number > 2, the algebraic expression remains positive. So, solution would be all integers >2 (not = 2 since at 2, the expression becomes 0)
Attachments

wavy line.PNG
wavy line.PNG [ 6.41 KiB | Viewed 4650 times ]

Intern
Intern
avatar
B
Joined: 08 Nov 2015
Posts: 12
Re: List the negative integral values of x that render the algebraic expre  [#permalink]

Show Tags

New post 08 Sep 2016, 23:42
Hi Rajaram,

The question asks for negative integral values of x. Hence, the solution of all integers > 2 will be incorrect in this case.
e-GMAT Representative
User avatar
V
Joined: 04 Jan 2015
Posts: 3074
Re: List the negative integral values of x that render the algebraic expre  [#permalink]

Show Tags

New post 18 Nov 2016, 02:57
2
1
Solution

Hey Everyone,

Please find below the solution of the given problem.

Rewriting the inequality to easily identify the zero points

We want the given algebraic expression to be positive.

So, we need to find the range of values of x for the following inequality:

\((x – 5)^8 (x – 2)^3>0\)


After we find the range, we need to choose the negative integers in this range since the question asks for negative integral values that satisfy the above inequality.


Plotting the zero points and drawing the wavy line:

Image

Required Range:

Per the wavy line drawn above, it is clear that 2 < x < 5 and x > 5 render the given expression positive.

However, question asks us to choose only negative integral values for x.
Note that these ranges do NOT contain any negative integers.

Therefore, no negative integral value exists for x such that the given expression can be rendered positive.

Correct Answer: Option E
_________________
Intern
Intern
avatar
B
Joined: 07 Jan 2017
Posts: 19
Location: India
Concentration: Other, Other
Schools: UConn"19
WE: Medicine and Health (Pharmaceuticals and Biotech)
Reviews Badge
Re: List the negative integral values of x that render the algebraic expre  [#permalink]

Show Tags

New post 01 Feb 2017, 12:16
Payal : can u plz elaborate on the negative integral values for an expression in general
Intern
Intern
avatar
B
Joined: 04 May 2014
Posts: 45
Concentration: Strategy, Operations
Re: List the negative integral values of x that render the algebraic expre  [#permalink]

Show Tags

New post 05 Aug 2018, 12:46
Sachin07 wrote:
Payal : can u plz elaborate on the negative integral values for an expression in general


Those negative integers (like -2, -3, -1..etc) for which the expression holds true. In this case, for all negative integers the expression is less than zero. Hence, there is no -ve integral / integer value for which expression is > 0 i.e positive.
GMAT Club Bot
Re: List the negative integral values of x that render the algebraic expre   [#permalink] 05 Aug 2018, 12:46
Display posts from previous: Sort by

List the negative integral values of x that render the algebraic expre

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne