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

It is currently 20 Oct 2018, 19:03

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

If x is any integer from -6 to 2 inclusive, how many

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

Hide Tags

CEO
CEO
User avatar
D
Joined: 12 Sep 2015
Posts: 3021
Location: Canada
If x is any integer from -6 to 2 inclusive, how many  [#permalink]

Show Tags

New post 24 Oct 2016, 14:56
Top Contributor
29
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

35% (02:46) correct 65% (02:56) wrong based on 417 sessions

HideShow timer Statistics

If x is any integer from -6 to 2 inclusive, how many values of x satisfy the following inequality: 2 - |x³ + 10x² - 24x| < 2 ?

A) 5
B) 6
C) 7
D) 8
E) 9

*Kudos for all correct solutions

_________________

Brent Hanneson – GMATPrepNow.com
Image
Sign up for our free Question of the Day emails

Most Helpful Expert Reply
CEO
CEO
User avatar
D
Joined: 12 Sep 2015
Posts: 3021
Location: Canada
Re: If x is any integer from -6 to 2 inclusive, how many  [#permalink]

Show Tags

New post 25 Oct 2016, 08:37
2
Top Contributor
5
GMATPrepNow wrote:
If x is any integer from -6 to 2 inclusive, how many values of x satisfy the following inequality: 2 - |x³ + 10x² - 24x| < 2 ?

A) 5
B) 6
C) 7
D) 8
E) 9


My solution:

First note that there are 9 integers from -6 to 2 inclusive.

Given: 2 - |x³ + 10x² - 24x| < 2
Add |x³ + 10x² - 24x| to both sides: 2 < 2 + |x³ + 10x² - 24x|
Subtract 2 from both sides to get: 0 < |x³ + 10x² - 24x|
Now let's apply some number sense.
We know that the absolute value of something will always be greater than or equal to zero. So the ONLY values that DON'T satisfy the inequality 0 < |x³ + 10x² - 24x| will be those values where |x³ + 10x² - 24x| = 0
In other words, x³ + 10x² - 24x = 0
Factor to get: x(x² + 10x - 24) = 0
Factor more: x(x + 12)(x - 2) = 0
Solve to get: x = 0, or x = -12 or x = 2
So, x = 0, or x = -12 or x = 2 are the ONLY values of x that DON'T satisfy the inequality 0 < |x³ + 10x² - 24x|
Since x = -12 is not within the given range of values (-6 to 2 inclusive), we need only consider the 2 values (x = 0 and x = 2)
So, the number of integer values that DO satisfy the inequality = 9 - 2 = 7

Answer:

RELATED VIDEOS
[you-tube] https://www.youtube.com/watch?v=LHz74_lvLI8[/you-tube]


_________________

Brent Hanneson – GMATPrepNow.com
Image
Sign up for our free Question of the Day emails

General Discussion
Manager
Manager
avatar
Joined: 28 Jun 2016
Posts: 207
Location: Canada
Concentration: Operations, Entrepreneurship
Re: If x is any integer from -6 to 2 inclusive, how many  [#permalink]

Show Tags

New post 24 Oct 2016, 15:16
1
3
GMATPrepNow wrote:
If x is any integer from -6 to 2 inclusive, how many values of x satisfy the following inequality: 2 - |x³ + 10x² - 24x| < 2 ?

A) 5
B) 6
C) 7
D) 8
E) 9

*Kudos for all correct solutions


Total 9 integers are there in the given range.

2 - |x³ + 10x² - 24x| < 2

Find the number of values for which the equation inside modulus is zero. Then subtract that number from total

x³ + 10x² - 24x=0

x(x^2+10x-24)=0

x(x+12)(x-2)=0

So the inequality doesn't hold good when x= 0,-12 or 2

0 and 2 are there in given range.

Answer = 9-2=7

C


Sent from my iPhone using GMAT Club Forum mobile app
Director
Director
User avatar
P
Joined: 05 Mar 2015
Posts: 995
If x is any integer from -6 to 2 inclusive, how many  [#permalink]

Show Tags

New post Updated on: 29 Nov 2016, 10:48
1
1
GMATPrepNow wrote:
If x is any integer from -6 to 2 inclusive, how many values of x satisfy the following inequality: 2 - |x³ + 10x² - 24x| < 2 ?

A) 5
B) 6
C) 7
D) 8
E) 9

*Kudos for all correct solutions


2 - |x³ + 10x² - 24x| < 2
=|x³ + 10x² - 24x| > 0 (cancelling 2 both sides and multiplying by -1 both sides ,flipping the sign)
factor out:- x³ + 10x² - 24x = x(x-2)(x+12)
After removing mod sign,Two cases:-
Case 1:-
if x(x-2)(x+12) > 0
then -12<x<0 & x>2
but as x is integer between -6 & 2 x satisfies for -6,-5,-4,-3,-2,-1 (5 nos.)

Case 2:-
if x(x-2)(x+12) < 0
then x<-12 & 0<x<2
but as x is integer between -6 & 2 x satisfies for 1 (1 nos.)

x cannot be 0 & 2 or -12(not in range) ..because then inequality does not hold and equation =0

Total satisfying values =-6,-5,-4,-3,-2,-1(case 1) && 1(case 2)=7nos.

Ans C

Originally posted by rohit8865 on 24 Oct 2016, 20:39.
Last edited by rohit8865 on 29 Nov 2016, 10:48, edited 1 time in total.
Current Student
User avatar
B
Status: DONE!
Joined: 05 Sep 2016
Posts: 384
If x is any integer from -6 to 2 inclusive, how many  [#permalink]

Show Tags

New post 29 Nov 2016, 09:22
-6: 2 - |(-6)(-8)(6)| < 2 - VALID
-5: 2 - |(-5)(-7)(7)| < 2 - VALID
-4: 2 - |(-4)(-6)(8)| < 2 - VALID
-3: 2 - |(-3)(-5)(9)| < 2 - VALID
-2: 2 - |(-2)(-4)(10)| < 2 - VALID
-1: 2 - |(-1)(-2)(11)| < 2 - VALID
0: 2 - |0| < 2 - INVALID
1: 2 - |1(-1)(13)| < 2 - VALID
2: 2 - |0| < 2 - INVALID

Interior (of the abs value) can be rewritten as: 2 - |x(x-2)(x+12)| < 2 --> This is why 2 and 0 do not work for this eqn
Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 8486
Premium Member
Re: If x is any integer from -6 to 2 inclusive, how many  [#permalink]

Show Tags

New post 12 May 2018, 20:52
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

GMAT Club Bot
Re: If x is any integer from -6 to 2 inclusive, how many &nbs [#permalink] 12 May 2018, 20:52
Display posts from previous: Sort by

If x is any integer from -6 to 2 inclusive, how many

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


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

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®.