GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

It is currently 22 Jan 2020, 00:23

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 2x/ (root(-3x^2 + 27)) is not a real number

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

Hide Tags

Find Similar Topics 
Intern
Intern
avatar
S
Status: MBA Student
Joined: 20 Nov 2017
Posts: 27
Location: India
Concentration: Strategy, Marketing
GPA: 3.9
WE: Consulting (Consumer Electronics)
If 2x/ (root(-3x^2 + 27)) is not a real number  [#permalink]

Show Tags

New post 10 Jul 2018, 01:48
2
6
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

53% (01:16) correct 47% (01:36) wrong based on 133 sessions

HideShow timer Statistics

If \(\frac{2x}{\sqrt{-3x^2 + 27}}\) is not a real number, which of the following specifies all the possible values of x?

A. \(x\leq-3\) or \(x\geq3\)
B. \(x\leq-3\)
C. \(x\geq3\)
D. \(x\leq-4\) or \(x\geq4\)
E. \(-3 \leq x \leq 3\)
Most Helpful Expert Reply
MBA Section Director
User avatar
V
Affiliations: GMATClub
Joined: 22 May 2017
Posts: 2847
GPA: 4
WE: Engineering (Computer Software)
GMAT ToolKit User Reviews Badge
If 2x/ (root(-3x^2 + 27)) is not a real number  [#permalink]

Show Tags

New post 10 Jul 2018, 01:55
6
1
GIven \(\frac{2x}{\sqrt{-3x^2 + 27}}\) is not a real number

=> The number inside the square root sign is < 0. Also since the square root is in denominator, the number is not a real number if denominator is 0

=> \(-3x^2 + 27 \leq 0\)

=> \(3x^2 - 27 \geq 0\)

=> \(3x^2 \geq 27\)

=> \(x^2 \geq 9\)

=> \(x\leq-3\) or \(x\geq3\)

Hence option A
_________________
General Discussion
Director
Director
avatar
G
Joined: 04 Aug 2010
Posts: 514
Schools: Dartmouth College
Re: If 2x/ (root(-3x^2 + 27)) is not a real number  [#permalink]

Show Tags

New post 10 Jul 2018, 04:54
1
Karthik200 wrote:
If \(\frac{2x}{\sqrt{-3x^2 + 27}}\) is not a real number, which of the following specifies all the possible values of x?

A. \(x\leq-3\) or \(x\geq3\)
B. \(x\leq-3\)
C. \(x\geq3\)
D. \(x\leq-4\) or \(x\geq4\)
E. \(-3 \leq x \leq 3\)


Since the GMAT is constrained to real numbers, I would disregard this problem.
_________________
GMAT and GRE Tutor
New York, NY

Available for tutoring in NYC and long-distance.
For more information, please email me at GMATGuruNY@gmail.com.
MBA Section Director
User avatar
V
Affiliations: GMATClub
Joined: 22 May 2017
Posts: 2847
GPA: 4
WE: Engineering (Computer Software)
GMAT ToolKit User Reviews Badge
Re: If 2x/ (root(-3x^2 + 27)) is not a real number  [#permalink]

Show Tags

New post 10 Jul 2018, 05:03
GMATGuruNY wrote:

Since the GMAT is constrained to real numbers, I would disregard this problem.



Good to know about this constraint. Thank you.
_________________
VP
VP
User avatar
V
Joined: 12 Feb 2015
Posts: 1009
Re: If 2x/ (root(-3x^2 + 27)) is not a real number  [#permalink]

Show Tags

New post 15 Jul 2018, 10:13
Although I got this question right, I am just curious to check is this a GMAT like question? I was told by someone that imaginary numbers are not tasted on GMAT.
_________________
________________
Manish :geek:

"Only I can change my life. No one can do it for me"
Intern
Intern
avatar
S
Status: MBA Student
Joined: 20 Nov 2017
Posts: 27
Location: India
Concentration: Strategy, Marketing
GPA: 3.9
WE: Consulting (Consumer Electronics)
Re: If 2x/ (root(-3x^2 + 27)) is not a real number  [#permalink]

Show Tags

New post 18 Jul 2018, 18:22
workout wrote:
GIven \(\frac{2x}{\sqrt{-3x^2 + 27}}\) is not a real number

=> The number inside the square root sign is < 0. Also since the square root is in denominator, the number is not a real number if denominator is 0

=> \(-3x^2 + 27 \leq 0\)

=> \(3x^2 - 27 \geq 0\)

=> \(3x^2 \geq 27\)

=> \(x^2 \geq 9\)

=> \(x\leq-3\) or \(x\geq3\)

Hence option A


Thanks workout for the nice explanation :)
Manager
Manager
avatar
S
Joined: 07 Feb 2017
Posts: 173
Re: If 2x/ (root(-3x^2 + 27)) is not a real number  [#permalink]

Show Tags

New post 18 Jul 2018, 19:56
-3x^2+27<0
3x^2-27>0
3(x^2-9)>0
x^2-9>0
(x+3)(x-3)>0

x+3>0 and x-3>0
x>-3 and x>3

x+3<0 and x-3<0
x<-3 and x<3
Answer A

Grade school algebra questions rly comfortable easy :cool:
Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 13993
Re: If 2x/ (root(-3x^2 + 27)) is not a real number  [#permalink]

Show Tags

New post 21 Jan 2020, 09:20
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 Club Bot
Re: If 2x/ (root(-3x^2 + 27)) is not a real number   [#permalink] 21 Jan 2020, 09:20
Display posts from previous: Sort by

If 2x/ (root(-3x^2 + 27)) is not a real number

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





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