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

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

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10 Jul 2018, 01:48
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6
00:00

Difficulty:

55% (hard)

Question Stats:

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

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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. $$-3 \leq x \leq 3$$
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If 2x/ (root(-3x^2 + 27)) is not a real number  [#permalink]

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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
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Re: If 2x/ (root(-3x^2 + 27)) is not a real number  [#permalink]

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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.
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Re: If 2x/ (root(-3x^2 + 27)) is not a real number  [#permalink]

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10 Jul 2018, 05:03
GMATGuruNY wrote:

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

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Re: If 2x/ (root(-3x^2 + 27)) is not a real number  [#permalink]

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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.
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Re: If 2x/ (root(-3x^2 + 27)) is not a real number  [#permalink]

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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
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Posts: 173
Re: If 2x/ (root(-3x^2 + 27)) is not a real number  [#permalink]

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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

Grade school algebra questions rly comfortable easy
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Posts: 13993
Re: If 2x/ (root(-3x^2 + 27)) is not a real number  [#permalink]

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21 Jan 2020, 09:20
Hello from the GMAT Club BumpBot!

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Re: If 2x/ (root(-3x^2 + 27)) is not a real number   [#permalink] 21 Jan 2020, 09:20
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The text passage provided is a GMAT question and solution, specifically a problem-solving question in the quantitative section. It involves a mathematical expression and asks for the range of values for which the expression is not a real number.
single_question_with_answer
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
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# If 2x/ (root(-3x^2 + 27)) is not a real number

Author Message
TAGS:

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Intern
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

10 Jul 2018, 01:48
2
6
00:00

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. $$-3 \leq x \leq 3$$
MBA Section Director
Affiliations: GMATClub
Joined: 22 May 2017
Posts: 2847
GPA: 4
WE: Engineering (Computer Software)
If 2x/ (root(-3x^2 + 27)) is not a real number  [#permalink]

### Show Tags

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

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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.
_________________
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New York, NY

Available for tutoring in NYC and long-distance.
MBA Section Director
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GPA: 4
WE: Engineering (Computer Software)
Re: If 2x/ (root(-3x^2 + 27)) is not a real number  [#permalink]

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10 Jul 2018, 05:03
GMATGuruNY wrote:

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

_________________
VP
Joined: 12 Feb 2015
Posts: 1009
Re: If 2x/ (root(-3x^2 + 27)) is not a real number  [#permalink]

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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

"Only I can change my life. No one can do it for me"
Intern
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

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
Joined: 07 Feb 2017
Posts: 173
Re: If 2x/ (root(-3x^2 + 27)) is not a real number  [#permalink]

### Show Tags

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

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

### Show Tags

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.
_________________
Re: If 2x/ (root(-3x^2 + 27)) is not a real number   [#permalink] 21 Jan 2020, 09:20
Display posts from previous: Sort by
user
The text passage provided is a GMAT question and solution, specifically a problem-solving question in the quantitative section. It involves a mathematical expression and asks for the range of values for which the expression is not a real number.

TYPE: SINGLE_QUESTION_WITH_ANSWER