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

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Intern
Joined: 20 Nov 2017
Posts: 28
Location: India
GRE 1: Q158 V150
GPA: 3.9
WE: Consulting (Consumer Electronics)
If 2x/ (root(-3x^2 + 27)) is not a real number  [#permalink]

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10 Jul 2018, 00:48
1
6
00:00

Difficulty:

55% (hard)

Question Stats:

51% (00:59) correct 49% (01:19) wrong based on 150 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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MBA Section Director
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Joined: 22 May 2017
Posts: 1491
Concentration: Nonprofit
GPA: 4
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If 2x/ (root(-3x^2 + 27)) is not a real number  [#permalink]

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10 Jul 2018, 00:55
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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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Senior Manager
Joined: 04 Aug 2010
Posts: 310
Schools: Dartmouth College
Re: If 2x/ (root(-3x^2 + 27)) is not a real number  [#permalink]

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10 Jul 2018, 03:54
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, 04:03
GMATGuruNY wrote:

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

Good to know about this constraint. Thank you.
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Posts: 617
Re: If 2x/ (root(-3x^2 + 27)) is not a real number  [#permalink]

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15 Jul 2018, 09:13
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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Intern
Joined: 20 Nov 2017
Posts: 28
Location: India
GRE 1: Q158 V150
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Re: If 2x/ (root(-3x^2 + 27)) is not a real number  [#permalink]

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18 Jul 2018, 17:22
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: 188
Re: If 2x/ (root(-3x^2 + 27)) is not a real number  [#permalink]

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18 Jul 2018, 18:56
-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
Re: If 2x/ (root(-3x^2 + 27)) is not a real number &nbs [#permalink] 18 Jul 2018, 18:56
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# If 2x/ (root(-3x^2 + 27)) is not a real number

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