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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
2
6
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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
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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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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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Re: If 2x/ (root(-3x^2 + 27)) is not a real number  [#permalink]

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21 Jan 2020, 09:20
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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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