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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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New post 10 Jul 2018, 01:48
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52% (00:58) correct 48% (01:19) wrong based on 141 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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New post 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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New post 10 Jul 2018, 04:54
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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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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.
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Re: If 2x/ (root(-3x^2 + 27)) is not a real number  [#permalink]

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

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

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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:
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Re: If 2x/ (root(-3x^2 + 27)) is not a real number &nbs [#permalink] 18 Jul 2018, 19:56
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