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GRE prep Club test question

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Intern
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Joined: 12 May 2016
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GRE prep Club test question [#permalink] New post 28 Jul 2017, 09:33
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If \(x=5\sqrt{-37}\) then which of the following must be true?

A. \(\sqrt{(-x)}>2\)

B. \(x >-2\)

C. \(x^2< 4\)

D. \(x^3<-8\)

E. \(x^4>32\)
[Reveal] Spoiler: OA
Director
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Joined: 20 Apr 2016
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CAT Tests
Re: GRE prep Club test question [#permalink] New post 22 Sep 2017, 12:20
saumya17lc wrote:
If x=5√−37
then which of the following must be true?

√−x>2
x>−2
x2<4
x3<−8
x4>32


GREPREP club question- Quant test 6 Question 11 of 20 ID: Q02-99

Just want to add few details in the explanation-

Points to remember- Odd roots have same signs

eg \(3\sqrt{-125}\) =-5 and \(3\sqrt{125}\) =5


Now back to question-

we know \(5\sqrt{32}\)=2 so \(5\sqrt{-37}\)≈2.1 ( it should be slightly greater than \(2^5\))

Now we can check with each option-
only option D fits the sol. because \((-2.1)^3\) < -8 so \(x^3\)<−8
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Re: GRE prep Club test question   [#permalink] 22 Sep 2017, 12:20
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