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# If X=(-37)^1/5 which of the following is true?

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If X=(-37)^1/5 which of the following is true? [#permalink]  21 Sep 2016, 06:53
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Hello there,

If $$X=(-37)^{\frac{1}{5}}$$ which of the following is true?

A. $$(-x)^1/2 > 2$$

B. $$x^2 > -2$$

C. $$x^2 < 4$$

D.$$x^3 < -8$$

E. $$x^4 > 32$$

I did not understand how it is derived.
can anyone help?

Thankyou!
[Reveal] Spoiler: OA

Last edited by IlCreatore on 29 Sep 2017, 08:16, edited 2 times in total.
Edited by Carcass
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GRE 1: Q167 V156
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Re: Single Choice- Algebra [#permalink]  21 Sep 2016, 07:10
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Aravindan wrote:
Hello there,

If X=(-37)^1/5 which of the following is true? (It is fifth root of 37 with a negative sign, just in case.)

A. (-x)^1/2 >2
B. x^2>-2
C. x^2<4
D. x^3<-8
E. x^4>32

I did not understand how it is derived.
can anyone help?

Thankyou!

Dear Aravindan,

Please share the source of the question. It seems a bit ambiguous to be a GRE question.

In the equation above x has 5 values. 1 real and 4 imaginary. If we consider the real value. The real value would be a little less than -2 (as $$2^5=32$$). Putting x=-2.1 (say).

Only option D is satisfied.

Hence option D is a possible solution.
_________________

Sandy
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Re: If X=(-37)^1/5 which of the following is true? [#permalink]  12 Nov 2016, 04:27
I think option (B) also holds true. lets say as explained by Sandy X= (-2.1) then X^2 = 4.41 which means X^2 >-2 . Option (D) is also correct.
Re: If X=(-37)^1/5 which of the following is true?   [#permalink] 12 Nov 2016, 04:27
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