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# If x^5 + x^2 < 0, then which one of the following must be true?

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Joined: 02 Sep 2009
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If x^5 + x^2 < 0, then which one of the following must be true?  [#permalink]

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02 Apr 2019, 04:01
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35% (medium)

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66% (01:02) correct 34% (01:18) wrong based on 29 sessions

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If $$x^5 + x^2 < 0$$, then which one of the following must be true?

(A) $$x < –1$$

(B) $$x < 0$$

(C) $$x > 0$$

(D) $$x > 1$$

(E) $$x^4 < x^2$$

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Re: If x^5 + x^2 < 0, then which one of the following must be true?  [#permalink]

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02 Apr 2019, 04:09
Bunuel wrote:
If $$x^5 + x^2 < 0$$, then which one of the following must be true?

(A) $$x < –1$$

(B) $$x < 0$$

(C) $$x > 0$$

(D) $$x > 1$$

(E) $$x^4 < x^2$$

Given,

$$x^5 + x^2 < 0$$

$$x^2 \geq 0$$

$$x^5$$must be negative.

So, x is negative. but we don't know whether x is fraction or integer.

x must be integer. Fraction doesn't wok here.

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Re: If x^5 + x^2 < 0, then which one of the following must be true?  [#permalink]

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02 Apr 2019, 05:02
$$x^5$$+$$x^2$$<0
$$x^2$$*($$x^3$$+1)<0
As $$x^2$$ cant be negative, so ($$x^3$$+1) is negative and x<-1

IMO
Ans: A
Manager
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Re: If x^5 + x^2 < 0, then which one of the following must be true?  [#permalink]

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02 Apr 2019, 06:05
IMO A

C and D both give positive values

E will not hold true for negative fraction say -1/2

for B , put x=-1 and it make expression = 0 , again out of scope

So IMP A .

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Re: If x^5 + x^2 < 0, then which one of the following must be true?  [#permalink]

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03 Apr 2019, 03:50
Bunuel wrote:
If $$x^5 + x^2 < 0$$, then which one of the following must be true?

(A) $$x < –1$$

(B) $$x < 0$$

(C) $$x > 0$$

(D) $$x > 1$$

(E) $$x^4 < x^2$$

x^5+x^2<0
shall stand valid only when x is -ve and <-1
IMO A
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Re: If x^5 + x^2 < 0, then which one of the following must be true?  [#permalink]

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07 Apr 2019, 18:24
Bunuel wrote:
If $$x^5 + x^2 < 0$$, then which one of the following must be true?

(A) $$x < –1$$

(B) $$x < 0$$

(C) $$x > 0$$

(D) $$x > 1$$

(E) $$x^4 < x^2$$

Let’s simplify the inequality:

x^5 + x^2 < 0

x^2(x^3 + 1) < 0

Divide both sides by x^2 (notice that x can’t be 0, so x^2 is positive):

x^3 + 1 < 0

x^3 < -1

x < ^3√(-1)

x < -1

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Re: If x^5 + x^2 < 0, then which one of the following must be true?   [#permalink] 07 Apr 2019, 18:24
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