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# Given that x ≠ 0, is x^(1/3) > x^(1/5)?

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Math Expert
Joined: 02 Sep 2009
Posts: 51280
Given that x ≠ 0, is x^(1/3) > x^(1/5)?  [#permalink]

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13 Aug 2018, 02:45
00:00

Difficulty:

65% (hard)

Question Stats:

48% (01:08) correct 52% (01:19) wrong based on 107 sessions

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Given that x ≠ 0, is $$\sqrt[3]{x} > \sqrt[5]{x}$$?

(1) x < 1

(2) x > –1

_________________
Director
Status: Learning stage
Joined: 01 Oct 2017
Posts: 931
WE: Supply Chain Management (Energy and Utilities)
Given that x ≠ 0, is x^(1/3) > x^(1/5)?  [#permalink]

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Updated on: 13 Aug 2018, 07:28
Bunuel wrote:
Given that x ≠ 0, is $$\sqrt[3]{x} > \sqrt[5]{x}$$?

(1) x < 1

(2) x > –1

Question stem:- Is $$\sqrt[3]{x} > \sqrt[5]{x}$$?

St1:- x < 1
a) when x=1/2, answer to question stem is No.
b) When, x=-1/2, answer to question stem is Yes.
c) When, x=-1, answer to question stem is No.
d) For any value of x less than -1, answer to question stem is No.

Question stem is inconsistent.

St2:- x > –1
]a) When, x=-1/2, answer to question stem is Yes.
b) when x=1/2, answer to question stem is No.

c) When, x=1, answer to question stem is No.
d) For any value of x greater than 1, answer to question stem is yes.

Question stem is inconsistent.
Insufficient.

Combined, we have -1<x<1.
Refer the highlighted points of x, Question stem is still inconsistent.
Insufficient.

Ans. (E)
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Regards,

PKN

Rise above the storm, you will find the sunshine

Originally posted by PKN on 13 Aug 2018, 05:24.
Last edited by PKN on 13 Aug 2018, 07:28, edited 1 time in total.
CEO
Status: GMATINSIGHT Tutor
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Posts: 2711
Location: India
GMAT: INSIGHT
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Given that x ≠ 0, is x^(1/3) > x^(1/5)?  [#permalink]

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Updated on: 02 Dec 2018, 23:14
Bunuel wrote:
Given that x ≠ 0, is $$\sqrt[3]{x} > \sqrt[5]{x}$$?

(1) x < 1

(2) x > –1

Question : is $$\sqrt[3]{x} > \sqrt[5]{x}$$?

$$\sqrt[3]{x} > \sqrt[5]{x}$$? only if x is either greater than 1 or less than -1

Statement 1: x < 1

x may be 0.5 or -5 hence

NOT SUFFICIENT

Statement 2: x > -1

x may be -0.5 or 5 hence

NOT SUFFICIENT

Combining the two statements

-1 < x < 1

Hence answer to the question is NO for -0.5 and yes for 0.5 hence

NOT SUFFICIENT

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Originally posted by GMATinsight on 13 Aug 2018, 05:57.
Last edited by GMATinsight on 02 Dec 2018, 23:14, edited 1 time in total.
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Status: GMATINSIGHT Tutor
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Location: India
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Re: Given that x ≠ 0, is x^(1/3) > x^(1/5)?  [#permalink]

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13 Aug 2018, 06:10
PKN wrote:
Bunuel wrote:
Given that x ≠ 0, is $$\sqrt[3]{x} > \sqrt[5]{x}$$?

(1) x < 1

(2) x > –1

Question stem:- Is $$\sqrt[3]{x} > \sqrt[5]{x}$$?

Let $$\sqrt[3]{x} > \sqrt[5]{x}$$
Or, $$\frac{1}{x^3}-\frac{1}{x^5}>0$$
Or, $$\frac{x^2-1}{x^5}>0$$
Or, $$\frac{\left(x+1\right)\left(x-1\right)}{x^5}>0$$
So, -1<x<0 or, x>1-----------(1)

St1:- x < 1
Question stem is inconsistent. (consistent in the range -1<x<0 and inconsistent in the range (0,1))
Insufficient.

St2:- x > –1
Question stem is inconsistent. (consistent in the range -1<x<0 or, x>1 and inconsistent in the range (0,1))
Insufficient.
Combined, we have -1<x<1.----------(2)
Question stem is inconsistent. (consistent in the range -1<x<0 or, x>1 and inconsistent in the range (0,1))
Insufficient.

Ans. (E)

$$\sqrt[3]{x}$$ does NOT mean 1/x^3 instead that means x^(1/3)
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Director
Status: Learning stage
Joined: 01 Oct 2017
Posts: 931
WE: Supply Chain Management (Energy and Utilities)
Re: Given that x ≠ 0, is x^(1/3) > x^(1/5)?  [#permalink]

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13 Aug 2018, 06:21
GMATinsight wrote:
PKN wrote:
Bunuel wrote:
Given that x ≠ 0, is $$\sqrt[3]{x} > \sqrt[5]{x}$$?

(1) x < 1

(2) x > –1

Question stem:- Is $$\sqrt[3]{x} > \sqrt[5]{x}$$?

Let $$\sqrt[3]{x} > \sqrt[5]{x}$$
Or, $$\frac{1}{x^3}-\frac{1}{x^5}>0$$
Or, $$\frac{x^2-1}{x^5}>0$$
Or, $$\frac{\left(x+1\right)\left(x-1\right)}{x^5}>0$$
So, -1<x<0 or, x>1-----------(1)

St1:- x < 1
Question stem is inconsistent. (consistent in the range -1<x<0 and inconsistent in the range (0,1))
Insufficient.

St2:- x > –1
Question stem is inconsistent. (consistent in the range -1<x<0 or, x>1 and inconsistent in the range (0,1))
Insufficient.
Combined, we have -1<x<1.----------(2)
Question stem is inconsistent. (consistent in the range -1<x<0 or, x>1 and inconsistent in the range (0,1))
Insufficient.

Ans. (E)

$$\sqrt[3]{x}$$ does NOT mean 1/x^3 instead that means x^(1/3)

I completely misread the question. Thanks for noticing GMATinsight.
_________________

Regards,

PKN

Rise above the storm, you will find the sunshine

Director
Joined: 14 Dec 2017
Posts: 518
Location: India
Re: Given that x ≠ 0, is x^(1/3) > x^(1/5)?  [#permalink]

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13 Aug 2018, 12:00
Bunuel wrote:
Given that x ≠ 0, is $$\sqrt[3]{x} > \sqrt[5]{x}$$?

(1) x < 1

(2) x > –1

Given: $$\sqrt[3]{x} > \sqrt[5]{x}$$

We can raise the inequality to an odd power, hence we have $$x^{5/3} > x$$

Statement 1: $$x < 1$$

For x = 1/8, we get $$x^{5/3} = (1/8)^{5/3}$$ = $$(1/2)^{5}$$ $$< 1/8$$......Hence NO

For x = -1/8, we get $$x^{5/3} = (-1/8)^{5/3}$$ = $$(-1/2)^{5}$$ $$> -1/8$$......Hence YES

Statement 1 is Not Sufficient.

Statement 2: $$x > –1$$

We can use same examples as above & can show Statement 2 is Not Sufficient.

Combining both statements we get $$-1 < x < 1$$

We can use same same examples as above & can show that combining is also Not Sufficient.

Thanks,
GyM
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Joined: 26 Mar 2013
Posts: 1919
Given that x ≠ 0, is x^(1/3) > x^(1/5)?  [#permalink]

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02 Dec 2018, 10:11
GMATinsight wrote:
Bunuel wrote:
Given that x ≠ 0, is $$\sqrt[3]{x} > \sqrt[5]{x}$$?

(1) x < 1

(2) x > –1

Question : is $$\sqrt[3]{x} > \sqrt[5]{x}$$?

$$\sqrt[3]{x} > \sqrt[5]{x}$$? only if x is either greater than 1 or less than -1

Statement 1: x < 1

x may be 0.5 or -5 hence

NOT SUFFICIENT

Statement 2: x > -1

x may be -0.5 or 5 hence

NOT SUFFICIENT

Combining the two statements

-1 < x < 1

Hence answer to the question is always NO hence

SUFFICIENT

Dear GMATinsight

The highlighted is not the same.

Also, 0.5 & -0.5 satisfies both cases, giving different answer to the question.

0.5 gives no $$\sqrt[3]{0.5}$$=0.79 & $$\sqrt[5]{0.5}$$=0.83

-0.5 gives yes $$\sqrt[3]{-0.5}$$=-0.79 & $$\sqrt[5]{-0.5}$$=-0.83

CEO
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2711
Location: India
GMAT: INSIGHT
WE: Education (Education)
Re: Given that x ≠ 0, is x^(1/3) > x^(1/5)?  [#permalink]

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02 Dec 2018, 23:15
Mo2men wrote:
GMATinsight wrote:
Bunuel wrote:
Given that x ≠ 0, is $$\sqrt[3]{x} > \sqrt[5]{x}$$?

(1) x < 1

(2) x > –1

Question : is $$\sqrt[3]{x} > \sqrt[5]{x}$$?

$$\sqrt[3]{x} > \sqrt[5]{x}$$? only if x is either greater than 1 or less than -1

Statement 1: x < 1

x may be 0.5 or -5 hence

NOT SUFFICIENT

Statement 2: x > -1

x may be -0.5 or 5 hence

NOT SUFFICIENT

Combining the two statements

-1 < x < 1

Hence answer to the question is always NO hence

SUFFICIENT

Dear GMATinsight

The highlighted is not the same.

Also, 0.5 & -0.5 satisfies both cases, giving different answer to the question.

0.5 gives no $$\sqrt[3]{0.5}$$=0.79 & $$\sqrt[5]{0.5}$$=0.83

-0.5 gives yes $$\sqrt[3]{-0.5}$$=-0.79 & $$\sqrt[5]{-0.5}$$=-0.83

Thank you... made correction.. I don't know how I made this mistake while same values are taken in statement 2...
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Re: Given that x ≠ 0, is x^(1/3) > x^(1/5)? &nbs [#permalink] 02 Dec 2018, 23:15
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