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GRE Prep Club Team Member
Joined: 20 Feb 2017
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Which of the following inequalities, if true, is sufficient
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20 Mar 2020, 23:23
20 Mar 2020, 23:23
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Which of the following inequalities, if true, is sufficient alone to show that \(\sqrt[3]{x} < \sqrt[5]{x}\) ?
(A) \(-1 < x < 0\)
(B) \(x > 1\)
(C) \(|x| < - 1\)
(D) \(|x| > 1\)
(E) \(x < -1\)
(A) \(-1 < x < 0\)
(B) \(x > 1\)
(C) \(|x| < - 1\)
(D) \(|x| > 1\)
(E) \(x < -1\)
Re: Which of the following inequalities, if true, is sufficient
[#permalink]
08 May 2020, 13:22
08 May 2020, 13:22
1
Expert Reply
Raising to the odd power won't change the sign of inequality.
\([\sqrt[3]{x}]^{15} < [\sqrt[5]{x}]^{15}\)
\(x^5 < x^3\)
\(x^3(1-x^2) <0\)
case 1
if x<0, then \(1 - x^2>0\)
x<-1
case 2
if x >0, then \(1-x^2<0\)
0<x<1
E is the answer
\([\sqrt[3]{x}]^{15} < [\sqrt[5]{x}]^{15}\)
\(x^5 < x^3\)
\(x^3(1-x^2) <0\)
case 1
if x<0, then \(1 - x^2>0\)
x<-1
case 2
if x >0, then \(1-x^2<0\)
0<x<1
E is the answer
gmatclubot
Re: Which of the following inequalities, if true, is sufficient [#permalink]
08 May 2020, 13:22
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