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If a>0, is (a)^1/3 > (a)^1/2 ?

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If a>0, is (a)^1/3 > (a)^1/2 ?  [#permalink]

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New post 19 Aug 2015, 01:56
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If a>0, is \((a)^\frac{1}{3} > (a)^\frac{1}{2}\) ?

(1) \((a)^\frac{1}{2} > a\)

(2) \((a)^\frac{1}{3} > (a)^\frac{2}{3}\)

Source : Aristotle Prep

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Re: If a>0, is (a)^1/3 > (a)^1/2 ?  [#permalink]

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New post 19 Aug 2015, 05:19
2
3
Gnpth wrote:
If a>0, is \((a)^\frac{1}{3} > (a)^\frac{1}{2}\) ?

(1) \((a)^\frac{1}{2} > a\)

(2) \((a)^\frac{1}{3} > (a)^\frac{2}{3}\)

Source : Aristotle Prep


IMO : D


St 1: \((a)^\frac{1}{2} > a\)

This is only possible when 0<a<1.
Eg: for a = 1/4 ---> 1/2 > 1/4
Thus for
is \((a)^\frac{1}{3} > (a)^\frac{1}{2}\) answer would be Yes

St 2: \((a)^\frac{1}{3} > (a)^\frac{2}{3}\)

Let \((a)^\frac{1}{3} = b\)
Then b > \(b^2\)
which is same as statement 1 .

Hence both alone enough
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Re: If a>0, is (a)^1/3 > (a)^1/2 ?  [#permalink]

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New post 19 Aug 2015, 09:26
You can "translate" the question to "If a>0, is 0<a<1?"
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Re: If a>0, is (a)^1/3 > (a)^1/2 ?  [#permalink]

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New post 19 Jul 2018, 00:24
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Re: If a>0, is (a)^1/3 > (a)^1/2 ? &nbs [#permalink] 19 Jul 2018, 00:24
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