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

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Current Student
Status: It always seems impossible until it's done!!
Joined: 29 Aug 2012
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Location: India
WE: General Management (Aerospace and Defense)
If a>0, is (a)^1/3 > (a)^1/2 ?  [#permalink]

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19 Aug 2015, 01:56
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00:00

Difficulty:

25% (medium)

Question Stats:

80% (01:47) correct 20% (02:22) wrong based on 147 sessions

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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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GMAT 1: 710 Q50 V34
Re: If a>0, is (a)^1/3 > (a)^1/2 ?  [#permalink]

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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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##### General Discussion
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Joined: 08 May 2015
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GMAT 1: 630 Q39 V38
GMAT 2: 670 Q44 V38
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Re: If a>0, is (a)^1/3 > (a)^1/2 ?  [#permalink]

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19 Aug 2015, 09:26
You can "translate" the question to "If a>0, is 0<a<1?"
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Joined: 09 Sep 2013
Posts: 8801
Re: If a>0, is (a)^1/3 > (a)^1/2 ?  [#permalink]

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19 Jul 2018, 00:24
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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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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