Inequalities and Equations in DS questions

[oquiella]

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


These are common, what is the quickest approach to these type of questions within DS?



Explanation
Statement (1)
(a)1/2 > a
(a)1/2 (1 - (a)1/2) > 0
(a)1/2 is always non-negative.
Therefore (1 - (a)1/2) > 0
This implies 0 < a < 1
Therefore (a)1/3 > (a)1/2
Hence SUFFICIENT.
Remember when any number n is greater than 1, (n)1/3 < (n)1/2
And when 0<n<1, (n)1/3 > (n)1/2
Substitute a few values to check.
Statement (2)
(a)1/3 > (a)2/3
(a)1/3(1 - (a)1/3) > 0
Again here as (a)1/3is always greater than 0, (1 - (a)1/3) > 0
This implies 0 < a < 1
Therefore (a)1/3 > (a)1/2
Hence SUFFICIENT.
The correct answer is D;