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I. a > b > c


Let a = 25, b= 2 and c=1

Applying to the condition √a > b^2 > c^3, we get,

5 > 4 > 1 which is true.

It also satisfies given condition I, 25 > 2 > 1.

So keep the choices that contain I. Eliminate B.


II. c > b > a

In this case, we want an example, where c to be the largest number at the same time c^3 is the smallest.
Also note, since GMAT covers only real numbers a cannot be negative :)
That means a,b and c all must be positive.

Consider c to be between 0< c < 1, then a and b should be less than 1 .

Let c = 1/3, b= 1/4 and a=1/64
Applying to the condition √a > b^2 > c^3, we get,

1/8 > 1/16 > 1/27 is true.

Also, here c > b > a is true.

So keep the choices that contain II.


Eliminate A and D. So the remaining options are C and E.


III. a > c > b

Let us consider b = -2, c= -1 and a = 25.


Applying to the condition √a > b^2 > c^3, we get,

5 > 4 > -1 which is true.

Also here a > c > b is true.

So keep the choice that contains III.

Eliminate C.

So the correct answer choice is E.
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First we see the question.
a^1/2 > b^2 > c^3
Which of the folowing can be true.

1. a>b>c

So both question and answer is in same direction. I would pick numbers which has sufficiently large difference between them and any operation on them are inconsequential.

eg: a^1/2 > b^2 > c^3 -> 1000,100,1
So a>b>c -> 10^6,10,1

2. a<b<c
Here root(a) should be largest then a becomes smallest
and c^3 should be smallest then c becomes largest.

These are usually the property of 0<x<1
For easier manipulation lets take them as decimal numbers
(0.1)^2 = 0.01
(0.008)^1/3 = .2

So we can see that its in right direction.
So first I pick 0.1,X,0.008

I like to keep things simple. So I would go to -ve if things doesnt work out only and always keep decimals in easily rootable format.
So by this standard, I would have picked b^2=0.04 then b=0.2 (Thats same as our C). Since there is less room in the middle. I would try move C further. I will pick c^3 = 0.027 then c=.3

eg: a^1/2 > b^2 > c^3 -> 0.1,0.04,0.027
So a<b<c -> 0.01<0.2<0.3

3. Its almost same as first except now square root is smaller than cube root.
Easiest way would be to take a negative root of the one you want to make smaller.
eg: a^1/2 > b^2 > c^3 -> 1000,100,1
So a>c>b -> 10^6,1,-10
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