Data Sufficiency

Is a^3 > a^2?
(1) 1/a > a
(2) a^5 > a^3

Please Help !!

dhairya275 wrote:Is a^3 > a^2?
(1) 1/a > a
(2) a^5 > a^3

a³ > a² only if a≠0.
If a≠0, then a² is positive, implying that we can safely divide each side of the question stem by a²:
a³/a² > a²/a²
a>1.

Question rephrased: Is a>1?

Statement 1: 1/a > a
No value greater than 1 will work here:
SUFFICIENT.

Statement 2: a� > a³
a� > a³ only if a≠0.
If a≠0, then a² is positive, implying that we can safely divide each side here by a²:
a�/a² > a³/a²
a³ > a.
It's possible that a=2, since 2³ > 2.
It's possible that a=-1/2, since (-1/2)³ > -1/2.
INSUFFICIENT.

The correct answer is A.

Mitch,
Just to clarify one point -

When we say a^3 > a^2, we also know that this is possible only if a>0 in addition to a#0, right ?

kindly let me know in case i am missing anything.

rahulsehgal wrote:Mitch,
Just to clarify one point -

When we say a^3 > a^2, we also know that this is possible only if a>0 in addition to a#0, right ?

kindly let me know in case i am missing anything.

In this case, a>0.
As my rephrase of the question stem shows, a³ > a² only if a>1.

But the reasoning is not contingent on a>0.
To divide by a², the only requirement is that a≠0.

Another example:
a� > a²
Since a� > a² only if a≠0, we can safely divide each side by a²:
a�/a² > a²/a²
a² > 1.

The resulting inequality implies that a>1 or a<-1.
Thus, to divide by a², it is NOT necessary that a>0.
The only requirement is that a≠0.