This question is a DS question from Inequalities.

Is a^{3} > a^{2}?

1. 1/a > a

2. a^{5} > a^{3}

Correct Answer

The correct answer is Choice A. Statement 1 alone is sufficient.

Let us evaluate each of these statements independently

**Statement 1 :**1/a > a

For positive values of ‘a’ if 1/a is > a, a has to lie in the interval 0 < a < 1.

In this interval a

^{3}< a^{2}For negative values of ‘a’ a^{3} < a^{2}

Hence, from statement 1 we can conclude that a^{3} is not greater than a^{2}

Statement 1 is SUFFICIENT.

Statement 2 : a^{5} > a^{3}

For positive values of ‘a’ if a

^{5}> a^{3}a has to be greater than 1. In this interval a^{3}> a^{2}^{ }For negative values of ‘a’ a

Hence we will not be able conclude whether a

Statement 2 is NOT SUFFICIENT.

Choice A is the answer

^{3}< a^{2}Hence we will not be able conclude whether a

^{3}> a^{2}^{ }Statement 2 is NOT SUFFICIENT.

Choice A is the answer

aditi says

when we say a is greater than 1, for a^5> a^3 to be true as per the statement given. Then y are we considering negatve values of a?