This question is a DS question from Inequalities.

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

1. 1/a > a

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

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

Is a

1. 1/a > a

2. a

Correct Answer

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

Let us evaluate each of these statements independently

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 negative values of 'a' a^{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

For negative values of 'a' a

Hence, from statement 1 we can conclude that a

Statement 1 is SUFFICIENT.

Statement 2 : a

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