Bunuel wrote:

Is x a positive integer?

(1) The reciprocal of x is greater than x

(2) x > | y |

(1) The reciprocal of x is greater than xx can be either a negative integer or a positive fraction:

x = -4, 1/x = -1/4, -1/4 > -4 ------> 1/x > x

or

x = 1/2, 1/x = 2, 2 > 1/2 -------> 1/x > x

Sufficient.

(2) x > | y |It tells us that x is always positive, because absolute value is always positive.

But it does not tell us is x integer or not. x can be 1, 2, 1/3 ... Even if y is an integer it does not mean that x should be. Insufficient.

(1) & (2) together. That gives us a fraction between 0 and 1. No positive integer can have inverse greater than itself. (2 > 1/2)

x = 1/3, 1/x = 3, 3 > 1/3 --------> 1/x > x. Sufficient.

Answer C