Explanation

In this question, the fact that a and b are both positive is convenient, because it means that we can multiply both sides of the inequality by the variables without having to worry about flipping the sign of the inequality. So we can multiply by a and by b to obtain



Again, since a and b are both positive, that simplifies this situation a bit. If, , then we have . For example, and . It's also true for fractions between 0 and 1; they will get smaller when they are squared, but the inequality will hold. Let's turn to the data statements, separately first.

Statement (1) can be manipulated into a form that allows us to compare b and a more obviously:



Since both numbers are positive, this statement tells us that is definitively false and hence we can answer the stated question definitively in the negative. Statement (1) is sufficient.

Statement (2), similarly, tells us that b is greater than a--6 greater, in fact. By the same logic as above, it's sufficient.

The correct answer is (D).