Explanation

This question gives us a definition that is unique to the question, indicated by the zoomy arrow over the variable z. Questions that involve a unique symbolism are visually distracting but can be dismantled by relying on your innate verbal sense, however strong you consider that sense to be. Here, the zoomy arrow indicates an integer less than or equal to the thing that has, evidently, been nearly missed by the arrow. And we're asked whether that is 1. By the definition, "z zoomed" is less than z, so z is greater than z zoomed. So z could be 2. And it looks like z could be 1. So this question is asking, to paraphrase it in more straightforward terms, is ? With that knowledge in hand, let's evaluate the statements, separately first.

Statement (1), after moving z terms to the left and non-z terms to the right, tells us that . Therefore, , and that means that it is definitively not between 1 and 2. Therefore, we can answer the question definitively in the negative. Statement (1) is sufficient.

Statement (2), meanwhile, tells us exactly what we wanted to know. The question asks, is ? And Statement (2) tells us: . Not exactly what we were looking for, but if , then . If, visually speaking, that seems obscure, try speaking the inequalities aloud, and the connection between the two should be clearer. So, Statement (2) is sufficient.

The correct answer is (D).