If [x] denotes the greatest integer less than or equal to x

Here, the notation [x] is to make the problem harder than it seems. Just replace [x] with another variable which is easier and more natural to grasp - y. The question can be rephrased as: "If y denotes the greatest integer less than or equal to x, is y = 0 ?"

Integers comprise of the set of numbers which can be written without a fractional component. They can be positive, negative or zero.

Let's go to the follow on equations given. The first equation can be solved as x= 2/3. In which case, y would be 0 (greatest integer less than or equal to x). So, we can answer this question with option (1) alone.
The second inequality equation mentions x is in between 0 and 1. Hence, y would be 0 again because it is the greatest integer less than or equal to x which is a fraction between 0 and 1. Hence, option (2) alone is also sufficient to answer the question.

So the answer to this question is option D - EACH statement ALONE is sufficient.