If −y<x<y, the value of x is either between −y and 0 or between 0 and y, so statement I, |x|<y is true. It is possible that the value of x is greater than zero, but x could be negative. For example, a counterexample to statement II, x>0, is x=−2 and y=3, yielding −3<−2<3, so the given condition is satisfied. Statement III must be true since −y<x<yimplies that −y<y, so y must be greater than 0. Therefore, statements I and III are the only statements that must be true. Choices A, B, and D are incorrect because each of these choices either omits a statement that must be true or includes a statement that could be false.