The problem states that x is between 0 and 1, so x must be a positive fraction (or decimal) less than 1. We can pick a number to get to the correct answer(s) here because both the question and the answer choices have variables. The decimal 0.5 is in the middle of the given range, so it’s a good starting point. (A) Incorrect. Doubling any positive value always produces a greater value, not a lesser value. (B) Incorrect. 2 × 0.5 = 1; a smaller fraction could make this statement true, but our correct answer(s) must always be true. (C) Incorrect. 2 × 0.5 = 1; a larger fraction could make this statement true, but our correct answer(s) must always be true. (D) Correct. 0.52 = 0.25; the square of any number between 0 and 1 (exclusive) will be less than the original number. This example illustrates that property. (E) Correct. 0.25 < 1; the square of any number between 0 and 1 (exclusive) will be less than 1. This is an example of that property. So, the correct answers are (D) and (E).