OE
Throughout, x represents the same thing—a number between 1 and 3. If x is 2, then \(x^2\) and 2x are each 4, and in this case the two quantities are equal. We can, therefore, eliminate the first two choices: neither Quantity A nor Quantity B is greater all the time. However, in order for the correct answer to be “The two quantities are equal,” the quantities would have to be equal all the time. Are they? Note that although 2 is the only integer between 1 and 3, it is not the only number between 2 and 3: x could be 1.1 or 2.5 or any of infinitely many other numbers. And in those cases the quantities are not equal (for example, \(2.5^2\) = 6.25, whereas 2(2.5) = 5). The quantities are not always equal, and so the correct answer is the fourth choice: It is impossible to determine which quantity is greater.
Answer: D