If x is a positive number and a=\sqrt{x} * x - x , which of the following must be true? I. a is even II. a is positive III. a is an integer A. I only B. II only C. III only D. I and II E. None of the above

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maztho

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21 Oct 2025, 11:35

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I like the solution - it’s helpful.

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I like the solution - it’s helpful.

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Can we get some similar questions like these ? Bunuel

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officiisestyad

Can we get some similar questions like these ? Bunuel

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14 Apr 2026, 20:13

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I did not quite understand the solution. To assume a= fraction is a far cry, as my mind went on to assume x either as perfect square or an imperfect one. Please specify theory and reason why a cannot be even?

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harjas2222

The question asks which of the following must be true. For this kind of question, if you can show that a statement is not true for even one valid value, then that statement is not always true and therefore cannot be the correct answer.

So the goal here is not to prove that the statements could be true. The goal is to show that they are not necessarily true. Of course, a could be even, positive, or an integer for some values of x. For example, if x = 4, then a = 4, which is all three. That is why the solution tries a value like x = 1/4, because it gives a = -1/8, which is not even, not positive, and not an integer. So none of the statements must be true.