The key to these types of problems is to look for a number that will disqualify the answer choice:
If m and n are integers such that mn = 500, which of the following statements must be true?
The only choice for which we were unable to find an exception is Choice (D), so it's the correct answer.
It would have been easy to pick numbers to make the statements in the answer choices true. But, if we'd done that, we wouldn't have been able to eliminate any choices! The key for "must be true" questions is to find numbers that can make four of the five choices not true.
And one more note: Because this is a "Which of the following" question you should have started with Choice E to reinforce your test day habit. But you couldn't have stopped when you got to Choice (D) and found that you couldn't find an exception. That's because this is a "must be true" question. You can prove that something cannot be true by counterexample, which is what we did when we eliminated choices above. But you can't prove that it must be true by picking numbers, because it might be that you simply hadn't picked the correct numbers! Eliminating down to one choice remaining was the only way to apply picking numbers to this problem with certainty.
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