DON’T FREAK OUT.
If you see something—a symbol, a word—you’ve never seen before, chances are the test
makers just made it up to test your ability to stay cool in the face of something new and
unfamiliar.Symbolism questions often look intimidating at first, but you’ll find that, on closer inspection, they
merely teach you some invented rule and then ask you to show that you understand the rule. Of
course, on a test as challenging as the Math 2, symbolism questions often include a twist or two.
Here, for example, you’re told that means one thing whenever x > y, but something different
whenever x ≤ y. And you’re expected to juggle these definitions in the context of a Roman Numeral
question.
Take one issue at a time. You know that x y < 0. What does that tell you about the relationship
between x and y themselves ? Could x be greater than y ? No. When x is greater than y,
. But absolute value is always nonnegative and (because x and y are nonzero)
squares must be positive in this question, so must be positive. Because, again, x y < 0, you
must be dealing here with the other definition: . And that’s the definition that holds if and
only if x ≤ y.
Having invested some time thinking about the meaning of the question stem, notice now how
breezily you move through the statements. Which one(s) have x ≤ y ? In I, in order for x^3 = y^3 , x and y
themselves must be equal. (The same would be true of x and y raised to any odd power, though not
to even powers, in which case x could equal ±y.) So given x ≤ y, “could it be true” that x = y ? Yes. So I
must be included in the answer: eliminate (B), (C), and (E).
(D) I and II(E) II and III