ApproachingMathICQuestions(2)

　　If p and q are odd integers, then which of the following must be odd?

　　(A)p + q

　　(B)p – q

　　(C)p2 + q2

　　(D)p2　q2

　　(E)p + q2

　　It might be hard to conceptualize how the two variables in this problem interact. But what if you chose two odd numbers, let's say 5 and 3, to represent the two variables? You get:(A)p + q = 5 + 3 = 8

　　(B)p – q = 5 – 3 = 2

　　(C)p2 + q2 = 25 + 9 = 34

　　(D)p2　q2 = 25　9 = 225

　　(E)p + q2 = 5 + 9 = 14

　　The answer has to be D, p2　q2 since it multiplies to 225. (Of course, you could have answered this question without any work at all, as two odd numbers, when multiplied, always result in an odd number.)　　Substituting numbers can help you transform problems from the abstract to the concrete. However, you have to remember to keep the substitution consistent. If you're using a 5 to represent p, don't suddenly start using 3. Choose numbers that are easy to work with and that fit the definitions provided by the question.

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