Strategy Used: Picking Numbers
Sometimes you can get stuck on a math question just because
it's too general or abstract. A good way to get a handle on such
a question is to make it more explicit by substituting specific
numbers that are easy to work with for any variables in the
question. This "picking numbers" strategy works particularly well
with even-odd questions.
Consider this example:
If a is an odd integer and b is an even integer,
which of the following must be odd?
Rather than try to think this one through abstractly, it's
easier for most people simply to pick numbers for a and
b. There are rules that predict the evenness or oddness of
sums, differences, and products, but there's no need to memorize
these rules. When it comes to adding, subtracting, and
multiplying evens and odds, what happens with one pair of numbers
generally happens with all similar pairs.
Just say, for the time being, that a = 3 and b =
2. Plug those values into the answer choices, and there's a good
chance that only one choice will be odd:
- 2a + b = 2(3) + 2 = 8
- a + 2b = 3 + 2(2) = 7
- ab = (3)(2) = 6
- a2b = (32)(2) = 18
- ab2 = (3)(22) = 12
Choice (B) is the only odd one for a = 3 and b =
2, so it must be the one that's odd no matter what odd number
a and even number b actually stand for. The answer
is (B).
Try the strategy out with
these practice questions!
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