Picking Numbers
Picking numbers is a variation of plugging in and should only be used when the answer choices contain variables. A modified version of our original sample question shows what kind of problems might lend themselves to picking numbers.
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A baseball player travels from his home city, Jasonville, to Giambia City for a baseball game. He drives at m miles an hour. After the game, he travels back home, and takes a flight instead at p miles an hour. If the distance from Jasonville to Giambia City is v miles, and it took him j longer to drive than to fly, what is j? |
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(A) |
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(B) |
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(C) |
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(D) |
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(D) |
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This question asks you to figure out which set of variables in the answer choices is the right one. But thinking in terms of variables can be confusing to some people. Picking numbers allows you to transform variables into concrete numbers.
To use the picking numbers method, you need to select numbers and plug them into the answer choices. You’re essentially testing the relationships between the variables in each given answer and ensuring they remain true. It doesn’t matter what specific numbers you plug into a problem. The same answer choice will always surface as long as you plug in consistently and follow all guidelines given by the problem.
For example, in the baseball player problem, let
m = 5,
v = 100, and
p = 10. Clearly, these numbers aren’t realistic (who flies at 10 miles an hour?), but your goal is to pick easy-to-manipulate numbers. Using our numbers, it takes the baseball player 100
5 = 20 hours to drive and 100
10 = 10 hours to fly. So, it takes him 20 – 10 = 10 hours longer to drive. After plugging m, v, and p into all the answer choices, we find that only
D produces an answer of 10.
Very rarely, more than one answer choice will result in the correct answer for the first set of numbers you picked. When this occurs, simply plug in a different set of numbers. You will almost never have to plug in more than two sets of numbers.
When picking numbers, you must check through all the answer solutions with your chosen numbers. Obviously, this will slow you down, but that’s the price you pay for using this method. Picking numbers gives you a mechanical method of solving tricky problems, and it also allows you to check your math for careless calculations, but it is time-consuming.
Finally, when you are picking numbers, avoid 0, 1, or any numbers that appear in the answer choices. Picking these numbers can overly simplify the expressions you are dealing with and cause you to pick the wrong answer.
The Bottom Line
As you can see, there is no “right” method to solving all algebra problems. Some methods work best some times, and others work best at other times. Part of your practice for the Math IC test will be to get comfortable with algebra questions so that you can choose which method you want to use for every question.
