Math Strategy: Picking Numbers - Part I

General Math Strategies

Math Strategy: Picking Numbers - Part I

Lesson by Linnea Newman

Magoosh Expert

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Math Strategy: Picking Numbers - Part II

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Lesson by Linnea Newman

Magoosh Expert

Summary

Plugging in turns many ACT algebra questions into faster, less error-prone arithmetic. Use it when answer choices contain variables, when the question asks for an equivalent expression or something written in terms of variables, and when fractions or percents apply to an unknown total.

Variables in the answer choices are a major signal that plugging in can work, especially with prompts such as "in terms of" or "equivalent expression."
Choose easy values like 2, 3, 5, 10, or 100, and usually avoid 0 and 1 because they can make different answer choices produce the same result.
After substituting your numbers into the original expression, compute a target value and then test every answer choice against that value.
If more than one answer choice matches your first test, plug in a different set of values to eliminate the remaining choices.
An expression such as y/(1 + x) + y/(1 - x) can be solved quickly by plugging in values like x = 2 and y = 3, producing a target value of -2 and identifying the correct equivalent expression.
Hidden plugging in works when the problem involves fractions or percents of an unknown quantity; 100 is especially useful for percent problems, and common multiples help with fraction denominators.
For percent-change problems, plugging in 100 makes the arithmetic immediate, and tools like a calculator or Desmos can help when the computation becomes messy.

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