Guides / Plug in your own numbers
Plug in your own numbers when a question has no real values
Pick simple numbers yourself, substitute everywhere the variable appears, then see which answer choice matches.
When a math question and every answer choice are written entirely in variables, with no numbers anywhere, pick simple numbers yourself. Substitute them everywhere the variable appears, solve the problem concretely, then check which answer choice matches your number. Abstract algebra is optional. Arithmetic isn't.
How to do it
- Pick small, easy numbers, 2, 3, or 5 work well. Avoid 0 and 1, since they can make different answer choices equal to each other and hide which one is really correct.
- Substitute your chosen number for the variable everywhere it appears in the question, and work out the real numeric answer.
- Plug that same number into each answer choice and see which one produces your result.
- If two choices tie, pick a second number and retest only those two.
If x is increased by 50% and then the result is decreased by 20%, which expression gives the final value in terms of x?
Let x = 100. A 50% increase gives 150. A 20% decrease from 150 gives 120. That's 1.2 times the original 100, matching choice C. No need to track percent changes abstractly, just work the numbers.
Turn abstract into arithmetic, every time.
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