Short answer: on multiple-choice questions, the correct answer is one of four numbers. If the question asks for a value, try the choices instead of solving. Start with the middle values, and stop when one works.
The idea
Every multiple-choice question hides its answer in plain sight. Solving algebraically is not always the shortest path. Testing four numbers can take twenty seconds.
Example
Question: What is the positive value of x that satisfies x² - 8x = 33?
A) 3 B) 8 C) 11 D) 33
Algebra route: rewrite as x² - 8x - 33 = 0 and factor into (x - 11)(x + 3) = 0. That gives x = 11 or x = -3, so the positive value is 11.
Plug-in route: test C) 11 first. 11² - 8(11) = 121 - 88 = 33. It works. Done in one step.
Check one more to be safe: B) 8 gives 64 - 64 = 0, which is not 33.
How to choose which to test
- When the choices are in order, test the second or third one. The result tells you whether to go higher or lower.
- When the question is a word problem about quantities, read the answer as a quantity and rebuild the story with it.
- When the answers are expressions with x, pick an easy value for x (such as 2) and test which choice gives the same result as the original.
When not to plug in
If the choices are very messy numbers or the question has no numeric answers, solve instead. If you can see a one-step algebra move, do it. Plugging in is a tool, not a rule.
Where this fits
Answer-choice testing is the second method in the course after Desmos. Book a free call to see which methods fit your own mistakes.