Plugging in numbers and backsolving are two strategies that let you answer ACT Math questions without full algebra. You either pick your own simple numbers for the variables, or you test the answer choices to see which one works. They will not replace knowing the math, but they turn a lot of scary problems into quick, checkable ones.
Strategy 1: Plugging in your own numbers
This works when a problem has variables in both the question and the answer choices. Instead of solving abstractly, pick easy numbers, work the problem, and match your result to the choices.
Say a question asks for an expression equal to "the total cost if a shirts cost 3 dollars each and b hats cost 5 dollars each." Rather than reason it out symbolically, let a be 2 and b be 4. The real cost is 2 times 3 plus 4 times 5, which is 26. Now plug a equals 2 and b equals 4 into each answer choice, and pick the one that gives 26. Done.
A few tips for choosing numbers:
- Pick small, easy values that are simple to compute with.
- Avoid 0 and 1, since they can make several choices look correct.
- Do not reuse the same number for different variables.
- If more than one choice matches, pick new numbers and test only those.
Strategy 2: Backsolving from the answer choices
When the answer choices are plain numbers, you can work backward by testing them in the problem. Because the ACT usually lists numerical choices in order, start with the middle value. If it is too big or too small, you often know which direction to go, so you might only test two choices.
For example, if a question leads to an equation and asks "what is x," try the middle answer choice in the original equation. If it does not balance, the size of the miss tells you whether to try a larger or smaller choice next. This is especially handy on word problems where setting up the equation is the hard part.
When these strategies shine
- Word problems where translating into algebra is the tricky step.
- Problems with variables in the answer choices.
- Questions where you blank on the "proper" method but can still test values.
- Times when you want to verify an answer you got algebraically.
When to just do the algebra
These tools are not always fastest. If you instantly see the direct method, use it. Plugging in shines when the algebra is messy or you are stuck, not when a clean one-step solution is staring at you. Part of getting good is knowing which approach is quicker for a given problem, which comes from practice. Build that judgment with the math topics on the ACT and how to improve your ACT Math score.
Practice them until they are automatic
The mistake students make is trying these for the first time on test day. Practice plugging in and backsolving during your prep so they become instinctive and fast. Used well, they also help you dodge the trap answers we cover in the most common ACT Math mistakes, because you are verifying against the real question. For the toughest problems, pair them with the ideas in how to get a 36 on ACT Math.
The bottom line
Plugging in your own numbers and backsolving from the choices are reliable ways to crack problems when the algebra feels heavy. Learn them, practice them until they are quick, and keep them ready for the moments a question tries to intimidate you.
Start practicing
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This article offers general ACT prep guidance. The ACT can change from year to year, including its format, scoring, policies, test dates, and fees, so always confirm the latest details on the official ACT website at act.org before you make decisions. ACT® is a registered trademark of ACT, Inc. thirty-six is not affiliated with, endorsed by, or sponsored by ACT.