What is backsolving on the SAT or ACT?

Backsolving means substituting each multiple-choice answer directly into the problem to see which one satisfies every condition, instead of solving for the variable algebraically. It works well whenever the answer choices are plain numbers.

Which answer choice should I start with when backsolving?

Start with a middle choice, B or C on a four-option SAT question, C on a five-option ACT question. Answer choices are almost always ordered, so a middle guess tells you immediately which direction to adjust if it's wrong.

When doesn't backsolving work?

It doesn't apply when the answer choices are expressions or variables rather than plain numbers, since there's nothing concrete to test. In that case, plugging in your own numbers for the variable is the better shortcut.

Plug the Answers Into the Question Instead of Solving

Start with a middle answer choice. If it's too big or too small, that tells you which direction to move, and you're often at the right answer in two tries instead of a full algebraic solve.

How to do it

Look at the answer choices before you start solving. If they're plain numbers and roughly in order, backsolving is available.
Start with choice B or C on the SAT's four options, or C on the ACT's five. Answer choices are almost always ordered, so a middle guess tells you which direction to adjust.
Substitute that value into the problem and check if it satisfies every condition, not just the first equation you see.
If it's too high, try a smaller choice. If too low, try a larger one. You'll usually land on the answer within two tries.

Try one for yourself · Math · Algebra

3(y − 1) / 2 = 9 / (y − 2)

What value of y satisfies the equation above?

A −1

B 2

C 3

D 4

Reasoning

Backsolve with D: 3(4−1)/2 = 9/2, and 9/(4−2) = 9/2. Both sides match, so D works. That's faster and safer than cross-multiplying into a trinomial and solving algebraically, since there's no chance of a sign slip mid-equation.

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Plug the answers into the question instead of solving

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