SAT Math Shortcuts • Topic 1 of 4

Backsolving

Backsolving means plugging the answer choices into the problem instead of solving for the unknown. Since exactly one choice works, you can test them — and because choices are usually in order, start with B or C: if it’s too big, go smaller; too small, go bigger, so you rarely test all four. It shines on equations with awkward algebra or word problems where setting up is hard but checking is easy. For “a number such that 3x − 5 = 16,” trying the middle choice quickly lands on x = 7. Backsolving trades clever algebra for reliable arithmetic — often the faster, safer route under time pressure.

✅ Solved examples

1. Solve 3x − 5 = 16 by backsolving choices {5, 7, 9, 11}.
Try 7: 3(7) − 5 = 16 ✓ — the answer is 7.
2. Why start backsolving from B or C?
They’re middle values, so the result tells you to go up or down — fewer tests.
3. When is backsolving best?
When the choices are numbers and checking is easier than solving.
4. Backsolve: which value satisfies 2x + 4 = 20? {6, 8, 10}
Try 8: 2(8) + 4 = 20 ✓.

✏️ Practice — try these, take hints as needed

1. Backsolve 4x − 3 = 17 from {3, 5, 7}.
Try the middle.
4(5) − 3.
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x = 5.
2. Backsolving means plugging in the ___.
Not solving forward.
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Answer choices.
3. Best first choice to test when they’re ordered?
Middle.
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B or C.
4. Backsolve x/2 + 1 = 6 from {8, 10, 12}.
Try 10: 10/2 + 1.
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x = 10.
5. Backsolving needs the question to be in which format?
Has options.
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Multiple choice.
Picking Numbers →