SAT Math Shortcuts • Topic 3 of 4

Answer Choice Testing

Answer-choice testing uses the options as information. Scan them first: their spread tells you how precise you must be (far apart means estimate; close together means compute carefully). Test choices against every condition in the problem — “must be divisible by 3,” “greater than 10,” “an integer” — and discard any that fail. On “which of the following must be true” questions, a single counterexample kills a choice. Combine with elimination: rule out the impossible, then test what remains. This is less about a formula and more about treating the four options as a set of claims you can check one by one.

✅ Solved examples

1. Choices are 12, 15, 18, 21 and the answer must be divisible by 3. Which survive?
All are divisible by 3 — test further conditions to decide.
2. A “must be true” choice fails for one example. Keep it?
No — one counterexample eliminates it.
3. The four choices are far apart. What does that allow?
Estimation — you don’t need an exact value to choose.
4. Answer must be > 10; a choice is 8. Keep it?
No — it fails the condition; eliminate.

✏️ Practice — try these, take hints as needed

1. A single counterexample to a “must be true” choice means:
It’s dead.
—
—
Eliminate it.
2. Widely spaced choices invite which technique?
Rough is enough.
—
—
Estimation.
3. Answer must be even; choice 9 is:
Parity.
—
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Eliminated.
4. Closely spaced choices mean you must:
Be precise.
—
—
Compute carefully.
5. Treat each answer choice as a ___ you can check.
A statement.
—
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Claim.
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