SAT Problem Solving Framework • Topic 4 of 4

Logical Elimination

Before (or instead of) full computation, use logic to throw out answers that can’t be right. Check the sign — if the answer must be positive, drop the negatives. Check the size — a part can’t exceed the whole; a discounted price can’t be higher than the original. Check conditions in the problem — if it says “x is an integer,” fractional choices are out. Test parity (odd/even) or divisibility when relevant. Often elimination alone leaves one choice, and even when it doesn’t, it shrinks the field so a guess is strong. Logical elimination is your safety net on every multiple-choice question.

✅ Solved examples

1. The answer is a probability; a choice is 1.3. Keep it?
No — probabilities are ≤ 1; eliminate.
2. A discounted price is asked; a choice exceeds the original. Keep it?
No — a discount lowers the price; eliminate.
3. “x is a positive integer”; a choice is 2.5. Keep it?
No — not an integer; eliminate.
4. A length is asked; a choice is −4. Keep it?
No — lengths are positive; eliminate.

✏️ Practice — try these, take hints as needed

1. A count of people is asked; choice −3 is:
Counts ≥ 0.
—
—
Eliminated.
2. A probability choice of 2 is:
Must be 0–1.
—
—
Eliminated.
3. “n is even”; choice 7 is:
Parity.
—
—
Eliminated.
4. A fraction of a whole is asked; a choice bigger than the whole is:
Part ≤ whole.
—
—
Eliminated.
5. After eliminating impossible choices, you should:
Decide among the rest.
—
—
Choose (or guess) among what remains.
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