SAT Math Shortcuts • Topic 2 of 4

Picking Numbers

When a problem is all variables (no numbers), pick your own concrete values, compute the result, and see which answer choice matches. Choose easy numbers that obey any conditions — small integers usually, but avoid 0 and 1 (they make several choices coincide) and avoid numbers already in the problem. For “if a is even, which expression is always odd?”, let a = 2 and test each choice. For percent problems with no given total, pick 100. If two choices both match your numbers, pick a second set to break the tie. Picking numbers converts abstract algebra into concrete arithmetic you can trust.

✅ Solved examples

1. For percent problems with no stated total, what number is easiest?
100 — percentages become direct.
2. Which numbers should you avoid when picking?
0 and 1 (and any number already in the problem).
3. “If a is even, a + 1 is…?” Test a = 4.
4 + 1 = 5, odd — so a + 1 is always odd.
4. Two choices both match your picked value. Next step?
Pick a second set of numbers to break the tie.

✏️ Practice — try these, take hints as needed

1. No total given in a percent problem — pick:
Round and easy.
—
—
100.
2. Two values to avoid when picking numbers:
They coincide too often.
—
—
0 and 1.
3. “If n is odd, 2n is…?” Test n = 3.
2 × 3.
—
—
Even (6).
4. If two choices match your numbers, you should:
Try again.
—
—
Pick a second set.
5. Picking numbers works best when the problem is mostly:
No concrete numbers.
—
—
Variables.
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