On this page
Percentages show up all over the Digital SAT Math section: discounts, growth, data tables, word problems. Almost all of it reduces to two ideas: part over whole, and percent change. Nail those and the trap answers stop working on you.
Key takeaways
- Percent = part ÷ whole × 100.
- Percent change = (new − old) ÷ old × 100. Always divide by the original.
- An increase of p\% multiplies by (1 + p/100); a decrease multiplies by (1 - p/100).
- The #1 trap: dividing the change by the new value instead of the old.
Percent change: divide by the original
This is where most points are lost. Percent change always compares the change to where you started. Grew from 250 to 300? The change is 50, and you divide by the original 250, not the new 300. (Percent setups lean on the same scaling logic as ratios and proportions.)
\dfrac{\text{new} - \text{old}}{\text{old}}. Dividing by the new value is the single most common percent mistake on the test, and a wrong answer is always sitting there for it.
Try one
A town’s population grew from 250 to 300 over a decade. What was the percent increase?
Chained percent changes
When percentages stack (a price rises 20%, then drops 20%), don’t add them. Multiply the factors. Up 20% then down 20% is 1.20 \times 0.80 = 0.96, a net 4% decrease, not zero.
The trap
Adding or subtracting stacked percents (+20% then −20% = 0%).
The move
Multiply the factors: 1.2 \times 0.8 = 0.96 → a 4% net decrease.
Translate the phrase before you compute
Most percent errors happen in translation, not arithmetic. "Of" and "more than" are different multipliers, and the wrong answers assume you’ll blur them. Convert the English to a multiplier first and the setup writes itself.
| When the question says… | Write… |
|---|---|
| 20% of x | 0.20x |
| 20% more than x / increased by 20% | 1.20x |
| 20% less than x / decreased by 20% | 0.80x |
| a is what percent of b? | \dfrac{a}{b} \times 100 |
| x is what percent greater than y? | \dfrac{x - y}{y} \times 100 |
Working backward from the new value
The hardest common percent question runs the change in reverse: you’re given the value after the change and asked for the original. Undo the multiplier by dividing. If a price fell 30%, the tag shows 70% of the original, so divide by 0.7. Adding 30% back on never works, because 30% of the smaller number is less than 30% of the original.
A jacket costs $84 after a 30% discount. What was the original price of the jacket?
Drill percent change and part-of-whole with a tutor that catches the divide-by-wrong-number slip.
Practice Percentages →Frequently asked questions
- How do you calculate percent change on the SAT?
- Percent change = (new value − old value) ÷ old value × 100. Always divide by the original (old) value, not the new one.
- How do you handle two percent changes in a row?
- Multiply the factors instead of adding the percents. A 20% increase then a 20% decrease is 1.2 × 0.8 = 0.96, a 4% net decrease.
- What’s the most common percentage mistake?
- Dividing the change by the new value instead of the original. The denominator in percent change is always the starting amount.
- How do I find the original price before a percent discount?
- Divide the sale price by the discount multiplier. After a 30% discount the tag shows 70% of the original, so original = sale price ÷ 0.70. Adding the percent back onto the sale price undershoots, because the discount was taken from a larger number.