SAT Math: Percent Change
39+ practice questions in Praczo
The concept, explained
- 1
Percent change = [(New − Original) / Original] × 100. Positive = increase; negative = decrease.
- 2
Always divide by the ORIGINAL value, not the new one. This is the single most common error on SAT percent-change problems.
- 3
To find the new value after a percent increase: New = Original × (1 + r). For decrease: New = Original × (1 − r), where r is the decimal rate.
- 4
"Percent greater than" uses the smaller value as the base; "percent of" uses the reference value. These differ — the SAT exploits this distinction.
- 5
Successive percent changes multiply: a 20% increase then 10% decrease is 1.20 × 0.90 = 1.08, an overall 8% increase.
- ✗ Dividing by the new value instead of the original: going from $50 to $60, the increase is 10/50 = 20%, not 10/60.
- ✗ Assuming two successive changes "cancel": a 20% increase then 20% decrease is 1.20 × 0.80 = 0.96 — a 4% net decrease, not zero.
SAT-style practice
A jacket originally costs $80. Its price is reduced by 25%, then the reduced price is increased by 10%. What is the final price?
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