The idea
A percentage expresses a quantity per hundred of a reference quantity. For a percentage change, identify the original quantity first: a decrease of p percent multiplies it by 1 − p/100, and an increase multiplies it by 1 + p/100.
A step-by-step method
- Identify the original quantity and whether the change is an increase or a decrease.
- Convert the percentage to a decimal and calculate the change, or use the corresponding multiplier.
- Check the units and whether the result should be greater or smaller than the original quantity.
Worked example
Attempt this original question, then open the reasoning to compare your approach.
A jacket originally costs $80. Its price is reduced by 25%. What is the new price?
- $20
- $55
- $60
- $100
Show answer and reasoning
Answer: C · $60
The discount is 0.25 × $80 = $20.
Subtract the discount: $80 − $20 = $60. Equivalently, 0.75 × $80 = $60.
Why each option works or fails
- $20 is the discount, not the new price.
- Subtracting 25 dollars treats a percentage as a dollar amount.
- Correct: the new price is 75% of $80.
- This adds the 25% change instead of subtracting it.
Try a new question
Work independently before opening the explanation. Check what changed and whether the same rule still applies.
A store increases the price of an item by 20%, then reduces the increased price by 25%. The final price is $144. What was the price before either change?
- $144
- $151.58
- $160
- $192
Show answer and reasoning
Answer: C · $160
Let P be the original price. The successive multipliers give 0.75(1.20P) = 0.90P.
Thus 0.90P = 144, so P = 160. Check: $160 increases to $192, then decreases by $48 to $144.
The percentages use different reference prices. Their combined effect is a 10% decrease, not 25% − 20% = 5%.
Why each option works or fails
- This ignores the changes.
- This incorrectly combines the changes into a 5% decrease.
- Correct: 160 × 1.20 × 0.75 = 144.
- $192 is the intermediate price after the increase.
Common mistakes
- The percentage applies to its stated reference quantity, not automatically to the final quantity.
- A change from 20% to 25% is 5 percentage points, but a 25% relative increase in the percentage itself.
Sources and related guides
This guide was prepared with AI assistance. Its rules and worked examples were checked against the references below; no independent expert review is claimed. Examples are original and are not official SAT questions.
Revision: Original examples distinguish reference quantities in successive percentage changes.