SAT Math: SAT Math: Percentages Practice Questions
Test yourself on SAT Math: Percentages with 10 original SAT practice questions. Pick an answer to see instant feedback and a full explanation.
Free original practice questions for study purposes. Open Exam Prep is an independent study resource and is not affiliated with, endorsed by, or sponsored by the makers of SAT.
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Answer the questions below — you get instant feedback and a full explanation for each.
1. A shirt originally priced at $40 is on sale for 25% off. What is the sale price?
Explanation. 25% of 40 is 0.25 × 40 = 10. Sale price = 40 − 10 = $30. Alternatively, paying 75%: 0.75 × 40 = 30.
2. If 30 is 40% of a number, what is the number?
Explanation. 40% of x = 30 means 0.40x = 30, so x = 30 ÷ 0.40 = 75.
3. A population increases from 200 to 250. What is the percent increase?
Explanation. Percent change = (change ÷ original) × 100 = (50 ÷ 200) × 100 = 25%.
4. A laptop costs $600. After a 10% increase followed by a 10% decrease, what is the final price?
Explanation. After 10% increase: 600 × 1.10 = 660. After 10% decrease: 660 × 0.90 = 594. Successive percent changes don't cancel because they apply to different bases.
5. In a class, 60% of students are girls. If there are 18 boys, how many students are in the class?
Explanation. If 60% are girls, then 40% are boys. So 0.40x = 18, giving x = 18 ÷ 0.40 = 45.
6. A value is increased by 20%, then the result is increased by 50%. By what overall percent did the original value increase?
Explanation. Multiply factors: 1.20 × 1.50 = 1.80, which is an 80% increase. Adding 20% + 50% = 70% is incorrect because the second increase applies to the already-increased amount.
7. A store reduces a price by 40%. By what percent must the new price be increased to return to the original price?
Explanation. Let original = 100. After 40% off: 60. To go from 60 back to 100, increase = 40 ÷ 60 = 0.6667 ≈ 66.7%.
8. The price p of an item after a 15% sales tax is added equals $92. What was the price before tax?
Explanation. Price × 1.15 = 92, so price = 92 ÷ 1.15 = 80. Subtracting 15% of 92 is wrong because tax was computed on the pre-tax price.
9. What is 25% of 25% of 800?
Explanation. 25% of 800 = 200. Then 25% of 200 = 50. Multiply: 0.25 × 0.25 × 800 = 0.0625 × 800 = 50.
10. A quantity grows by 8% per year. Which expression gives its value after 3 years if it starts at A?
Explanation. Each year multiplies by 1.08, so after 3 years it is A(1.08)^3. The linear form A(1 + 0.24) ignores compounding.
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FAQ
How should I handle 'percent of' versus 'percent change' problems?
For 'percent of,' multiply: 30% of x means 0.30x. For percent change, use (new − old) ÷ old × 100, always dividing by the original (starting) value.
Why don't successive percent changes simply add up?
Each percentage applies to a different base. A 10% increase then a 10% decrease gives a 1% net loss (1.10 × 0.90 = 0.99). Always multiply the decimal factors rather than adding the percentages.
What's the fastest way to reverse a percent change to find the original?
Set up an equation: if a final value results from multiplying by a factor (like 1.15 for tax or 0.60 for 40% off), divide the final value by that factor. Avoid just subtracting the percent of the final amount.