The rules that solve most questions
- p% of n = (p/100) × n.
- Percent change = (new − old) / old × 100. Always divide by the original value.
- An increase of p% means multiplying by (1 + p/100); a decrease means multiplying by (1 − p/100).
- Successive changes multiply: a 10% increase then a 10% decrease is 1.10 × 0.90 = 0.99, a 1% decrease overall.
Traps the wrong answers are built on
- Dividing the change by the new value instead of the original.
- Adding or subtracting successive percent changes.
Worked example
A store raises the price of a jacket by 25%. Later, it lowers the new price by 20%. Compared with the original price, what is the overall change?
- A. Increase of 45%
- B. Increase of 5%
- C. No change
- D. Decrease of 5%
Answer: C. Use a starting price of $100. After a 25% increase: $125. A 20% decrease applies to $125: $125 × 0.80 = $100. Compared with $100, that's no change. Percent changes don't simply add: 25% − 20% = 5% is the trap.
Practice set
Answer each question to see whether you're right and why. When you finish, draw a new set: the numbers change every time.
0 of 10 answered · 0 correct · set 1
- Question 1Harder
A store raises the price of a jacket by 25%. Later, it lowers the new price by 20%. Compared with the original price, what is the overall change?
Show answer and explanation
Answer: C
Use a starting price of $100. After a 25% increase: $125.
A 20% decrease applies to $125: $125 × 0.80 = $100.
Compared with $100, that's no change. Percent changes don't simply add: 25% − 20% = 5% is the trap.
- Question 2Harder
A store raises the price of a jacket by 50%. Later, it lowers the new price by 20%. Compared with the original price, what is the overall change?
Show answer and explanation
Answer: C
Use a starting price of $100. After a 50% increase: $150.
A 20% decrease applies to $150: $150 × 0.80 = $120.
Compared with $100, that's a increase of 20%. Percent changes don't simply add: 50% − 20% = 30% is the trap.
- Question 3Harder
A store raises the price of a jacket by 10%. Later, it lowers the new price by 25%. Compared with the original price, what is the overall change?
Show answer and explanation
Answer: A
Use a starting price of $100. After a 10% increase: $110.
A 25% decrease applies to $110: $110 × 0.75 = $82.50.
Compared with $100, that's a decrease of 17.5%. Percent changes don't simply add: 10% − 25% = −15% is the trap.
- Question 4Harder
A store raises the price of a jacket by 20%. Later, it lowers the new price by 10%. Compared with the original price, what is the overall change?
Show answer and explanation
Answer: B
Use a starting price of $100. After a 20% increase: $120.
A 10% decrease applies to $120: $120 × 0.90 = $108.
Compared with $100, that's a increase of 8%. Percent changes don't simply add: 20% − 10% = 10% is the trap.
- Question 5Medium
The price of an item changed from $180 to $216. By what percent did the price increase?
Show answer and explanation
Answer: C
Percent change = (new − old) / old × 100.
($216 − $180) / $180 × 100 = 36 / 180 × 100 = 20%.
Divide by the original price, not the new one: dividing by $216 gives 16.7%, a common trap.
- Question 6Medium
The price of an item changed from $110 to $44. By what percent did the price decrease?
Show answer and explanation
Answer: D
Percent change = (new − old) / old × 100.
($44 − $110) / $110 × 100 = −66 / 110 × 100 = −60%.
Divide by the original price, not the new one: dividing by $44 gives 150%, a common trap.
- Question 7Easier
What is 20% of 720?
Show answer and explanation
Answer: B
20% means 20/100.
20/100 × 720 = 144.
- Question 8Easier
What is 20% of 220?
Show answer and explanation
Answer: A
20% means 20/100.
20/100 × 220 = 44.
- Question 9Harder
A store raises the price of a jacket by 50%. Later, it lowers the new price by 50%. Compared with the original price, what is the overall change?
Show answer and explanation
Answer: D
Use a starting price of $100. After a 50% increase: $150.
A 50% decrease applies to $150: $150 × 0.50 = $75.
Compared with $100, that's a decrease of 25%. Percent changes don't simply add: 50% − 50% = 0% is the trap.
- Question 10Easier
What is 30% of 500?
Show answer and explanation
Answer: B
30% means 30/100.
30/100 × 500 = 150.
More Problem-Solving and Data Analysis practice
Questions people ask
Is this percentages practice like the real SAT?
The questions follow the format of the digital SAT's Problem-Solving and Data Analysis domain: four answer choices built from common mistakes. They are written for this site; they are not official College Board questions.
How many practice questions are there?
As many as you want. Each math question is generated from a template with new numbers, and its answer is checked by code. Use "New set" for another ten.
Where is the domain on the test?
Problem-Solving and Data Analysis is one of the four content domains of the SAT Math section, alongside Algebra, Advanced Math, Geometry and Trigonometry.