Percentages Increase and Decrease — SAT Math Guide
Percentages increase and decrease SAT questions test your ability to calculate percentage changes and solve real-world problems involving growth and decline. These problems appear frequently in the Problem Solving and Data Analysis domain, making up about 2-3 questions per test. You'll encounter scenarios involving price changes, population growth, sales increases, and discount calculations that mirror situations you might face in college and beyond.
What You Need to Know
Percent increase formula: ((New Value - Original Value) / Original Value) × 100
Percent decrease formula: Same formula, but the result will be negative
Finding new value after increase: Original × (1 + percent increase as decimal)
Finding new value after decrease: Original × (1 - percent decrease as decimal)
Successive percentage changes: Apply each change step by step, not all at once
Original value from final value: Final Value ÷ (1 ± percent change as decimal)
📐 KEY FORMULA: Percent Change = ((New - Original) / Original) × 100
💡 PRO TIP: When dealing with successive percentage changes, never add or subtract the percentages directly — calculate each step separately.
How to Solve Percentages Increase and Decrease on the SAT
Example Question 1 — Medium Difficulty
A store increases the price of a jacket from $80 to $92. What is the percent increase in the price?
A) 12%
B) 13%
C) 15%
D) 18%
Solution:
Step 1: Identify the original value ($80) and new value ($92)
Step 2: Apply the percent increase formula: ((92 - 80) / 80) × 100
Step 3: Calculate: (12 / 80) × 100 = 0.15 × 100 = 15%
✅Answer: C — The price increased by 15% from the original value.
Example Question 2 — Hard Difficulty
The population of a town decreased by 20% in the first year and then increased by 25% in the second year. If the final population is 15,000, what was the original population?
A) 12,500
B) 15,000
C) 18,750
D) 20,000
Solution:
Step 1: Set up the equation with original population as x
Step 2: After 20% decrease: x × 0.8, then after 25% increase: x × 0.8 × 1.25
Step 3: Solve: x × 0.8 × 1.25 = 15,000, so x × 1.0 = 15,000, therefore x = 15,000
Wait, let me recalculate: x × 0.8 × 1.25 = x × 1.0 = 15,000, so the original population was 15,000.
✅Answer: B — After a 20% decrease followed by a 25% increase, the population returns to its original value.
Common SAT Math Mistakes to Avoid
❌Mistake: Adding successive percentage changes directly (20% decrease + 25% increase = 5% net increase)
✅Fix: Apply each percentage change step by step to the actual values
❌Mistake: Using the wrong base when calculating percentage change
✅Fix: Always use the original value as the denominator, not the new value
❌Mistake: Forgetting to convert percentages to decimals in calculations
✅Fix: Remember that 25% = 0.25, and 25% increase means multiply by 1.25
❌Mistake: Mixing up increase and decrease formulas
✅Fix: For increases, multiply by (1 + rate); for decreases, multiply by (1 - rate)
Practice Question — Try It Yourself
A laptop originally costs $800. After a 15% discount, the price is further reduced by 10%. What is the final price of the laptop?
A) $612
B) $680
C) $720
D) $760
Show Answer
Answer: A — First discount: $800 × 0.85 = $680, then second discount: $680 × 0.90 = $612
Key Takeaways for the SAT
Always identify whether you're calculating the percentage change or finding a new value after a known change
Use the original value as your base when calculating percentage increases or decreases
For successive changes, apply each percentage change one at a time to avoid errors
Convert percentages to decimals before multiplying: add 1 for increases, subtract from 1 for decreases
Double-check your work by verifying that your percentage change makes sense with the given values
Related SAT Math Topics
Strengthen your SAT math prep with these related topics:
Ratios proportions rates →
Data interpretation statistics →