📊 Percent Change — SAT Math Mastery
The complete guide to every percent change concept tested on the SAT
SAT Frequency: 3–5 questions per test · Appears in both Calculator & No-Calculator sections
1. What Is Percent Change?
Percent change measures how much a quantity increases or decreases relative to its original value, expressed as a percentage.
🔑 Master Formula
Percent Change = ((New Value − Original Value) / Original Value) · 100%
- If the result is positive → percent increase
- If the result is negative → percent decrease
📈 Percent Increase
((New − Original) / Original) · 100%
Example: Price goes from $80 to $100
= (100 − 80) / 80 · 100% = 25% increase
📉 Percent Decrease
((Original − New) / Original) · 100%
Example: Price goes from $100 to $80
= (100 − 80) / 100 · 100% = 20% decrease
⚠️ Critical SAT Insight: The Base Matters!
The same dollar change gives DIFFERENT percent changes depending on direction!
$80 → $100
25% increase
Base = 80
$100 → $80
20% decrease
Base = 100
Same $20 difference, but different percentages because the BASE (original value) is different!