Working With Percent Change
Percent change questions appear in almost every numerical reasoning test. Here's how to calculate them correctly and avoid common mistakes.
The Basic Formula
Percent change = ((New − Old) ÷ Old) × 100
- Positive result = increase
- Negative result = decrease
- Always use the original (old) value as the denominator, not the new one
Common Mistakes
Wrong base – Using the new value as denominator. If revenue goes from 100 to 150, the increase is (150 − 100) ÷ 100 = 50%, not (150 − 100) ÷ 150 ≈ 33%.
Percentage points vs percent – "Increased by 5 percentage points" means the value went from e.g. 20% to 25%. "Increased by 5%" means 20% × 1.05 = 21%. Don't confuse them.
Reversing old and new – For a decrease, you still use (New − Old) ÷ Old. The result will be negative. E.g. 80 to 60: (60 − 80) ÷ 80 = −25%.
Reverse Calculations
If you know the percent change and the new value, find the old value:
Old = New ÷ (1 + percent change as decimal)
Example: After a 20% increase, revenue is 120. Old = 120 ÷ 1.20 = 100.
For a decrease: Old = New ÷ (1 − percent change as decimal). E.g. After 25% decrease, value is 75. Old = 75 ÷ 0.75 = 100.
Compound Growth
When growth happens over multiple periods, don't add the percentages. Example: 10% growth in Year 1, then 10% in Year 2. Total growth is not 20%. It's (1.10 × 1.10) − 1 = 21%.
Practice with numerical reasoning questions and the numerical reasoning test.
Frequently Asked Questions
What if the old value is zero?
Percent change is undefined when the base is zero. In practice, tests usually avoid this. If you see it, the question may ask for something else (e.g. absolute change).
How do I calculate percent change when there are multiple values?
Identify which is the "before" and "after" for the specific question. Sometimes you need to sum categories first, then calculate.
What's the difference between "of" and "more than"?
"50% of 100" = 50. "50% more than 100" = 100 + 50 = 150. "50% less than 100" = 100 − 50 = 50.