What is the percent change when the value changes from 42 to 56?

• A. 23%
• B. 33%
• C. 41%
• D. 26%

Answer: (B)

Percent change compares how much something has increased or decreased relative to where it started. You take the difference between the new value and the original value, divide by the original value, and multiply by 100.

From 42 to 56, the change is 56 − 42 = 14. The 14 increase is one third of 42, since 42 ÷ 3 = 14. One third as a percent is 33.3%, which we typically round to 33 percent. So the percent change is about 33 percent.

Why this makes sense: you're measuring how big the change is in relation to the starting amount, and the change you added (14) is exactly one third of the starting value (42), which corresponds to a 33% increase.