If a price increases by 20% and then decreases by 20% of the new amount, is it back to the original price?

• A. Yes
• B. It depends
• C. Not enough information
• D. No

Answer: (D)

When a price changes by a percent, you scale it by the factor 1 plus that percent. So a 20% increase makes the price 1.20 times the original. If you then decrease by 20% of that new amount, you multiply by 0.80 (because you’re taking 20% off the boosted price). The overall effect is 1.20 × 0.80 = 0.96 of the original price. So the final price is 96% of what you started with—4% lower, not the original amount. The reason is that the second change is taken from the increased amount, not from the original price, so the changes don’t cancel each other out.