A store raises the price of a jacket by 20%, then discounts the new price by 20%. The final price is what percent of the original price?
- A100%
- B98%
- C96%
- D104%
- E102%
Successive percent changes do not cancel out
Try it before you scroll. Two minutes on the clock, then commit to an answer.
Correct answer: C
The trap is assuming that +20% and −20% cancel. They do not, because the two percentages apply to different bases.
Let the original price be 100. After the 20% raise, the price is 100 × 1.20 = 120. The discount then takes 20% off 120, not off 100: 120 × 0.80 = 96.
So the final price is 96% of the original, a net decrease of 4%.
A quick rule worth memorizing: a raise of p% followed by a cut of p% always nets to a loss of p²/100 percent. Here 20²/100 = 4%.
- (A) is the intuitive but wrong “they cancel” answer.
- (B) and (E) come from arithmetic slips on the second step.
- (D) treats both percentages as applying to the original price with the raise counted twice.