GMAT Focus EditionQuantitative ReasoningMedium
A store offers a 20% discount on all items. If a customer uses a coupon for an additional 10% off the discounted price, what is the total effective discount percentage?
- A28%
- B30%
- C35%
- D32%
Show answer & explanationAnswer & explanation
Correct answer: A. 28%
This is a successive percentage change problem. Assume an original price of $100. First discount: $100 * (1 - 0.20) = $80. Second discount on the new price: $80 * (1 - 0.10) = $72. The final price is $72, so the total discount is $100 - $72 = $28. As a percentage, this is 28/100 = 28%.
Why the other options are wrong
- B. This is a common error of simply adding the percentages (20% + 10% = 30%), which is incorrect for successive discounts.
- C. This is an unlikely result from standard successive discount calculations.
- D. This might result from an incorrect calculation or a misunderstanding of the base for the second discount.
Successive Percentage Change
Successive percentage changes are applied one after another, with each subsequent change based on the new, adjusted value.
- Changes are multiplicative, not additive.
- Order of application does not affect the final result.
- To find the final value, multiply the original value by (1 +/- %change1) * (1 +/- %change2) etc.
Memory trick: Each discount takes a bite from what's left, not the original pie.