SAT Math · Percentages · medium

A price is increased by 20% and then the new price is decreased by 25%. What is the overall percent change from the original price?

A price is increased by 20% and then the new price is decreased by 25%. What is the overall percent change from the original price?

Answer and explanation

Answer: B: A 10% decrease

Use multipliers. A 20% increase multiplies the price by 1.201.20, and a 25% decrease multiplies by 0.750.75. The overall multiplier is 1.20×0.75=0.901.20 \times 0.75 = 0.90, which is a 10% decrease, choice B. Try $100: it rises to $120, then falls by 25% of 120, which is $30, giving $90. Choice A (a 5% increase) comes from computing 20−25=−520 - 25 = -5 with a sign slip. Choice C (no change) assumes the percents cancel, but the 25% applies to a larger amount. Choice D (a 45% decrease) adds the percents, 20+2520 + 25. Successive percent changes multiply; they do not add.

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