- A car's value depreciates by 15% each year. After 3 years, the car is worth about $12,900. What was the original value of the car?
Answer: $21,000
Each year the car keeps 85% of its value, so after 3 years it is worth the original value times 0.853=0.614125.
Test the choices:
21,000×0.614125≈12,897, which is about $12,900.
$20,000×0.614125≈12,283$, too low.
22,000×0.614125≈13,511, too high.
24,000×0.614125≈14,739, much too high.
So the original value was $21,000.
A common mistake is to subtract 15% three times from the original amount, a total of 45%, which treats the depreciation as simple rather than compounding and points toward a larger original value such as $24,000. Working forward from each choice avoids that error. - A shirt originally costs $80. During a sale, it is marked down by 30%. After the sale, the discounted price is increased by what percent to return to the original price?
Answer: 42.86%
After a 30% markdown, the price becomes $80 × 0.70 = $56. To return to $80, we need to find what percent increase is required: ($80 - $56)/$56 = $24/$56 ≈ 0.4286 = 42.86%. Choice A assumes the same percentage that was decreased. Choice B is close but represents a common rounding error. Choice D comes from calculating 30/70 instead of 24/56.
- A stock price increases by 40% on Monday, decreases by 25% on Tuesday, and then increases by 10% on Wednesday. If the stock price at the end of Wednesday is $46.20, what was the stock price at the beginning of Monday?
Answer: $40.00
Let the original price be P. After Monday's 40% increase: 1.40P. After Tuesday's 25% decrease: 1.40P × 0.75 = 1.05P. After Wednesday's 10% increase: 1.05P × 1.10 = 1.155P. Since the final price is $46.20, we have 1.155P = 46.20, so P = 46.20 ÷ 1.155 = $40.00. Choice A results from incorrectly calculating the net effect as 1.54 instead of 1.155. Choice B comes from errors in the percentage calculations. Choice D results from not properly accounting for all three changes.
- After a 15\% price increase, a paperback novel costs $13.80. What was its price before the increase?
Answer: $12.00
A 15% increase makes the new price 115% of the original price. If p is the original price, then 1.15p = $13.80, so p = $13.80 ÷ 1.15 = $12.00.
Check: 15% of $12.00 is $1.80, and $12.00 + $1.80 = $13.80.
$12.50 is too high: 15% more than $12.50 is about $14.38. $13.00 is higher still and would become $14.95. $11.50 is too low; it would need a 20% increase to reach $13.80. Taking 15% off $13.80 gives about $11.73, which is also wrong, because the 15% increase was figured on the smaller original price, not on $13.80.
- A store marks up the wholesale price of an item by 60%. During a clearance sale, the store offers a 40% discount off the marked price. What is the percent change from the wholesale price to the final sale price?
Answer: 4% decrease
Let the wholesale price be W. After a 60% markup: 1.60W. After a 40% discount: 1.60W × 0.60 = 0.96W. The final price is 0.96W, which represents a 4% decrease from the original wholesale price W. Choice B incorrectly calculates the direction of change. Choice C results from subtracting percentages directly (60% - 40% = 20%) and assuming a decrease. Choice D makes the same error but assumes an increase.
- The price of a concert ticket increased by 20% from last year to this year. Next year, the organizers plan to decrease the price by 15% from this year's price. If next year's ticket price will be $61.20, what was last year's ticket price?
Answer: $60.00
Let last year's price be P. This year's price is 1.20P. Next year's price will be 1.20P × 0.85 = 1.02P. Since next year's price is $61.20, we have 1.02P = 61.20, so P = 61.20 ÷ 1.02 = $60.00. Choice B results from incorrectly calculating the net effect. Choice C comes from errors in the percentage calculations. Choice D results from not properly accounting for the compound effect of the changes.
- The population of a town decreased by 15% in the first year and then increased by 20% in the second year. If the population at the end of the second year was 40,800, what was the population at the beginning of the first year?
Answer: 40,000
Let the original population be P. After decreasing by 15%, the population becomes 0.85P. After increasing by 20%, it becomes 0.85P × 1.20 = 1.02P. Since the final population is 40,800, we have 1.02P = 40,800, so P = 40,800 ÷ 1.02 = 40,000. Choice A results from miscalculating the combined effect as 0.95 instead of 1.02. Choice C comes from incorrectly thinking the net effect is a 5% increase (20% - 15%). Choice D results from only considering one of the percentage changes.
