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Percent Change and Growth - Quantitative Reasoning

  1. Two stores each reduce the price of the same item by $15. In Store X, the original price was $60; in Store Y, the original price was $75. The percent decrease is based on each store's original price. In which store is the percent decrease greater?
    Answer: Store X This question tests comparing percent decreases across different bases for the same absolute discount. Percent decrease is defined as the decrease divided by each store's original base price, multiplied by 100%. For Store X: $15 / $60 × 100% = 25%. For Store Y: $15 / $75 × 100% = 20%. The greater percent decrease is in Store X because of its smaller base. A common mistake assumes equal percentages due to same absolute decrease, ignoring base differences. Another error might claim indeterminacy without calculating.
  2. A tank contains 90 liters of fuel. After refueling, the amount of fuel increases by 20% from the original amount. Then, 15 liters are used. How many liters of fuel remain?
    Answer: 93 This question tests percent increase followed by a fixed decrease in fuel amount. Percent increase is defined relative to the original base, as (increase / original) × 100%. Fuel increases by 20% from 90 liters to 90 × 1.20 = 108 liters. Then 15 liters are used, leaving 108 - 15 = 93 liters. This is correct as it applies the percentage first, then subtracts absolutely. A common mistake like 105 adds 20% after subtracting 15. Another error, such as 108, omits the usage step.
  3. An investor buys a stock for $100 per share. The price increases by 30% and then decreases by 20%, each time relative to the most recent price. What is the final price per share?
    Answer: $104 This question tests percent change with successive increase and decrease in stock price. Percent change is defined relative to the current base price at each step, as (change / base) × 100%. From $100, a 30% increase gives $100 × 1.30 = $130. Then a 20% decrease from $130 gives $130 × 0.80 = $104. This final price is correct because each percentage uses the updated base. A common mistake like $100 assumes the changes cancel, ignoring base differences. Another error, such as $120, might apply both to the original base.
  4. A printer cartridge originally prints 600 pages. After a redesign, it prints 660 pages. The percent increase is based on the original 600-page capacity. What is the percent increase?
    Answer: 10% This question tests percent increase in printer cartridge capacity. Percent increase is defined as the increase divided by the original base capacity, multiplied by 100%. The increase from 600 to 660 is 60 pages, so (60 / 600) × 100% = 10%. This is correct because it uses the original capacity as the base. The calculation justifies the relative improvement accurately. A common mistake like 11% uses the new capacity as base (60 / 660 ≈ 9.09%, rounded wrong). Another error, such as 9%, miscalculates 60/660 directly without multiplying by 100%.
  5. A car was listed at $18,000. The dealer offered a discount of 15% from the listed price. What is the sale price of the car?
    Answer: $15,300 This question tests percent change, specifically a percent discount on a car's listed price. Percent change is defined as the change divided by the original base price, multiplied by 100%. The discount is 15% of the $18,000 listed price, so the discount amount is 0.15 × 18,000 = $2,700. The sale price is then $18,000 - $2,700 = $15,300. This result is correct because the percentage is applied directly to the original price as stated. A common mistake like $16,200 assumes a 10% discount instead of 15%. Another error, such as $20,700, might add the discount instead of subtracting it.
  6. A town had a population of 12,000. Over one year, the population increased by 10% from the original population. By what percent did the population then need to decrease (from the new population) to return to 12,000?
    Answer: 1011\frac{10}{11}% (about 9.09%) This question tests percent change, specifically the percent decrease needed to reverse a prior percent increase in population. Percent change is defined relative to the base value before the change, as (change / base) × 100%. The population increases by 10% from 12,000 to 13,200. To return to 12,000, the decrease is 1,200 from the new base of 13,200, so the percent decrease is (1,200 / 13,200) × 100% ≈ 9.09%, or exactly 100/11%. This is correct because the decrease percentage uses the increased population as its base. A common incorrect choice like 10% fails by assuming symmetric percentages, ignoring that the base for decrease is larger. Another error, such as 11%, might reverse the fraction incorrectly.
  7. A store has 200 jackets in stock. After a sale, the stock decreases by 15%15\%, and then the store receives a new shipment that increases the remaining stock by 20%20\%. What is the final number of jackets in stock?
    Answer: 204 This question tests percent change applied in two successive steps. Percent change is calculated as (change/original) × 100%, where the base changes with each step. First, a 15% decrease from 200 jackets gives us 200 - 0.15(200) = 200 - 30 = 170 jackets. Then, a 20% increase from this new base of 170 gives us 170 + 0.20(170) = 170 + 34 = 204 jackets. The final stock is 204 jackets. A common error would be to apply both percentages to the original 200, but percent changes must be applied sequentially with updated bases.
  8. A recipe originally calls for 300 grams of flour. The recipe is adjusted so that the amount of flour is decreased by 20%20\%. What is the new amount of flour?
    Answer: 240 grams This question tests calculating a new amount after a percent decrease. Percent decrease is calculated by multiplying the original amount by (1 - percent decrease). The original amount is 300 grams, and we need to decrease it by 20%. The new amount is 300 - 0.20(300) = 300 - 60 = 240 grams. Alternatively, we can calculate 80% of 300: 0.80(300) = 240 grams. The answer is 240 grams. A common error might be subtracting 20 grams instead of 20% of 300 grams.
  9. A company's revenue was $500,000 last year. This year, revenue increased by 20% from last year's revenue and then decreased by 10% from the increased amount. What is the company's revenue this year?
    Answer: $540,000 This question tests compound percent change, where multiple percent changes are applied sequentially. When calculating percent change, each percentage is based on the value at that stage, not the original. First, revenue increases by 20% from $500,000: $500,000 × 1.20 = $600,000. Then it decreases by 10% from this new amount: $600,000 × 0.90 = $540,000. The final revenue is $540,000. A common mistake is to combine the percentages incorrectly, such as thinking +20% - 10% = +10% overall, which would incorrectly yield $550,000.
  10. A membership fee is currently $72 after a 20% increase from last year's fee. What was last year's membership fee?
    Answer: $60 This question tests working backwards from a percent increase to find the original value. If the current fee is the result of a 20% increase, then the current fee represents 120% of last year's fee. Setting up the equation: 1.20 × (last year's fee) = $72. Solving: last year's fee = $72 ÷ 1.20 = $60. The answer is $60. A common mistake is to calculate 20% of $72 and subtract it, which would give $57.60, but this incorrectly uses the new value as the base for the percentage.
  11. A bookstore sold 120 copies of a novel in January. In February, it sold 30% fewer copies than in January. In March, it sold 25% more copies than in February. How many copies did the bookstore sell in March?
    Answer: 105 This question tests multiple sequential percent changes with different bases. Each percent change uses the previous month's value as its base. January sales: 120 copies. February sales are 30% fewer: 120 × 0.70 = 84 copies. March sales are 25% more than February: 84 × 1.25 = 105 copies. The bookstore sold 105 copies in March. A common mistake is to apply both percentages to the January amount or to incorrectly combine the percentages.
  12. A company's monthly website visits were 50,000 in January. In February, visits increased by 20% from January, and in March, visits decreased by 25% from February. What were the website visits in March?
    Answer: 45,000 This question tests percent change and growth over multiple periods for website visits. Percent change is defined relative to the base value at the start of each period, calculated as (change / base) × 100%. In February, visits increase by 20% from January's 50,000, resulting in 50,000 × 1.20 = 60,000. In March, visits decrease by 25% from February's 60,000, yielding 60,000 × 0.75 = 45,000. This is the correct final amount because each percentage is applied sequentially to the updated base. A common mistake like 50,000 assumes no net change, ignoring that a 25% decrease on a larger base is not offset by the prior 20% increase. Another error, such as 47,500, might arise from averaging the percentages incorrectly.
  13. A bookstore had 150 copies of a novel. It sold 40% of the copies, based on the original number of copies. How many copies remain?
    Answer: 90 This question tests percent decrease in the number of book copies after sales. Percent change is defined as the sold amount divided by the original base number, multiplied by 100%. Sold is 40% of 150, so 0.40 × 150 = 60 copies sold. Remaining copies are 150 - 60 = 90. This is correct because it applies the percentage to the original stock. A common mistake like 60 confuses sold with remaining. Another error, such as 110, might subtract 27% instead of 40%.
  14. A store sold a jacket for an original price of $80. During a sale, the store decreased the price by 25%25\% from the original price. What was the sale price of the jacket?
    Answer: $60 This question tests percent change, specifically calculating a discounted price after a percentage decrease. Percent change is always calculated relative to the original or base value, which here is the original price of $80. To find the sale price after a 25% decrease, we calculate 25% of $80, which equals 0.25 × $80 = $20. Since this is a decrease, we subtract this amount from the original price: $80 - $20 = $60. Therefore, the sale price of the jacket is $60. A common error would be to calculate 25% of some other value or to add instead of subtract the discount amount.
  15. Town A had a population of 40,000. Town B had a population of 50,000. Each town's population increased by 10% from its own original population. The increase in Town A's population is what percent of the increase in Town B's population?
    Answer: 80% This question tests comparing percent changes between different base values. Percent change is calculated relative to each town's original population. Town A increases by 10% of 40,000 = 4,000 people, while Town B increases by 10% of 50,000 = 5,000 people. The question asks what percent Town A's increase (4,000) is of Town B's increase (5,000): (4,000 ÷ 5,000) × 100% = 80%. The answer is 80%. A common mistake is to compare the populations themselves rather than the increases.
  16. A product's price increased from $40 to $50. The percent increase is based on the original price of $40. By what percent did the price increase?
    Answer: 25%25\% This question tests the calculation of percent increase using the correct base value. Percent increase is defined as the change in value divided by the original value, multiplied by 100%. The change in price is $50 - $40 = $10, and the original price (the base) is $40. Therefore, the percent increase is ($10/$40) × 100% = 0.25 × 100% = 25%. The price increased by 25%. A common error is using the new price ($50) as the base instead of the original price ($40), which would incorrectly give 20%.
  17. A company's monthly rent was originally $2,000\$2{,}000. The rent is increased by 10%10\% for one year and then decreased by 10%10\% the next year. What is the rent after the two changes?
    Answer: $1,980\$1{,}980 This question tests successive percent changes where increases and decreases of the same percentage don't cancel out. Percent change uses the current value as the base for each calculation. Starting with $2,000, a 10% increase gives us $2,000 + 0.10($2,000) = $2,200. Then a 10% decrease from this new base gives us $2,200 - 0.10($2,200) = $2,200 - $220 = $1,980. The final rent is $1,980, which is less than the original $2,000. The key insight is that a 10% decrease from a larger amount ($2,200) removes more dollars than a 10% increase from the original amount ($2,000) added.
  18. A bookstore sold 120 copies of a novel in January. In February, it sold 150 copies. The percent increase is based on the January sales of 120 copies. Which of the following represents the percent increase from January to February?
    Answer: 30120×100%\dfrac{30}{120}\times 100\% This question tests identifying the correct formula for percent increase. Percent increase is calculated as (new value - old value) / old value × 100%, where the old value serves as the base. The bookstore sold 120 copies in January (the base) and 150 copies in February. The increase is 150 - 120 = 30 copies. Therefore, the percent increase is 30/120 × 100%, which matches option C. This represents a 25% increase in sales. Option A incorrectly uses 150 as the base, while options B and D represent different calculations that don't match the percent increase formula.
  19. A recipe calls for 200 grams of flour. A baker increases the amount of flour by 15% based on the original amount. What is the new amount of flour used?
    Answer: 230 grams This question tests percent increase in the amount of flour for a recipe. Percent increase is defined as the increase divided by the original base amount, multiplied by 100%. The increase is 15% of 200 grams, so 0.15 × 200 = 30 grams added. The new amount is 200 + 30 = 230 grams. This is correct because the percentage is applied to the original as specified. A common incorrect choice like 215 adds only 7.5% mistakenly. Another error, such as 200, ignores the increase entirely.
  20. A laptop is listed at $800. A coupon reduces the listed price by 25%25\%, and then a sales tax of 8%8\% is applied to the discounted price. What is the final price of the laptop?
    Answer: $648 This question tests applying a percent discount followed by a percent tax, with each percentage based on different values. Percent change calculations must use the appropriate base value for each step. The 25% discount on $800 gives us $800 - 0.25($800) = $800 - $200 = $600. Then, 8% tax is applied to this discounted price: $600 + 0.08($600) = $600 + $48 = $648. The final price is $648. A common mistake is calculating the tax on the original $800 price rather than on the discounted $600 price.

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