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Percent Increase & Decrease - Accuplacer Arithmetic

  1. A manager's annual bonus of $1,850 is increased by 8%. What is the new bonus amount?
    Answer: $1,998 First, calculate the amount of the increase: 8% of $1,850 is 0.08 1850 = $148. Then, add this to the original bonus: $1,850 + $148 = $1,998. Alternatively, an 8% increase means the new amount is 108% of the original: $1,850 1.08 = $1,998.
  2. The length of each side of a square is increased by 20%. By what percentage does the area of the square increase?
    Answer: 44% Let the original side length be s. The original area is s². The new side length is s * (1 + 0.20) = 1.2s. The new area is (1.2s)² = 1.44s². The new area is 1.44 times the original area, which means it is 144% of the original. The increase is 144% - 100% = 44%.
  3. The total price of a meal, including a 15% tip, was $51.75. What was the price of the meal before the tip was added?
    Answer: $45.00 The total price ($51.75) is the original price plus 15% of the original price, which is 115% of the original price. Let P be the original price. Then 1.15 * P = $51.75. To find P, divide $51.75 by 1.15, which equals $45.00.
  4. This year, the population of a town is 8,250. This represents a 10% increase from last year. What was the population of the town last year?
    Answer: 7,500 This year's population (8,250) is 100% + 10% = 110% of last year's population. Let P be last year's population. Then 1.10 * P = 8,250. To find P, divide 8,250 by 1.10, which equals 7,500.
  5. A salesperson's commission rate increased from 5% to 6%. By what percentage did the commission rate itself increase?
    Answer: 20% The question asks for the percent increase of the rate, not the simple difference. The amount of increase is 6% - 5% = 1%. The original rate was 5%. The percent increase is (Amount of Increase / Original Amount) 100 = (1% / 5%) 100 = 0.20 * 100 = 20%.
  6. What is the result when the number 350 is decreased by 14%?
    Answer: 301 First, find the amount of the decrease: 14% of 350 is 0.14 350 = 49. Then, subtract this amount from the original number: 350 - 49 = 301. Alternatively, decreasing by 14% means finding 100% - 14% = 86% of the number: 350 0.86 = 301.
  7. A rectangular garden is 10 meters long and 8 meters wide. If its length is increased by 20% and its width is decreased by 10%, what is the percent change in the area of the garden?
    Answer: An 8% increase Original area = 10m 8m = 80 m². New length = 10 (1 + 0.20) = 12m. New width = 8 (1 - 0.10) = 7.2m. New area = 12m 7.2m = 86.4 m². The change in area is 86.4 - 80 = 6.4 m². The percent change is (change / original) 100 = (6.4 / 80) 100 = 0.08 * 100 = 8% increase.
  8. A factory's daily production decreased from 1,500 units to 1,200 units. What was the percent decrease in production?
    Answer: 20% The amount of decrease is 1,500 - 1,200 = 300 units. To find the percent decrease, divide the amount of decrease by the original production level and multiply by 100: (300 / 1,500) 100 = 0.20 100 = 20%.
  9. An investment's value changed by -8%, +12%, and -5% over three consecutive months. If the final value was $1,848, what was the percent change from the original investment amount?
    Answer: 2.4% decrease When you encounter consecutive percentage changes, remember that they compound—each percentage is applied to the result of the previous change, not the original amount. Let's work backward from the final value of $1,848. If we call the original investment xx, then after three months: x×(1−0.08)×(1+0.12)×(1−0.05)=1,848x \times (1 - 0.08) \times (1 + 0.12) \times (1 - 0.05) = 1,848 Calculate the combined multiplier: (0.92)×(1.12)×(0.95)=0.976(0.92) \times (1.12) \times (0.95) = 0.976 So: x×0.976=1,848x \times 0.976 = 1,848 Therefore: x=1,8480.976=1,893.44x = \frac{1,848}{0.976} = 1,893.44 The percent change from original to final is: 1,848−1,893.441,893.44×100%=−2.4%\frac{1,848 - 1,893.44}{1,893.44} \times 100\% = -2.4\% This confirms answer D: 2.4% decrease. Answer A (1% decrease) likely comes from incorrectly adding the percentages: -8% + 12% - 5% = -1%. However, this ignores the compounding effect. Answer B (3% decrease) might result from calculation errors when working with the decimal multipliers or rounding mistakes. Answer C (1% increase) could stem from the same addition error as A but with a sign mistake, possibly thinking that since there was a +12% gain, the overall result should be positive. Remember: percentage changes always compound in sequence. Never simply add or subtract the individual percentages. Instead, multiply the factors (1 ± percentage as a decimal) to find the overall effect, then calculate the total percentage change from the original amount.
  10. A jacket priced at $120 is first increased in price by 25%. After the increase, the new price is decreased by 25%. What is the final price of the jacket?
    Answer: $112.50 First, calculate the price increase: $120 0.25 = $30. The new price is $120 + $30 = $150. Next, calculate the decrease based on the new price: $150 0.25 = $37.50. The final price is $150 - $37.50 = $112.50.
  11. Maria's salary increased from $45,000 to $48,600. Her colleague Tom's salary increased from $52,000 to $54,600. Who had the greater percent increase, and by how much?
    Answer: Maria by 3 percentage points Maria's increase: ($48,600 - $45,000) ÷ $45,000 × 100% = 8%. Tom's increase: ($54,600 - $52,000) ÷ $52,000 × 100% = 5%. Maria had 3 percentage points more (8% - 5% = 3 percentage points). Choice B reverses who had the greater increase. Choices C and D confuse percentage points with relative percent differences.
  12. A store marks up a product by 60% above its cost, then offers a 30% discount from the marked price during a sale. If the store's cost for the item is $50, what is the percent increase from cost to the final sale price?
    Answer: 12% increase Marked price: $50 × 1.60 = $80. Sale price: $80 × 0.70 = $56. Percent increase from cost: ($56 - $50) ÷ $50 × 100% = 12% increase. Choice A incorrectly subtracts the percentages (60% - 30% = 30%). Choice C uses an incorrect calculation. Choice D represents a common computational error.
  13. Last year, a business had revenues of $80,000 and costs of $60,000. This year, its revenues increased by 10% and its costs increased by 5%. What was the percent increase in its profit?
    Answer: 25% First, find last year's profit: $80,000 - $60,000 = $20,000. Next, find this year's revenue: $80,000 1.10 = $88,000. Find this year's costs: $60,000 1.05 = $63,000. This year's profit is $88,000 - $63,000 = $25,000. The profit increased by $5,000. The percent increase is ($5,000 / $20,000) * 100 = 25%.
  14. A retailer increases prices by 25% at the beginning of the year, then decreases them by 20% during a mid-year sale. At year-end, prices are increased again by 10%. What is the overall percent change in prices from the beginning to the end of the year?
    Answer: 10% increase When you encounter questions involving multiple percentage changes, the key is to apply each change sequentially to the result of the previous change, not to the original value. Let's start with an original price of $100 to make calculations clear. First, prices increase by 25%: 100×1.25=125100 × 1.25 = 125. Next, they decrease by 20%: 125×0.80=100125 × 0.80 = 100. Finally, they increase by 10%: 100×1.10=110100 × 1.10 = 110. The final price is $110, which represents a 10% increase from the original $100. Choice A (15% increase) is what you'd get if you simply added and subtracted the percentages: +25% - 20% + 10% = +15%. This ignores the compounding effect of applying percentages to changing values rather than the original base. Choice B (8% increase) might result from incorrectly calculating the 20% decrease. If you applied 20% to the original $100 instead of to the increased price of $125, you'd get different intermediate results leading to this wrong answer. Choice C (12% increase) could come from computational errors in the sequential multiplication, possibly mixing up which percentage applies to which intermediate value. Choice D (10% increase) is correct because following the sequential changes: 100×1.25×0.80×1.10=110100 × 1.25 × 0.80 × 1.10 = 110. Study tip: For multiple percentage changes, always multiply the decimal forms sequentially (1.25 × 0.80 × 1.10), and remember that percentage changes compound—they don't simply add or subtract.
  15. A library had 800 books. It increased its collection by 25%. One year later, it removed 25% of its entire new collection. How many books did the library have after the removal?
    Answer: 750 First, calculate the increase: 25% of 800 is 0.25 800 = 200. The new collection size is 800 + 200 = 1,000 books. Next, calculate the removal based on the new total: 25% of 1,000 is 0.25 1000 = 250. The final number of books is 1,000 - 250 = 750.
  16. After a 20% discount, the price of a television is $360. What was the original price of the television?
    Answer: $450.00 The discounted price ($360) represents 100% - 20% = 80% of the original price. Let P be the original price. Then 0.80 * P = $360. To find P, divide $360 by 0.80, which equals $450.
  17. A car that cost $25,000 decreased in value by 12% in its first year. What was the value of the car after the first year?
    Answer: $22,000 To find the decrease in value, calculate 12% of $25,000: 0.12 25000 = $3,000. Subtract this from the original cost: $25,000 - $3,000 = $22,000. Alternatively, if the value decreased by 12%, it retained 100% - 12% = 88% of its value: $25,000 0.88 = $22,000.
  18. A restaurant's dinner sales increased from $2,400 in January to $2,880 in February. In March, the sales decreased by 15% from February's amount. What was the percent change in dinner sales from January to March?
    Answer: 2% increase First, find March sales: February sales decreased by 15%, so March = $2,880 × 0.85 = $2,448. Then calculate percent change from January to March: ($2,448 - $2,400) ÷ $2,400 × 100% = $48 ÷ $2,400 × 100% = 2% increase. Choice A uses the dollar change ($48) but calculates the percent incorrectly. Choice B incorrectly treats the overall change as a decrease. Choice D uses only the February increase percentage without considering March.
  19. A car's value depreciates by 18% in the first year and 12% in the second year. In the third year, the value increases by 8% due to it becoming a collector's item. If the car's value after three years is $23,616, what was the original purchase price?
    Answer: $30,000 Combined multiplier: 0.82 × 0.88 × 1.08 = 0.7872. Original price = $23,616 ÷ 0.7872 = $30,000. The other choices represent common errors in working backward through percentage changes or incorrect calculations of the combined multiplier.
  20. An electronics store reduced the price of a computer by 15%. If the new price is $1,020, what was the original price?
    Answer: $1,200 The new price of $1,020 represents 100% - 15% = 85% of the original price. Let P be the original price. The equation is 0.85 * P = $1,020. To find the original price, divide $1,020 by 0.85. P = 1020 / 0.85 = $1,200.

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