ACCUPLACER Arithmetic Quiz: Percent Increase And Decrease
20 questions · exam conditions
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Percent Increase And DecreaseQuestion 1 of 20

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?

1% decrease
3% decrease
1% increase
2.4% decrease
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ACCUPLACER Arithmetic Quiz

ACCUPLACER Arithmetic Quiz: Percent Increase And Decrease

Practice Percent Increase And Decrease in ACCUPLACER Arithmetic with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.

What this quiz covers

This quiz focuses on Percent Increase And Decrease, giving you a quick way to practice the rules, question types, and explanations that matter most for ACCUPLACER Arithmetic.

How to use this quiz

Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

All questions

Question 1

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?

  1. 1% decrease
  2. 3% decrease
  3. 1% increase
  4. 2.4% decrease (correct answer)
Explanation: 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 ,thenafterthreemonths:, 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) \times (1.12) \times (0.95) = 0.976 So: x \times 0.976 = 1,848 Therefore: x = \frac{1,848}{0.976} = 1,893.44 The percent change from original to final is: \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.

Question 2

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?

  1. Maria by 3 percentage points (correct answer)
  2. Tom by 1 percentage point
  3. Maria by 3% more than Tom's increase
  4. Tom by 1% more than Maria's increase
Explanation: Maria's increase: ($48,600 - $45,000) ÷ 45,000×10045,000 × 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.

Question 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?

  1. $43.99
  2. $45.00 (correct answer)
  3. $46.75
  4. $59.51
Explanation: 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.

Question 4

After a 20% discount, the price of a television is $360. What was the original price of the television?

  1. $300.00
  2. $420.00
  3. $432.00
  4. $450.00 (correct answer)
Explanation: 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.

Question 5

Last week, a share of stock was worth $40. This week, it is worth $45. What was the percent increase in the price of the stock?

  1. 5.0%
  2. 11.1%
  3. 12.5% (correct answer)
  4. 88.9%
Explanation: The amount of increase is $45 - $40 = 5.Tofindthepercentincrease,dividetheamountofincreasebytheoriginalpriceandmultiplyby100:(5. To find the percent increase, divide the amount of increase by the original price and multiply by 100: (5 / $40) * 100 = 0.125 * 100 = 12.5%.

Question 6

What is the result when the number 350 is decreased by 14%?

  1. 49
  2. 301 (correct answer)
  3. 336
  4. 399
Explanation: 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.

Question 7

A manager's annual bonus of $1,850 is increased by 8%. What is the new bonus amount?

  1. $1,702
  2. $1,858
  3. $1,998 (correct answer)
  4. $2,000
Explanation: 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.

Question 8

Due to a successful marketing campaign, a company's customer base grew from 2,400 to 3,000. What was the percent increase in the customer base?

  1. 20%
  2. 25% (correct answer)
  3. 60%
  4. 80%
Explanation: First, find the amount of the increase: 3,000 - 2,400 = 600 customers. Next, divide the increase by the original number of customers: 600 / 2,400 = 0.25. Finally, convert the decimal to a percentage: 0.25 * 100 = 25%.

Question 9

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?

  1. An 8% increase (correct answer)
  2. A 10% increase
  3. A 10% decrease
  4. A 12% increase
Explanation: 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.

Question 10

A salesperson's commission rate increased from 5% to 6%. By what percentage did the commission rate itself increase?

  1. 1%
  2. 1.2%
  3. 11%
  4. 20% (correct answer)
Explanation: 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%.

Question 11

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?

  1. $90.00
  2. $112.50 (correct answer)
  3. $120.00
  4. $150.00
Explanation: 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.

Question 12

The value of a stock decreased by 25% on Monday, then increased by 40% on Tuesday. If the stock was worth $80 at the start of Monday, what was the percent change from the original value to the end of Tuesday?

  1. 15% increase
  2. 5% increase (correct answer)
  3. 5% decrease
  4. 10% increase
Explanation: Monday: $80 × 0.75 = $60. Tuesday: $60 × 1.40 = 84.Percentchangefromoriginal:(84. Percent change from original: (84 - $80) ÷ $80 × 100% = 5% increase. Choice A incorrectly adds the percentages (40% - 25% = 15%). Choice C treats the result as a decrease. Choice D uses an incorrect calculation method.

Question 13

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?

  1. 30% increase
  2. 12% increase (correct answer)
  3. 18% increase
  4. 22% increase
Explanation: Marked price: $50 × 1.60 = $80. Sale price: $80 × 0.70 = 56.Percentincreasefromcost:(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.

Question 14

The population of a town increased by 20% in the first year and decreased by 16% in the second year. If the original population was 15,000, by what percent did the population change over the two-year period?

  1. 4% increase
  2. 0.8% increase (correct answer)
  3. 3.2% decrease
  4. 0.8% decrease
Explanation: After first year: 15,000 × 1.20 = 18,000. After second year: 18,000 × 0.84 = 15,120. Percent change: (15,120 - 15,000) ÷ 15,000 × 100% = 0.8% increase. Choice A incorrectly subtracts percentages (20% - 16% = 4%). Choice C uses incorrect calculation. Choice D treats the result as a decrease.

Question 15

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?

  1. 15% increase
  2. 8% increase
  3. 12% increase
  4. 10% increase (correct answer)
Explanation: 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,theydecreaseby20. Next, they decrease by 20%: 125×0.80=100125 × 0.80 = 100 .Finally,theyincreaseby10. 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: $$100 × 1.25 × 0.80 × 1.10 = 110$$. 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.

Question 16

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?

  1. 2.5% increase
  2. 5% decrease
  3. 2% increase (correct answer)
  4. 5% increase
Explanation: First, find March sales: February sales decreased by 15%, so March = $2,880 × 0.85 = 2,448.ThencalculatepercentchangefromJanuarytoMarch:(2,448. Then calculate percent change from January to March: (2,448 - $2,400) ÷ $2,400 × 100% = $48 ÷ 2,400×1002,400 × 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.

Question 17

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?

  1. $28,500
  2. $32,000
  3. $30,000 (correct answer)
  4. $29,200
Explanation: 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.

Question 18

The number of students in a school decreased by 15% from 2020 to 2021, then increased by 25% from 2021 to 2022. If there were 1,020 students in 2022, how many more students were there in 2022 compared to 2020, expressed as a percent increase from 2020?

  1. 6.25% increase (correct answer)
  2. 10% increase
  3. 8.5% increase
  4. 4.25% increase
Explanation: Working backward: 2021 students = 1,020 ÷ 1.25 = 816. 2020 students = 816 ÷ 0.85 = 960. Percent change from 2020 to 2022: (1,020 - 960) ÷ 960 × 100% = 6.25% increase. Choice B incorrectly adds percentages (-15% + 25% = 10%). Choice C and D represent common calculation errors.

Question 19

The length of each side of a square is increased by 20%. By what percentage does the area of the square increase?

  1. 20%
  2. 40%
  3. 44% (correct answer)
  4. 144%
Explanation: 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%.

Question 20

An item priced at $200 is first discounted by 10%, and then an additional 15% discount is applied to the sale price. What is the final price of the item?

  1. $150.00
  2. $153.00 (correct answer)
  3. $155.00
  4. $175.00
Explanation: First, calculate the 10% discount: $200 * 0.10 = $20. The first sale price is $200 - $20 = $180. Next, calculate the 15% discount on the new price: $180 * 0.15 = $27. The final price is $180 - $27 = $153.