Pre-Algebra Quiz: Percent Increase Decrease
10 questions · exam conditions
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Percent Increase DecreaseQuestion 1 of 10

A clothing store has a '30% off everything' sale. During the sale, an item that originally cost $150 is marked down. The next week, the store raises all sale prices by 25%. What is the final price of this item?

The final price is exactly $131.25 for this item
The final price is exactly $140.63 for this item
The final price is exactly $143.75 for this item
The final price is exactly $150.00 for this item
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Pre-Algebra Quiz

Pre-Algebra Quiz: Percent Increase Decrease

Practice Percent Increase Decrease in Pre-Algebra 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 Decrease, giving you a quick way to practice the rules, question types, and explanations that matter most for Pre-Algebra.

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

A clothing store has a '30% off everything' sale. During the sale, an item that originally cost $150 is marked down. The next week, the store raises all sale prices by 25%. What is the final price of this item?

  1. The final price is exactly $131.25 for this item (correct answer)
  2. The final price is exactly $140.63 for this item
  3. The final price is exactly $143.75 for this item
  4. The final price is exactly $150.00 for this item
Explanation: Original price: $150. After 30% discount: $150 × 0.70 = $105. After 25% increase on sale price: $105 × 1.25 = $131.25. Choice B makes an arithmetic error. Choice C incorrectly calculates 25% increase on original price instead of sale price. Choice D incorrectly assumes the changes cancel out exactly.

Question 2

Maria's salary increased by 8% in January and then by 12% in July. Her December salary was $50,400. By what percent did her salary increase from the previous December to this December?

  1. Her salary increased by exactly 20.0% over the year
  2. Her salary increased by approximately 21.8% over the year
  3. Her salary increased by approximately 19.2% over the year
  4. Her salary increased by exactly 20.96% over the year (correct answer)
Explanation: When you see consecutive percentage increases, remember that they compound - you can't simply add the percentages together. Each increase applies to the new amount, not the original. To find Maria's original salary, work backwards from her December salary of $50,400. If we call her previous December salary $xx ,thenafteran8, then after an 8% increase in January, her salary became 1.08x1.08x .Thenaftera12. Then after a 12% increase in July, it became 1.08x×1.12=1.2096x1.08x \times 1.12 = 1.2096x $. Since we know her final salary is $50,400, we can solve: 1.2096x=50,4001.2096x = 50,400, so x=50,400÷1.2096=41,666.67x = 50,400 ÷ 1.2096 = 41,666.67. The total percent increase is: 50,400−41,666.6741,666.67×100%=20.96%\frac{50,400 - 41,666.67}{41,666.67} \times 100\% = 20.96\% Alternatively, you can calculate this directly: when you have consecutive percentage increases, multiply the growth factors: 1.08×1.12=1.20961.08 \times 1.12 = 1.2096. This means the salary grew by a factor of 1.2096, which represents a 20.96% increase. Choice A incorrectly adds the percentages (8% + 12% = 20%). Choice B appears to use an approximation error, possibly from rounding intermediate calculations. Choice C might result from incorrectly calculating the percentage decrease needed to reverse the increases. Study tip: For consecutive percentage changes, always multiply the growth factors (1 + rate), then subtract 1 to find the overall percentage change. Never just add the individual percentages unless specifically told the changes don't compound.

Question 3

The value of a car depreciates by 20% each year. After 2 years, the car is worth $25,600. What was the original purchase price?

  1. The original price was exactly $32,000
  2. The original price was exactly $40,000 (correct answer)
  3. The original price was exactly $42,667
  4. The original price was exactly $51,200
Explanation: Let P be the original price. After 2 years with 20% annual depreciation: P × (0.80)² = P × 0.64 = $25,600. So P = $25,600 ÷ 0.64 = $40,000. Choice A incorrectly uses 80% of original (P × 0.8 = $25,600). Choice C uses incorrect calculation method. Choice D incorrectly doubles the current value.

Question 4

A restaurant bill increases from $80 to $95 when tax and tip are added. If the tax rate is 8%, what percent tip was added (calculated on the original bill amount)?

  1. The tip was exactly 10.5% of the original bill amount (correct answer)
  2. The tip was exactly 11.25% of the original bill amount
  3. The tip was exactly 15% of the original bill amount
  4. The tip was exactly 18.75% of the original bill amount
Explanation: Original bill: $80. Tax: $80 × 0.08 = $6.40. Amount after tax: $86.40. Total bill: $95. Tip amount: $95 - $86.40 = $8.60. Tip percentage: 8.60/8.60/80 = 0.105 = 10.5%. Choice B calculates tip as percentage of after-tax amount. Choice C assumes a standard tip rate. Choice D makes an arithmetic error or uses wrong base.

Question 5

A stock price falls 25% on Monday, then rises 30% on Tuesday. On Wednesday it falls 10%. What is the overall percent change from the original price?

  1. The stock decreased by 12.25% from its original price (correct answer)
  2. The stock decreased by 5% from its original price
  3. The stock increased by 2.75% from its original price
  4. The stock price returned exactly to its original value
Explanation: Starting with price P: After Monday: 0.75P. After Tuesday: 0.75P × 1.30 = 0.975P. After Wednesday: 0.975P × 0.90 = 0.8775P. The final price is 87.75% of original, so it decreased by 100% - 87.75% = 12.25%. Choice B incorrectly calculates -25% + 30% - 10% = -5%. Choice C makes an arithmetic error. Choice D incorrectly assumes the changes cancel out.

Question 6

The population of a town decreased by 15% in 2020, then increased by 20% in 2021. If the population at the end of 2021 was 40,800, what was the population at the beginning of 2020?

  1. The original population was approximately 39,200 people
  2. The original population was exactly 40,000 people (correct answer)
  3. The original population was exactly 42,000 people
  4. The original population was approximately 43,100 people
Explanation: Let P be the original population. After 15% decrease: 0.85P. After 20% increase: 0.85P × 1.20 = 1.02P = 40,800. Solving: P = 40,800 ÷ 1.02 = 40,000. Choice A uses incorrect arithmetic (possibly 40,800 ÷ 1.04). Choice C assumes the net effect is simply 20% - 15% = 5% increase, leading to 40,800 ÷ 1.05. Choice D makes an error in the direction of operations or calculation.

Question 7

The membership of a club increased from 180 to 225 members. Later, it decreased back to 180 members. What was the percent decrease in the second change?

  1. The membership decreased by exactly 25% in the second change
  2. The membership decreased by the same percentage as it initially increased
  3. The membership decreased by exactly 45% in the second change
  4. The membership decreased by exactly 20% in the second change (correct answer)
Explanation: When you encounter percent change problems, remember that the percent change always depends on what you're comparing to — the original value for that specific change. Let's work through this step by step. The membership decreased from 225 back to 180 members. To find the percent decrease, you need to calculate: amount of decreaseoriginal amount×100%\frac{\text{amount of decrease}}{\text{original amount}} \times 100\% The amount of decrease is 225−180=45225 - 180 = 45 members. The original amount for this second change is 225 members (not 180). So the percent decrease is: 45225×100%=0.2×100%=20%\frac{45}{225} \times 100\% = 0.2 \times 100\% = 20\% Choice A incorrectly calculates 45180=0.25=25%\frac{45}{180} = 0.25 = 25\%. This uses 180 as the denominator, but 180 is the final value, not the starting value for the decrease. Choice B falls into a common trap. The initial increase was 45180×100%=25%\frac{45}{180} \times 100\% = 25\%, but percent changes aren't symmetric. A 25% increase followed by a 25% decrease doesn't bring you back to the original number. Choice C simply states the absolute change (45) as a percentage without proper calculation, which doesn't represent any meaningful percent change. Choice D correctly identifies the 20% decrease. Study tip: Always identify the correct "original value" for each percent change calculation. For increases, it's the smaller starting number. For decreases, it's the larger starting number. The original value is your denominator.

Question 8

A store marks up an item 60% above cost, then offers a 'special discount' that brings the price down to 20% above the original cost. What percent discount did the store offer?

  1. The store offered a discount of exactly 33⅓% off the marked price
  2. The store offered a discount of exactly 40% off the marked price
  3. The store offered a discount of exactly 25% off the marked price (correct answer)
  4. The store offered a discount of exactly 75% off the marked price
Explanation: When you encounter markup and discount problems, you're working with sequential percentage changes. The key is to track the price through each step using the same reference point. Let's say the original cost is $100. After a 60% markup, the marked price becomes $100 + (0.60 × $100) = $160. The "special discount" brings the final price to 20% above the original cost, which means $100 + (0.20 × $100) = $120. Now you can find the discount percentage: the price dropped from $160 to $120, a decrease of $40. The discount percentage is $discount amountoriginal marked price=40160=0.25=25%\frac{\text{discount amount}}{\text{original marked price}} = \frac{40}{160} = 0.25 = 25\% $ Choice A (33⅓%) might tempt you if you incorrectly calculated \frac{40}{120} instead of \frac{40}{160} . Remember, discount percentages are always based on the price before the discount, not after. Choice B (40%) could result from confusing the dollar amount of the discount ($40) with the percentage, or from other calculation errors with the base. Choice D (75%) represents a major miscalculation, possibly from working backwards incorrectly or confusing which values to use in your percentage formula. The correct answer is C: exactly 25% off the marked price. Strategy tip: In sequential percentage problems, always work with concrete numbers (like $100 for the original cost) rather than trying to work abstractly with variables. This prevents calculation errors and makes the problem much clearer to follow.

Question 9

A store increases the price of a jacket from $80 to $92, then offers a 15% discount off the new price. What is the final price compared to the original price?

  1. The final price is 2.25% higher than the original price
  2. The final price is 2.25% lower than the original price (correct answer)
  3. The final price is exactly equal to the original price
  4. The final price is 15% higher than the original price
Explanation: The price increases from $80 to $92. Then a 15% discount is applied: $92 × 0.15 = $13.80 discount, so final price is $92 - $13.80 = 78.20.Comparingtooriginal:(78.20. Comparing to original: (78.20 - 80)/80)/80 = -1.80/1.80/80 = -0.0225 = -2.25%. The final price is 2.25% lower than the original. Choice A incorrectly assumes the final price is higher. Choice C would require the discounted price to equal $80. Choice D confuses the percentage discount with the overall change.

Question 10

The number of students in a school increased by 15% from 2019 to 2020, then decreased by 12% from 2020 to 2021. If there were 1,012 students in 2021, how many students were there in 2019?

  1. There were approximately 1,058 students in 2019
  2. There were approximately 967 students in 2019
  3. There were exactly 1,000 students in 2019 (correct answer)
  4. There were exactly 1,100 students in 2019
Explanation: When you encounter percent change problems that work backwards from a final value, you need to set up an equation that tracks each change step by step. Let's call the 2019 student count xx. After a 15% increase in 2020, there were x×1.15x \times 1.15 students. Then after a 12% decrease in 2021, there were x×1.15×0.88=1,012x \times 1.15 \times 0.88 = 1,012 students. Solving: x×1.15×0.88=1,012x \times 1.15 \times 0.88 = 1,012 x×1.012=1,012x \times 1.012 = 1,012 x=1,000x = 1,000 So there were exactly 1,000 students in 2019, making C correct. Looking at the wrong answers: A (1,058) represents a common error where students incorrectly add and subtract the percentages directly to the final number (1,012 + 15% - 12% ≈ 1,058). B (967) likely comes from reversing the operations or applying the percentages in the wrong direction. D (1,100) might result from rough mental math or incorrectly assuming the net change is simply 3% (15% - 12%). The key insight is that percent changes don't simply cancel out—a 15% increase followed by a 12% decrease doesn't equal a 3% net increase. You must multiply by the change factors: 1.15 (for +15%) and 0.88 (for -12%). Study tip: Always convert percent changes to multipliers and work systematically through multi-step percent problems. When working backwards, set up an equation that follows the chronological order of changes.