Praxis Math Quiz: Solve Percent Change
20 questions · exam conditions
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Solve Percent ChangeQuestion 1 of 20

A collectible was valued at $250. In one year, its value increased by 20%. The following year, due to market changes, its value decreased by 20% from its value at the end of the first year. What was the value of the collectible after the second year?

$240
$250
$260
$200
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Praxis Math Quiz

Praxis Math Quiz: Solve Percent Change

Practice Solve Percent Change in Praxis Math with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.

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This quiz focuses on Solve Percent Change, giving you a quick way to practice the rules, question types, and explanations that matter most for Praxis Math.

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Question 1

A collectible was valued at $250. In one year, its value increased by 20%. The following year, due to market changes, its value decreased by 20% from its value at the end of the first year. What was the value of the collectible after the second year?

  1. $240 (correct answer)
  2. $250
  3. $260
  4. $200
Explanation: This is a two-step problem. First, calculate the value after the 20% increase: $250 \times (1 + 0.20) = $250 \times 1.20 = $300. Second, calculate the value after the 20% decrease from the new value: $300 \times (1 - 0.20) = $300 \times 0.80 = $240.

Question 2

A television is on sale for $357 after a 15% discount. What was the original price of the television?

  1. $303.45
  2. $400.00
  3. $410.55
  4. $420.00 (correct answer)
Explanation: Let P be the original price. The sale price is the original price minus the 15% discount, so P×(1−0.15)=P \times (1 - 0.15) = 357.Thissimplifiesto. This simplifies to P \times 0.85 = 357357. To find the original price, divide the sale price by 0.85: P=$357/0.85=P = $357 / 0.85 = 420$.

Question 3

A department store offers a 20% discount on all purchases. A customer also has a coupon for an additional 10% off the discounted price. If these discounts are applied sequentially to a purchase of $150, what is the total percent discount the customer receives?

  1. 28% (correct answer)
  2. 30%
  3. 25%
  4. 32%
Explanation: First discount: $150 \times (1 - 0.20) = 120120. Second discount on the new price: $120 \times (1 - 0.10) = 108108. The total discount amount is $150 - $108 = 4242. To find the total percent discount, divide the discount amount by the original price: ($42 / $150) \times 100% = 28%. A common error is to simply add the percentages (20% + 10% = 30%).

Question 4

An investment of $1,200 increased by 25% in its first year and then increased by an additional 20% of its new value in the second year. What was the total percent increase of the investment over the two-year period?

  1. 45%
  2. 50% (correct answer)
  3. 55%
  4. 150%
Explanation: Instead of using the initial value, we can work with multipliers. The first year's increase results in a value of 1.251.25 times the original. The second year's increase results in a value of 1.201.20 times the first year's end value. The total multiplier is 1.25×1.20=1.501.25 \times 1.20 = 1.50. A multiplier of 1.50 corresponds to a 50% increase over the original value. The common error is adding the percentages (25% + 20% = 45%).

Question 5

An investor allocates 40% of a portfolio to bonds. Of that bond allocation, 25% is in municipal bonds. The municipal bonds then decrease in value by 5%. This decrease contributes to what percentage decrease for the entire portfolio?

  1. 0.5% (correct answer)
  2. 1.0%
  3. 5.0%
  4. 10.0%
Explanation: First, find the percentage of the entire portfolio that is in municipal bonds: 40%×25%=0.40×0.25=0.1040\% \times 25\% = 0.40 \times 0.25 = 0.10, or 10%. Next, calculate the impact of the 5% decrease on this portion relative to the whole portfolio: 10%×5%=0.10×0.05=0.00510\% \times 5\% = 0.10 \times 0.05 = 0.005. As a percentage, this is 0.5%.

Question 6

Store A offers a 40% discount on a $500 appliance. Store B offers a 25% discount on the same appliance, with an additional 20% off the discounted price. Which statement correctly compares the final prices?

  1. Store A is cheaper by $25.
  2. Store B is cheaper by $25.
  3. The final prices are the same. (correct answer)
  4. Store A is cheaper by $50.
Explanation: Store A price: $500 \times (1 - 0.40) = $500 \times 0.60 = 300300. Store B price: First discount is $500 \times (1 - 0.25) = 375375. The second discount is $375 \times (1 - 0.20) = 300300. The final prices are identical. The common mistake is to add the percentages for Store B (25% + 20% = 45%), which would incorrectly suggest a lower price.

Question 7

A gym's membership increased from 520 members to 650 members. The next year, membership increased by the same percentage as in the first year. To the nearest whole number, how many members did the gym have after the second year?

  1. 780
  2. 812
  3. 813 (correct answer)
  4. 825
Explanation: First, find the percent increase in the first year. The increase was 650−520=130650 - 520 = 130 members. The percent increase was (130/520)×100%=25%(130 / 520) \times 100\% = 25\%. Next, apply this same 25% increase to the new membership total: 650×(1+0.25)=650×1.25=812.5650 \times (1 + 0.25) = 650 \times 1.25 = 812.5. Rounded to the nearest whole number, this is 813 members.

Question 8

From 2010 to 2020, the price of a certain commodity increased by 50%. From 2020 to 2022, the price decreased by 40%. What was the net percent change in the price from 2010 to 2022?

  1. A 10% increase
  2. A 10% decrease (correct answer)
  3. A 20% decrease
  4. No change
Explanation: Let the original price in 2010 be P. After a 50% increase, the price in 2020 was 1.50×P1.50 \times P. After a 40% decrease from the 2020 price, the price in 2022 was (1.50×P)×(1−0.40)=(1.50×P)×0.60=0.90×P(1.50 \times P) \times (1 - 0.40) = (1.50 \times P) \times 0.60 = 0.90 \times P. A final price of 0.90P represents a 10% decrease from the original price P.

Question 9

A utility bill includes a fixed fee of $20 plus a charge for electricity usage. Last month, the usage charge was $80. This month, the utility company increased the per-unit electricity rate by 15%. If the customer's usage remains the same, what is the percent increase in their total utility bill?

  1. 12% (correct answer)
  2. 15%
  3. 18%
  4. 20%
Explanation: Last month's total bill was $20 (fixed) + $80 (usage) = 100100. The 15% rate increase applies only to the usage charge. The new usage charge is $80 \times (1 + 0.15) = $80 \times 1.15 = 9292. The new total bill is $20 (fixed) + $92 (usage) = 112112. The increase in the total bill is $112 - $100 = 1212. The percent increase for the total bill is ($12 / $100) \times 100% = 12%.

Question 10

In 2020, 30% of the residents of a town were over the age of 60. By 2025, the total population of the town had increased by 10%, and 35% of the residents were over the age of 60. What was the percent increase in the number of residents over the age of 60 from 2020 to 2025?

  1. 15.0%
  2. 28.3% (correct answer)
  3. 5.0%
  4. 35.5%
Explanation: Let the 2020 population be P. The number of residents over 60 was 0.30P0.30P. In 2025, the total population was 1.10P1.10P. The number of residents over 60 was 0.35×(1.10P)=0.385P0.35 \times (1.10P) = 0.385P. The percent increase in the over-60 population is [(0.385P−0.30P)/0.30P]×100%=(0.085P/0.30P)×100%≈28.3%[(0.385P - 0.30P) / 0.30P] \times 100\% = (0.085P / 0.30P) \times 100\% \approx 28.3\%.

Question 11

The number of defective parts produced by a machine decreased from 250 per day to 200 per day. What is the percentage decrease in the number of defective parts?

  1. 20% (correct answer)
  2. 25%
  3. 50%
  4. 80%
Explanation: The formula for percent decrease is [(Original Value - New Value) / Original Value] \times 100%. The decrease is 250−200=50250 - 200 = 50. The percentage decrease is (50/250)×100%=0.20×100%=20%(50 / 250) \times 100\% = 0.20 \times 100\% = 20\%. A common mistake is to divide by the new value (50/200 = 25%).

Question 12

A company had 800 employees in January. In February, the number of employees increased by 10%. In March, the number of employees decreased by 10%. How many employees did the company have at the end of March?

  1. 800
  2. 792 (correct answer)
  3. 808
  4. 720
Explanation: Number of employees in February: 800×(1+0.10)=800×1.10=880800 \times (1 + 0.10) = 800 \times 1.10 = 880. The 10% decrease in March is based on the February number: 880×(1−0.10)=880×0.90=792880 \times (1 - 0.10) = 880 \times 0.90 = 792. There were 792 employees at the end of March.

Question 13

Last year, a salesperson sold $80,000 worth of products. This year, they sold $100,000 worth of products. However, their commission rate was reduced from 12% last year to 9% this year. What was the percent change in the salesperson's total commission earnings?

  1. A 6.25% decrease (correct answer)
  2. A 25.0% increase
  3. A 6.25% increase
  4. A 3.0% decrease
Explanation: First, calculate the commission for each year. Last year: $80,000 \times 0.12 = 9,6009,600. This year: $100,000 \times 0.09 = 9,0009,000. The change in earnings is $9,000 - 9,600=−9,600 = -600$. The percent change is (Change / Original Amount) = (-$600 / $9,600) \times 100% = -6.25%. This is a 6.25% decrease.

Question 14

The number of employees at a company decreased by 20% in one year. The following year, the number of employees increased by 20%. If there were 100 employees initially, how many employees were there after the two changes?

  1. 96 (correct answer)
  2. 100
  3. 104
  4. 98
Explanation: Initially, there are 100 employees. A 20% decrease leaves 100×(1−0.20)=80100 \times (1-0.20) = 80 employees. The following year, a 20% increase is calculated on the new number of employees: 80×(1+0.20)=80×1.2=9680 \times (1+0.20) = 80 \times 1.2 = 96 employees. The common mistake is to assume the changes cancel each other out.

Question 15

A real estate agent's commission is 6% of a home's selling price. If the agent's commission was $21,600 for a sale, but this was after the agent gave 10% of their commission back to the buyer, what was the selling price of the home?

  1. $360,000
  2. $388,800
  3. $400,000 (correct answer)
  4. $324,000
Explanation: Let C be the agent's full commission. The agent received $21,600, which is 90% of the full commission (100% - 10%). So, $C \times 0.90 = 21,60021,600. The full commission was C=$21,600/0.90=C = $21,600 / 0.90 = 24,000.Thisfullcommissionis6. This full commission is 6% of the home's selling price (S). So, S \times 0.06 = 24,00024,000. The selling price was S=$24,000/0.06=S = $24,000 / 0.06 = 400,000$.

Question 16

A new car is purchased for $30,000. It depreciates by 15% in its first year. In its second year, it depreciates by 10% of its value at the start of the second year. What is the total percentage depreciation of the car over the two years, relative to its original price?

  1. 25.0%
  2. 23.5% (correct answer)
  3. 26.5%
  4. 22.0%
Explanation: Let's track the value. After year 1: $30,000 \times (1 - 0.15) = 25,50025,500. After year 2: $25,500 \times (1 - 0.10) = 22,95022,950. The total amount of depreciation is $30,000 - $22,950 = 7,0507,050. The total percentage depreciation is ($7,050 / $30,000) \times 100% = 23.5%. The common error is to add the percentages (15% + 10% = 25%).

Question 17

If the price of gasoline increases by 25%, by what approximate percentage must a driver reduce their gasoline consumption to keep their total gasoline spending the same?

  1. 15%
  2. 20% (correct answer)
  3. 25%
  4. 30%
Explanation: Let P be the original price and C be the original consumption. Spending is P×CP \times C. The new price is 1.25P1.25P. Let the new consumption be CnewC_{new}. We want the spending to be the same: (1.25P)×Cnew=P×C(1.25P) \times C_{new} = P \times C. Dividing by P gives 1.25×Cnew=C1.25 \times C_{new} = C. So, Cnew=C/1.25=0.8CC_{new} = C / 1.25 = 0.8C. The new consumption is 80% of the original, which means consumption must be reduced by 20%.

Question 18

A student's score on a test improved from 60 to 75. What was the percentage increase in the student's score?

  1. 15%
  2. 20%
  3. 25% (correct answer)
  4. 30%
Explanation: The formula for percent increase is [(New Value - Original Value) / Original Value] \times 100%. The increase in score is 75−60=1575 - 60 = 15. The percent increase is (15/60)×100%=0.25×100%=25%(15 / 60) \times 100\% = 0.25 \times 100\% = 25\%. A common error is to divide by the new value (15/75 = 20%).

Question 19

The base of a triangle is increased by 30% and its height is decreased by 20%. What is the net percent change in the area of the triangle?

  1. A 4% increase (correct answer)
  2. A 10% increase
  3. A 4% decrease
  4. A 10% decrease
Explanation: The area of a triangle is (1/2)×base×height(1/2) \times base \times height. Let the original base be B and height be H. The new base is $1.3B$ and the new height is 0.8H0.8H. The new area is (1/2)×(1.3B)×(0.8H)=(1/2)×(1.04×BH)=1.04×Areaoriginal(1/2) \times (1.3B) \times (0.8H) = (1/2) \times (1.04 \times BH) = 1.04 \times Area_{original}. A multiplier of 1.04 represents a 4% increase.

Question 20

A jacket priced at $160 is marked down by 25%. After a week, it is marked down an additional 20% from the sale price. What is the final selling price of the jacket?

  1. $88
  2. $96 (correct answer)
  3. $80
  4. $104
Explanation: First, apply the 25% discount: $160 \times (1 - 0.25) = $160 \times 0.75 = 120120. This is the first sale price. Next, apply the 20% discount to this new price: $120 \times (1 - 0.20) = $120 \times 0.80 = 9696. The final price is $96.