ACCUPLACER Quantitative Reasoning, Algebra & Statistics Quiz: Percent As Rate Per 100
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Percent As Rate Per 100Question 1 of 20

A car's value depreciates by 15% each year. After how many complete years will the car be worth less than 50% of its original value?

3 years
4 years
6 years
5 years
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ACCUPLACER Quantitative Reasoning, Algebra & Statistics Quiz

ACCUPLACER Quantitative Reasoning, Algebra & Statistics Quiz: Percent As Rate Per 100

Practice Percent As Rate Per 100 in ACCUPLACER Quantitative Reasoning, Algebra & Statistics 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 As Rate Per 100, giving you a quick way to practice the rules, question types, and explanations that matter most for ACCUPLACER Quantitative Reasoning, Algebra & Statistics.

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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.

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Question 1

A car's value depreciates by 15% each year. After how many complete years will the car be worth less than 50% of its original value?

  1. 3 years
  2. 4 years
  3. 6 years
  4. 5 years (correct answer)
Explanation: This is a compound depreciation problem where you need to find when a value falls below a certain threshold. When a car depreciates by 15% each year, it retains 85% of its value, so you multiply by 0.85 each year. Starting with an original value of 1 (representing 100%), the car's value after each year follows the pattern: Value=1×(0.85)n\text{Value} = 1 \times (0.85)^n where n is the number of years. You need to find when this value drops below 0.5 (50% of original value). Let's calculate year by year:
  • After 1 year: 1×0.85=0.851 \times 0.85 = 0.85 (85%)
  • After 2 years: 1×(0.85)2=0.72251 \times (0.85)^2 = 0.7225 (72.25%)
  • After 3 years: 1×(0.85)3=0.6141 \times (0.85)^3 = 0.614 (61.4%)
  • After 4 years: 1×(0.85)4=0.5221 \times (0.85)^4 = 0.522 (52.2%)
  • After 5 years: 1×(0.85)5=0.4441 \times (0.85)^5 = 0.444 (44.4%)
The car first drops below 50% after 5 complete years, making D correct. Choice A (3 years) leaves the car at 61.4% of original value—still well above 50%. Choice B (4 years) results in 52.2%, which is still above the 50% threshold. Choice C (6 years) would work but isn't the minimum number of complete years required. Strategy tip: For exponential decay problems, always calculate step-by-step until you cross the threshold. Don't try to solve algebraically unless you're very comfortable with logarithms—the arithmetic approach is more reliable and less error-prone on timed exams.

Question 2

A population of bacteria doubles every 3 hours. If the population increases by 300% over a certain time period, how many hours have passed?

  1. 15 hours
  2. 9 hours
  3. 12 hours
  4. 6 hours (correct answer)
Explanation: When you encounter exponential growth problems, focus on understanding what "increases by a percentage" actually means in terms of the final population size. If a population increases by 300%, this means it grows to 400% of its original size (the original 100% plus the 300% increase). In other words, the population becomes 4 times larger than it started. Since the bacteria population doubles every 3 hours, you need to find how long it takes to reach 4 times the original size. Starting with 1 unit, after 3 hours you have 2 units (doubled once), and after 6 hours you have 4 units (doubled twice). Since 22=42^2 = 4, it takes exactly 6 hours for the population to quadruple, which corresponds to a 300% increase. Choice A (15 hours) would mean the population doubled 5 times (25=322^5 = 32), resulting in a 3,100% increase. Choice B (9 hours) represents 3 doublings (23=82^3 = 8), giving a 700% increase. Choice C (12 hours) means 4 doublings (24=162^4 = 16), which equals a 1,500% increase. The correct answer is D) 6 hours. Remember this key distinction: when a problem states something "increases by X%," the final amount is the original plus X%, not just X% of the original. Always convert percentage increases to multiplication factors first—it makes exponential growth problems much clearer and helps you avoid the common trap of confusing "increases by" with "increases to."

Question 3

A person invests $5,000 in an account that earns 3% simple annual interest. After 2 years, they move the entire amount (principal plus all earned interest) to a new account that earns 4% simple annual interest. How much interest is earned in the first year at the new account?

  1. $200
  2. $212 (correct answer)
  3. $300
  4. $512
Explanation: First, calculate the interest earned in the first account over 2 years: (I = Prt = 5,000×0.03×2=5,000 \times 0.03 \times 2 = 300). The total amount moved to the new account is the original principal plus this interest: (5,000+5,000 + 300 = 5,300\). This new total becomes the principal for the second account. The interest earned in the first year at the new account is 4% of this new principal: \(0.04 \times 5,300 = $212).

Question 4

A 50-liter solution is 20% acid. How many liters of pure acid must be added to the solution to make it 50% acid?

  1. 15
  2. 25
  3. 30 (correct answer)
  4. 40
Explanation: The initial amount of acid is 20% of 50 liters, which is 0.20×50=100.20 \times 50 = 10 liters. Let xx be the number of liters of pure acid added. The new total amount of acid will be 10+x10 + x, and the new total volume of the solution will be 50+x50 + x. We want the new solution to be 50% acid, so we set up the equation: 10+x50+x=0.50\frac{10 + x}{50 + x} = 0.50. To solve for xx, multiply both sides by (50+x)(50 + x): 10+x=0.5(50+x)10 + x = 0.5(50 + x), which simplifies to 10+x=25+0.5x10 + x = 25 + 0.5x. Subtracting 0.5x0.5x from both sides gives 0.5x+10=250.5x + 10 = 25. Subtracting 10 gives 0.5x=150.5x = 15. Finally, dividing by 0.5 gives x=30x = 30.

Question 5

In a city, 60% of the population are registered voters. Of the registered voters, only 45% actually voted in the last election. What percentage of the total city population voted in the last election?

  1. 15%
  2. 27% (correct answer)
  3. 45%
  4. 52.5%
Explanation: This is a multi-step percent problem. To find the percentage of the total population that voted, you need to find 45% of 60%. Convert the percentages to decimals and multiply them: 0.45×0.60=0.270.45 \times 0.60 = 0.27. To convert this decimal back to a percentage, multiply by 100. So, 27% of the total city population voted.

Question 6

A wholesaler sells a product to a retailer for a 20% profit. The retailer then sells the product to a customer for a 40% profit over the price they paid. The customer's price is what percentage greater than the original wholesale cost?

  1. 60%
  2. 64%
  3. 68% (correct answer)
  4. 80%
Explanation: Let the original wholesale cost be CC. The wholesaler sells it for C×1.20C \times 1.20. The retailer buys it at this price and adds a 40% profit, selling it for (C×1.20)×1.40(C \times 1.20) \times 1.40. Calculating the combined multiplier: 1.20×1.40=1.681.20 \times 1.40 = 1.68. So the final price is 1.68C1.68C. This is 1.68 times the original cost, which means it is 68% greater than the original cost.

Question 7

The length of a rectangle is increased by 20%, and its width is decreased by 20%. What is the resulting percent change in the area of the rectangle?

  1. A 4% increase
  2. A 0% change
  3. A 4% decrease (correct answer)
  4. A 10% decrease
Explanation: Let the original length be LL and the original width be WW. The original area is A=L×WA = L \times W. The new length is 1.20L1.20L, and the new width is 0.80W0.80W. The new area is Anew=(1.20L)×(0.80W)=0.96×L×W=0.96AA_{new} = (1.20L) \times (0.80W) = 0.96 \times L \times W = 0.96A. The new area is 96% of the original area, which represents a decrease of 100100% - 96% = 4%.

Question 8

A company's annual budget is allocated as follows: 40% for salaries, 25% for research, 15% for marketing, and the rest for operational costs. If the amount allocated for marketing is $90,000, what is the amount allocated for operational costs?

  1. $60,000
  2. $120,000 (correct answer)
  3. $150,000
  4. $600,000
Explanation: First, determine the total budget. We know that 15% of the total budget (B) is $90,000. So, (0.15 \times B = 90,000\). This means \(B = \frac{90000}{0.15} = 600,000). Next, find the percentage for operational costs: 100100% - 40% - 25% - 15% = 20%. Finally, calculate the amount for operational costs, which is 20% of the total budget: (0.20 \times 600,000=600,000 = 120,000).

Question 9

A store offers two different discount plans on a $200 television. Plan A is a single 30% discount. Plan B is a 20% discount, followed by an additional 10% discount on the reduced price. Which statement accurately compares the final prices?

  1. The prices for both plans are the same.
  2. The price with Plan B is $20 less than the price with Plan A.
  3. The price with Plan B is $4 less than the price with Plan A.
  4. The price with Plan A is $4 less than the price with Plan B. (correct answer)
Explanation: For Plan A, a 30% discount on $200 is (0.30 \times 200 = 60\). The final price is \(200 - 60=60 = 140). For Plan B, the first discount is 20% of $200, which is (0.20 \times 200 = 40\). The price becomes \(200 - 40=40 = 160). The second discount is 10% of this new price: (0.10 \times 160 = 16\). The final price for Plan B is \(160 - 16=16 = 144). Comparing the two, Plan A ($140) is 4lessthanPlanB(4 less than Plan B (144).

Question 10

A stock's value increased by 20% on Monday. On Tuesday, its value decreased by 20% from its value at the end of Monday. What was the net percentage change in the stock's value from the start of Monday to the end of Tuesday?

  1. A 4% increase
  2. A 0% change
  3. A 1% decrease
  4. A 4% decrease (correct answer)
Explanation: Let the original value of the stock be VV. After a 20% increase, the value is V×1.20=1.2VV \times 1.20 = 1.2V. On Tuesday, this new value decreases by 20%. The decrease is 0.20×1.2V=0.24V0.20 \times 1.2V = 0.24V. The final value is 1.2V−0.24V=0.96V1.2V - 0.24V = 0.96V. Since the final value is 96% of the original value, there was a net decrease of 100100% - 96% = 4%.

Question 11

A survey of 2,400 students found that 35% chose history as their favorite subject, and 45% chose science. The remaining students chose English. If 25% of the students who chose science change their choice to English, how many students now choose English as their favorite subject?

  1. 270
  2. 480
  3. 750 (correct answer)
  4. 1,080
Explanation: First, find the initial number of students for each subject. Science: 0.45×2400=10800.45 \times 2400 = 1080. History: 0.35×2400=8400.35 \times 2400 = 840. The initial percentage for English is 100100% - 35% - 45% = 20%, so the initial number is 0.20×2400=4800.20 \times 2400 = 480. Next, calculate how many students change from science to English: 25% of the science students is 0.25×1080=2700.25 \times 1080 = 270. This number is added to the English group: 480+270=750480 + 270 = 750. The new number of students who choose English is 750.

Question 12

A sales representative earns a monthly salary of $2,500 plus a 4% commission on all sales. If the representative earned a total of $4,300 in one month, what was the total amount of their sales for that month?

  1. $7,200
  2. $45,000 (correct answer)
  3. $62,500
  4. $107,500
Explanation: First, find the amount earned from commission by subtracting the base salary from the total earnings: (4,300−4,300 - 2,500 = 1,800\). This $1,800 represents 4% of the total sales (let's call sales S). So, \(0.04 \times S = 1,800). To find the total sales, divide the commission amount by the commission rate: (S = \frac{1800}{0.04} = $45,000).

Question 13

A real estate agent earns commission based on home sales according to the following structure: 2% on the first $200,000 of a sale, 3% on the amount between $200,001 and $500,000, and 4% on any amount above $500,000.

If the agent sells a home for $650,000, what percentage of the total sale price does the commission represent?

  1. 2.77%
  2. 3.15%
  3. 3.23% (correct answer)
  4. 4.00%
Explanation: Commission calculation: First $200,000 at 2% = $4,000. Next 300,000(300,000 (200,001 to $500,000) at 3% = $9,000. Remaining 150,000(150,000 (500,001 to $650,000) at 4% = $6,000. Total commission = $4,000 + $9,000 + $6,000 = $19,000. As percentage of sale price: $19,000 ÷ $650,000 = 0.0323 = 3.23%. Choice A uses wrong tier calculations. Choice B assumes uniform 3% rate. Choice D assumes uniform 4% rate on entire amount.

Question 14

In a survey, 40% of respondents prefer Brand A, 35% prefer Brand B, and the remaining 120 people have no preference. What percentage of all respondents have no preference?

  1. 15%
  2. 20%
  3. 25% (correct answer)
  4. 30%
Explanation: Since 40% + 35% = 75% of respondents prefer either Brand A or B, then 100% - 75% = 25% have no preference. This can be verified: if 25% = 120 people, then the total is 120 ÷ 0.25 = 480 people. Choice A (15%) would mean 600 total respondents. Choice B (20%) would mean 480 total but miscalculates the remaining percentage. Choice D (30%) would mean only 400 total respondents, making the Brand A and B percentages incorrect.

Question 15

A store marks up items by 40% above wholesale cost, then offers a 25% discount from the marked price during a sale. If an item's wholesale cost is $60, what is the final sale price as a percentage of the wholesale cost?

  1. 105% (correct answer)
  2. 115%
  3. 120%
  4. 125%
Explanation: The marked price is $60 × 1.40 = $84. After a 25% discount, the sale price is $84 × 0.75 = $63. As a percentage of wholesale cost: $63 ÷ $60 = 1.05 = 105%. Choice B incorrectly subtracts the discount percentage from the markup percentage (40% - 25% = 15%, then adds 100%). Choice C assumes the discount is applied to wholesale cost instead of marked price. Choice D simply adds the net effect incorrectly (40% - 15% = 25%).

Question 16

In a class election, Candidate A received 40% of the votes, Candidate B received 25% more votes than Candidate A, and Candidate C received the remaining votes. What percentage of votes did Candidate C receive?

  1. 10% (correct answer)
  2. 15%
  3. 20%
  4. 25%
Explanation: Candidate A received 40% of votes. Candidate B received 25% more than A, so B got 40% × 1.25 = 50% of votes. Since A + B + C = 100%, Candidate C received 100% - 40% - 50% = 10% of votes. Choice B incorrectly calculates B as receiving 40% + 25% = 65%. Choice C assumes B received 25 percentage points more (40% + 25% = 65%), leaving 35% - 40% which is impossible. Choice D confuses the 25% increase with C's share.

Question 17

In January, a company's profit was $40,000. In February, the profit was $50,000. By what percentage did the profit increase from January to February?

  1. 20%
  2. 25% (correct answer)
  3. 80%
  4. 125%
Explanation: The formula for percent increase is (\frac{\text{New Value} - \text{Original Value}}{\text{Original Value}} \times 100%. The amount of increase is (50,000−50,000 - 40,000 = 10,000\). The original value is the January profit, $40,000. So the percent increase is \frac{10000}{40000} \times 100 = 0.25 \times 100 = 25%$.

Question 18

A scientist measures the mass of a sample to be 78 grams. The actual, known mass of the sample is 80 grams. What is the percent error of the measurement relative to the actual mass?

  1. 2.0%
  2. 2.5% (correct answer)
  3. 2.56%
  4. 25%
Explanation: Percent error is calculated using the formula: \frac{|\text{Measured Value} - \text{Actual Value}|}{\text{Actual Value}} \times 100\%. First, find the absolute error: \(|78 - 80| = 2 grams. Then, divide this error by the actual value: 280=0.025\frac{2}{80} = 0.025. Finally, multiply by 100 to express it as a percentage: 0.025×100=2.50.025 \times 100 = 2.5%.

Question 19

A jacket is priced at $150. It is on sale for 20% off. A customer buys the jacket and pays a sales tax of 8% on the discounted price. What is the total amount the customer pays?

  1. $110.40
  2. $129.60 (correct answer)
  3. $132.00
  4. $138.00
Explanation: First, calculate the discounted price. The discount is 20% of $150, which is (0.20 \times 150 = 30\). The sale price is \(150 - 30=30 = 120). Next, calculate the sales tax on this discounted price. The tax is 8% of $120, which is (0.08 \times 120 = 9.60\). Finally, add the tax to the sale price to find the total amount: \(120 + 9.60=9.60 = 129.60).

Question 20

A recipe that makes 2 dozen cookies requires 10 ounces of flour. A baker wants to make 3 dozen cookies. By what percentage must the amount of flour be increased?

  1. 33.3%
  2. 50% (correct answer)
  3. 66.7%
  4. 150%
Explanation: The original recipe makes 2 dozen cookies. The new batch is for 3 dozen cookies. The increase in the number of cookies is 3−2=13 - 2 = 1 dozen. The percent increase in the batch size is increaseoriginal=1 dozen2 dozen=0.5\frac{\text{increase}}{\text{original}} = \frac{1 \text{ dozen}}{2 \text{ dozen}} = 0.5, which is a 50% increase. Since the recipe is proportional, the amount of flour must also be increased by 50%.