ACCUPLACER Arithmetic Quiz: Finding Percent Of A Quantity
20 questions · exam conditions
0:00
Finding Percent Of A QuantityQuestion 1 of 20

A 500-milliliter bottle is filled with a solution that contains 12% alcohol. How many milliliters of the solution is NOT alcohol?

60
88
440
488
← Back to quizzes

ACCUPLACER Arithmetic Quiz

ACCUPLACER Arithmetic Quiz: Finding Percent Of A Quantity

Practice Finding Percent Of A Quantity 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 Finding Percent Of A Quantity, 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

A 500-milliliter bottle is filled with a solution that contains 12% alcohol. How many milliliters of the solution is NOT alcohol?

  1. 60
  2. 88
  3. 440 (correct answer)
  4. 488
Explanation: If 12% of the solution is alcohol, then the percentage that is not alcohol is 100%−12%=88%100\% - 12\% = 88\%. To find the volume of the non-alcoholic part, calculate 88% of 500 mL: 0.88×500=4400.88 \times 500 = 440 mL.

Question 2

A salesperson earns a 5% commission on the first $10,000 of sales and an 8% commission on all sales above $10,000. If the salesperson makes $22,000 in sales, what is their total commission?

  1. $960
  2. $1,100
  3. $1,460 (correct answer)
  4. $1,760
Explanation: The commission is calculated in two parts. First part: 5% of the first $10,000 is 0.05 \times 10,000 = \500.Secondpart:Theamountofsalesover$10,000is. Second part: The amount of sales over $10,000 is $22,000 - $10,000 = $12,000.Thecommissiononthisamountis8. The commission on this amount is 8% of $12,000, which is 0.08 \times 12,000 = $960.Thetotalcommissionisthesumofthetwoparts:. The total commission is the sum of the two parts: $500 + $960 = $1,460$.

Question 3

An investor puts $4,000 into an account earning 3% simple annual interest and $6,000 into an account earning 5% simple annual interest. What is the total amount of interest earned from both accounts in one year?

  1. $300
  2. $400
  3. $420 (correct answer)
  4. $500
Explanation: Calculate the interest for each account separately. For the first account: 3% of $4,000 is 0.03 \times 4,000 = \120.Forthesecondaccount:5. For the second account: 5% of $6,000 is 0.05 \times 6,000 = $300.Thetotalinterestisthesumoftheinterestfrombothaccounts:. The total interest is the sum of the interest from both accounts: $120 + $300 = $420$.

Question 4

A restaurant bill for a group of diners is $45.50 for food and $12.50 for drinks. What is the total cost, including an 18% tip calculated on the entire bill?

  1. $58.18
  2. $66.19
  3. $68.44 (correct answer)
  4. $78.88
Explanation: First, calculate the total bill before the tip: \45.50 + $12.50 = $58.00.Next,calculatethe18. Next, calculate the 18% tip on this amount: 0.18 \times 58.00 = $10.44.Finally,addthetiptothebilltofindthetotalcost:. Finally, add the tip to the bill to find the total cost: $58.00 + $10.44 = $68.44$.

Question 5

A recipe calls for 2.5 cups of flour. If Janet wants to make 40% more than the recipe yields but only has 80% of the required flour available, what percent of the intended increased batch can she actually make?

  1. Approximately 57% of the increased batch (correct answer)
  2. Approximately 67% of the increased batch
  3. Approximately 72% of the increased batch
  4. Approximately 80% of the increased batch
Explanation: For 40% more, Janet needs 2.5 × 1.4 = 3.5 cups of flour. She has 80% of 2.5 = 2.0 cups available. The percent she can make is 2.0 ÷ 3.5 = 0.571 ≈ 57%. Choice B incorrectly uses 2.4 cups (80% of 3.0 instead of 2.5). Choice C results from dividing available flour by original recipe amount. Choice D simply states the percentage of flour she has available.

Question 6

A retail store marks up all items by 35% above wholesale cost. During a clearance sale, the store offers 20% off the marked retail price. If a customer buys an item that originally cost the store $60 wholesale, what percent of the wholesale cost does the customer actually pay?

  1. 85% of the wholesale cost
  2. 115% of the wholesale cost
  3. 92% of the wholesale cost
  4. 108% of the wholesale cost (correct answer)
Explanation: When you encounter percentage markup and discount problems, you need to track how each percentage change affects the price step by step, working from the original wholesale cost through each transformation. Let's trace through this problem systematically. The wholesale cost is $60. First, the store marks up by 35%, so the retail price becomes: $60×1.35=8160 × 1.35 = 81 $ dollars. Next, during the clearance sale, customers get 20% off this marked retail price. The sale price becomes: 81 × 0.80 = 64.80 dollars. To find what percent of the wholesale cost the customer pays, divide the final price by the wholesale cost: \frac{64.80}{60} = 1.08 = 108% Looking at the wrong answers: Choice A (85%) likely comes from mistakenly thinking the customer pays 100% - 15% = 85% of wholesale, incorrectly combining the markup and discount. Choice B (115%) might result from adding the markup percentage (35%) and subtracting the discount percentage (20%) to get 15% above wholesale. Choice C (92%) could come from applying the 20% discount directly to the 115% figure, getting 115% - 23% ≈ 92%. The key insight is that percentages compound—you can't simply add and subtract them. Each percentage operates on the result of the previous calculation, not the original amount. Strategy tip: In multi-step percentage problems, always calculate each step sequentially and convert percentages to decimals (35% = 1.35 for increases, 20% off means multiply by 0.80). This prevents the common error of trying to combine percentages arithmetically.

Question 7

A clothing store offers a "buy 2, get 1 at 50% off" promotion on items that are already marked 30% off the original price. If someone buys 3 identical shirts originally priced at $45 each, what percent of the total original price do they actually pay?

  1. Approximately 70% of the original total price
  2. Approximately 58% of the original total price (correct answer)
  3. Approximately 65% of the original total price
  4. Approximately 75% of the original total price
Explanation: When you encounter multi-step discount problems, work through each promotion systematically to avoid compounding errors. First, calculate the 30% markdown on each $45 shirt: $45×0.30=13.5045 \times 0.30 = 13.50 ,soeachshirtcosts, so each shirt costs 45−13.50=31.5045 - 13.50 = 31.50 $ after the initial discount. Next, apply the "buy 2, get 1 at 50% off" promotion to the already-discounted prices. You pay full price for two shirts ( 31.50 \times 2 = 63.00 ) and half price for the third shirt ( 31.50 \times 0.50 = 15.75 ). Your total payment is 63.00 + 15.75 = 78.75 . The original total for three shirts was 45 \times 3 = 135 . To find what percentage you actually pay: \frac{78.75}{135} = 0.583 , or approximately 58%. Answer B is correct at approximately 58% of the original total price. Answer A (70%) likely comes from only applying the 30% initial discount and ignoring the second promotion. Answer C (65%) might result from incorrectly averaging the two discount percentages or applying them in the wrong order. Answer D (75%) probably comes from applying the 50% discount to the original price of just one shirt rather than to the already-discounted price. Remember: when multiple promotions stack, apply them sequentially in the order given, and always check that your final percentage makes sense—it should be less than what either discount would achieve alone.

Question 8

Maria's monthly salary increased by 8% in January, then decreased by 12% in March due to reduced hours. If her final salary is $2,376 per month, what was her original salary before the January increase?

  1. $2,400 per month originally
  2. $2,475 per month originally
  3. $2,500 per month originally (correct answer)
  4. $2,525 per month originally
Explanation: When you encounter percentage change problems with multiple steps, you need to work backwards from the final result to find the original value. This requires setting up an equation that accounts for all the changes in sequence. Let's call Maria's original salary xx. After an 8% increase in January, her salary became x×1.08x \times 1.08. Then after a 12% decrease in March, her salary became (x×1.08)×0.88=x×1.08×0.88=x×0.9504(x \times 1.08) \times 0.88 = x \times 1.08 \times 0.88 = x \times 0.9504. Since we know her final salary is $2,376, we can write: $x×0.9504=2376x \times 0.9504 = 2376 .Solvingfor. Solving for xx :: x=23760.9504=2500x = \frac{2376}{0.9504} = 2500 $. Let's verify: $2,500 × 1.08 = $2,700 (after January increase), then $2,700 × 0.88 = $2,376 (after March decrease). This confirms our answer. Choice A ($2,400) gives us $2,400 × 0.9504 = 2,281,whichistoolow.ChoiceB(2,281, which is too low. Choice B (2,475) gives us $2,475 × 0.9504 = 2,352,stilltoolow.ChoiceD(2,352, still too low. Choice D (2,525) gives us $2,525 × 0.9504 = $2,399, which is too high. These wrong answers likely represent common calculation errors or incorrect interpretations of the percentage changes. Remember that when working with sequential percentage changes, multiply the decimal forms together first (1.08 × 0.88 = 0.9504), then divide the final result by this combined factor to find the original value. Always verify your answer by working forward through the problem.

Question 9

A school's enrollment increased by 15% from last year to this year, reaching 1,380 students. Due to budget constraints, the school must reduce enrollment by 8% next year. How many students will be enrolled next year?

  1. 1,284 students will be enrolled next year
  2. 1,270 students will be enrolled next year (correct answer)
  3. 1,296 students will be enrolled next year
  4. 1,310 students will be enrolled next year
Explanation: When you encounter percentage problems involving sequential changes, you need to work step-by-step through each change rather than trying to combine percentages directly. First, find last year's enrollment. Since this year's 1,380 students represents a 15% increase from last year, you can set up: last year's enrollment × 1.15 = 1,380. Solving for last year: 1,380÷1.15=1,2001,380 ÷ 1.15 = 1,200 students. Next, calculate next year's enrollment by reducing this year's count by 8%. An 8% reduction means keeping 92% of current enrollment: 1,380×0.92=1,269.61,380 × 0.92 = 1,269.6, which rounds to 1,270 students. Looking at the wrong answers: Choice A (1,284) likely comes from incorrectly reducing last year's enrollment (1,200) by 8% instead of this year's enrollment, giving 1,200×0.92=1,1041,200 × 0.92 = 1,104, or from some other calculation error. Choice C (1,296) might result from reducing this year's enrollment by only 6% instead of 8% (1,380×0.94=1,297.21,380 × 0.94 = 1,297.2). Choice D (1,310) could come from mistakenly applying a 5% reduction instead of 8%. The key strategy here is to resist the urge to work backwards from the final answer or combine percentage changes. Instead, identify what each percentage change applies to: the 15% increase applied to an unknown previous amount, while the 8% decrease applies to the known current amount of 1,380 students. Always read carefully to determine the base amount for each percentage calculation.

Question 10

A school has 850 students. A survey reveals that 28% of the students own a pet. How many students at the school do NOT own a pet?

  1. 72
  2. 238
  3. 612 (correct answer)
  4. 822
Explanation: First, determine the percentage of students who do not own a pet: 100%−28%=72%100\% - 28\% = 72\%. Now, find 72% of the total number of students: 0.72×850=6120.72 \times 850 = 612. So, 612 students do not own a pet.

Question 11

A recipe that makes 24 muffins requires 300 grams of sugar. A baker wants to make a batch that is 175% of the standard recipe size. How many grams of sugar are needed?

  1. 225
  2. 475
  3. 525 (correct answer)
  4. 600
Explanation: To find the amount of sugar needed for the larger batch, calculate 175% of the original amount. Convert 175% to a decimal, which is 1.75. Then multiply by the original amount of sugar: 1.75×300=5251.75 \times 300 = 525 grams.

Question 12

What is the sum of 20% of 180 and 30% of 120?

  1. 60
  2. 72 (correct answer)
  3. 90
  4. 150
Explanation: This is a two-part calculation. First, find 20% of 180: 0.20×180=360.20 \times 180 = 36. Second, find 30% of 120: 0.30×120=360.30 \times 120 = 36. Finally, find the sum of these two results: 36+36=7236 + 36 = 72.

Question 13

The price of a television is increased by 10%. The new price is then decreased by 10%. If the original price was $150, what is the final price?

  1. $148.50 (correct answer)
  2. $150.00
  3. $151.50
  4. $165.00
Explanation: First, calculate the 10% increase: 10% of $150 is 0.10 \times 150 = \15.Thenewpriceis. The new price is $150 + $15 = $165.Next,calculatethe10. Next, calculate the 10% decrease on the new price: 10% of $165 is 0.10 \times 165 = $16.50.Thefinalpriceis. The final price is $165 - $16.50 = $148.50$.

Question 14

A savings account containing $2,500 earns 1.4% simple interest annually. How much interest is earned in one year?

  1. $3.50
  2. $35.00 (correct answer)
  3. $350.00
  4. $3,500.00
Explanation: To find the interest earned, multiply the principal amount by the interest rate. First, convert the percentage to a decimal: 1.4%=0.0141.4\% = 0.014. Then, multiply: \2,500 \times 0.014 = $35.00$.

Question 15

An employee earns $3,200 per month and contributes 12% of their income to a savings account. How much money will they have contributed to the account after 6 months?

  1. $384
  2. $1,920
  3. $2,304 (correct answer)
  4. $4,608
Explanation: First, calculate the amount saved each month: 12% of $3,200 is 0.12 \times 3,200 = \384.Then,multiplythismonthlyamountbythenumberofmonthstofindthetotalsaved:. Then, multiply this monthly amount by the number of months to find the total saved: $384 \times 6 = $2,304$.

Question 16

What is 12%\frac{1}{2}\% of 800?

  1. 4 (correct answer)
  2. 40
  3. 160
  4. 400
Explanation: First, convert 12%\frac{1}{2}\% to a decimal. 12%\frac{1}{2}\% is equal to 0.5%. To convert a percent to a decimal, divide by 100. So, 0.5÷100=0.0050.5 \div 100 = 0.005. Now, multiply this decimal by 800: 0.005×800=40.005 \times 800 = 4.

Question 17

A project is estimated to take 80 hours to complete. After some work is done, the project manager reports that 35% of the project is complete. How many hours of work are left to finish the project?

  1. 28
  2. 45
  3. 52 (correct answer)
  4. 65
Explanation: First, calculate the number of hours already completed: 35% of 80 hours is 0.35×80=280.35 \times 80 = 28 hours. To find the hours left, subtract the completed hours from the total: 80−28=5280 - 28 = 52 hours.

Question 18

A granola bar contains 250 calories, and 20% of the calories come from fat. If a person eats 60% of the bar, how many calories from fat did they consume?

  1. 30 (correct answer)
  2. 50
  3. 120
  4. 150
Explanation: First, find the total number of fat calories in the entire bar: 20% of 250 is 0.20×250=500.20 \times 250 = 50 fat calories. The person eats 60% of the bar, so they consume 60% of the fat calories: 60% of 50 is 0.60×50=300.60 \times 50 = 30 fat calories.

Question 19

A manufactured part is designed to be 80 centimeters long. The quality control standards allow for a margin of error of 0.5%. What is the maximum acceptable length for the part?

  1. 79.6 cm
  2. 80.4 cm (correct answer)
  3. 80.5 cm
  4. 84.0 cm
Explanation: First, calculate the allowed error amount: 0.5% of 80 cm. Convert 0.5% to a decimal: 0.5%=0.0050.5\% = 0.005. Then multiply: 0.005×80=0.40.005 \times 80 = 0.4 cm. The maximum acceptable length is the designed length plus the error margin: 80+0.4=80.480 + 0.4 = 80.4 cm.

Question 20

A car purchased for $24,500 loses 15% of its value in the first year. What is the value of the car after one year?

  1. $3,675
  2. $20,825 (correct answer)
  3. $24,485
  4. $28,175
Explanation: First, calculate the amount of value lost: 15% of $24,500 is 0.15 \times 24,500 = \3,675.Then,subtractthislossfromtheoriginalpricetofindthenewvalue:. Then, subtract this loss from the original price to find the new value: $24,500 - $3,675 = $20,825$.