ACCUPLACER Arithmetic Quiz: Estimating And Approximating
20 questions · exam conditions
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Estimating And ApproximatingQuestion 1 of 20

A delivery truck travels 342342 miles and uses 18.718.7 gallons of fuel. At the same fuel efficiency, approximately how many gallons would be needed for a 890890 mile trip?

4545 gallons
4040 gallons
5555 gallons
5050 gallons
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ACCUPLACER Arithmetic Quiz

ACCUPLACER Arithmetic Quiz: Estimating And Approximating

Practice Estimating And Approximating 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 Estimating And Approximating, 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 delivery truck travels 342342 miles and uses 18.718.7 gallons of fuel. At the same fuel efficiency, approximately how many gallons would be needed for a 890890 mile trip?

  1. 4545 gallons
  2. 4040 gallons
  3. 5555 gallons
  4. 5050 gallons (correct answer)
Explanation: This is a fuel efficiency problem that requires you to find a rate and then apply it to a new situation. When you see questions about consistent rates (miles per gallon, cost per item, etc.), you'll set up a proportion or calculate the unit rate. First, find the truck's fuel efficiency by dividing miles by gallons: 342÷18.7=18.29342 \div 18.7 = 18.29 miles per gallon. Now you can determine how many gallons are needed for 890 miles: 890÷18.29=48.7890 \div 18.29 = 48.7 gallons. Since the question asks for an approximation, this rounds to about 49 gallons, making 50 gallons the closest answer. Answer choice A (45 gallons) is too low and likely results from rounding the fuel efficiency up too much or making calculation errors early in the process. Answer choice B (40 gallons) is significantly too low, possibly from confusing the setup or incorrectly estimating the fuel efficiency as much higher than it actually is. Answer choice C (55 gallons) overestimates the fuel needed, which could happen if you underestimated the truck's efficiency or made errors when setting up the proportion. The correct answer is D (50 gallons) because it's closest to the calculated 48.7 gallons. For rate problems like this, always identify what stays constant (the fuel efficiency), calculate that rate clearly, then apply it to the new scenario. Double-check that your final answer makes logical sense—a longer trip should require proportionally more fuel.

Question 2

A restaurant bill is $48.35. A diner wants to leave a tip of approximately 15%. Which of the following is the closest estimate for the tip?

  1. $5.00
  2. $7.25 (correct answer)
  3. $9.50
  4. $12.00
Explanation: To estimate the tip, first round the bill to a convenient number, like $50. Then calculate 15% of $50. A simple way is to find 10% and 5% and add them. 10% of $50 is $5. 5% is half of that, which is 2.50. The estimated tip is \(5.00 + $2.50 = $7.50). Of the choices provided, $7.25 is the closest. (The exact tip is 0.15×48.35=7.25250.15 \times 48.35 = 7.2525).

Question 3

A company's annual profit was $4,188,900. If this profit were distributed equally among the company's 78 employees, which amount is the best estimate of what each employee would receive?

  1. $500
  2. $5,000
  3. $50,000 (correct answer)
  4. $500,000
Explanation: To estimate, round the profit to 4,000,000 and the number of employees to 80. The problem is now to calculate \(4,000,000 \div 80). You can cancel a zero from both numbers, which gives (400,000 \div 8\). Since 40 \div 8 = 5,then, then 400,000 \div 8 = 50,000$. So, each employee would receive approximately $50,000.

Question 4

A driver traveled 418 miles using 14.2 gallons of gasoline. Which of the following is the best estimate of the car's fuel efficiency in miles per gallon?

  1. 28
  2. 30 (correct answer)
  3. 35
  4. 40
Explanation: To estimate the miles per gallon, round the numbers to values that are easy to divide. Round 418 miles up to 420 miles and 14.2 gallons down to 14 gallons. The estimated fuel efficiency is 420÷14=30420 \div 14 = 30 miles per gallon. The exact answer is approximately 29.4, making 30 the best estimate.

Question 5

What is the approximate value of 119.7×4.120.3\frac{119.7 \times 4.1}{20.3}?

  1. 12
  2. 24 (correct answer)
  3. 30
  4. 48
Explanation: To estimate the value of the expression, round the numbers to values that are easy to work with. Round 119.7 to 120, 4.1 to 4, and 20.3 to 20. The expression becomes 120×420\frac{120 \times 4}{20}. You can simplify this by first dividing 120 by 20, which is 6. Then multiply by 4: 6×4=246 \times 4 = 24.

Question 6

A customer wants to buy a jacket for $89.95 and a pair of shoes for $48.50. Sales tax is approximately 6%. Which is the best estimate of the total cost, including tax?

  1. $140
  2. $148 (correct answer)
  3. $155
  4. $162
Explanation: First, estimate the subtotal by rounding the prices: (90+90 + 50 = 140\). Next, estimate the 6% tax on 140. One way is to find 1% ((140÷100=140 \div 100 = 1.40)) and multiply by 6 ((1.40×6=1.40 \times 6 = 8.40)). Finally, add the estimated subtotal and tax: ($140 + $8.40 = $148.40). The closest answer choice is $148.

Question 7

The population of City A is 2.8472.847 million, City B is 1.9231.923 million, and City C is 4.1864.186 million. If these three cities form a metropolitan area, approximately how many times larger is the combined population than City B alone?

  1. 3.53.5 times larger
  2. 4.54.5 times larger (correct answer)
  3. 5.05.0 times larger
  4. 6.56.5 times larger
Explanation: Estimate populations: City A ≈ 2.8 million, City B ≈ 1.9 million, City C ≈ 4.2 million. Combined: 2.8 + 1.9 + 4.2 = 8.9 million. Ratio: 8.9 ÷ 1.9 ≈ 9 ÷ 2 = 4.5. Choice A results from comparing only Cities A and C combined to City B. Choice C uses 10 ÷ 2 by over-rounding the total. Choice D incorrectly adds the individual ratios rather than finding the ratio of the sum.

Question 8

A shipping company charges 2.85$$ per pound for packages under $$50$$ pounds and 1.92perpoundforpackagesper pound for packages50poundsormore.Apackageweighspounds or more. A package weighs47.3pounds.Iftheweightlimitwereraisedbypounds. If the weight limit were raised by5$$ pounds, approximately how much money would the customer save?

  1. $$$45$$
  2. $$$90$$
  3. $$$44$$ (correct answer)
  4. $$$135$$
Explanation: Current cost: 47.3 × $2.85 ≈ 47 × $3 = $141. If limit raised to 55 pounds, the package would qualify for lower rate: 47.3 × $1.92 ≈ 47 × $2 = $94. Savings: $141 - $94 = $47 ≈ 44.ChoiceAuses45poundsinsteadof47.3.ChoiceBincorrectlycalculatesthedifferenceinratestimesweight(44. Choice A uses 45 pounds instead of 47.3. Choice B incorrectly calculates the difference in rates times weight (0.93 × 47 ≈ $90). Choice D adds both costs instead of finding the difference.

Question 9

A warehouse stores boxes in a rectangular arrangement. The width is 3838 boxes, the length is 127127 boxes, and boxes are stacked 1919 high. If each box weighs 12.712.7 pounds, which is the best estimate for the total weight?

  1. 1,000,0001,000,000 pounds
  2. 1,200,0001,200,000 pounds (correct answer)
  3. 1,500,0001,500,000 pounds
  4. 800,000800,000 pounds
Explanation: Estimate dimensions: 38 ≈ 40, 127 ≈ 130, 19 ≈ 20, weight ≈ 13 pounds. Total boxes: 40 × 130 × 20 = 104,000 ≈ 100,000. Total weight: 100,000 × 13 = 1,300,000 pounds ≈ 1,200,000 pounds. Choice A underestimates the weight per box significantly. Choice C overestimates by using 15 pounds per box. Choice D results from calculating only the base area times weight, forgetting the height dimension.

Question 10

A factory produces widgets at a rate of 127127 widgets per hour for 8.58.5 hours per day, 66 days per week. If 12%12\% of the widgets are defective and must be discarded, approximately how many usable widgets are produced per week?

  1. 5,7005,700 widgets (correct answer)
  2. 6,5006,500 widgets
  3. 6,0006,000 widgets
  4. 5,2005,200 widgets
Explanation: Daily production: 127 × 8.5 ≈ 130 × 9 = 1,170 widgets. Weekly production: 1,170 × 6 = 7,020 ≈ 7,000 widgets. Since 12% are defective, 88% are usable. Usable widgets: 88% of 7,000 = 0.88 × 7,000 = 6,160 ≈ 5,700 widgets. Choice B uses 90% instead of 88%. Choice C uses the total without accounting for defects. Choice D uses 75% instead of 88%.

Question 11

A construction crew needs to estimate the total cost of materials for a project. Steel beams cost 47.85$$ per foot, and they need approximately $$127$$ feet. Concrete costs 89.20percubicyard,andtheyneedapproximatelyper cubic yard, and they need approximately38$$ cubic yards. Which of the following is the best estimate for the total cost?

  1. $$$9,500$$
  2. $$$6,100$$
  3. $$$10,500$$ (correct answer)
  4. $$$12,200$$
Explanation: Round $47.85 to $50 and 127 feet to 130 feet: $50 × 130 = $6,500. Round $89.20 to $90 and 38 cubic yards to 40: $90 × 40 = $3,600. Total estimate: $6,500 + $3,600 = $10,100, which is closest to $10,500. Choice A uses poor rounding that underestimates both components. Choice B only accounts for one material type. Choice D overestimates by rounding up too aggressively.

Question 12

In a school district, elementary schools have an average of 287287 students, middle schools average 634634 students, and high schools average 1,2481,248 students. If there are 2323 elementary schools, 88 middle schools, and 55 high schools, approximately how many students are in the district?

  1. 18,00018,000 students (correct answer)
  2. 17,00017,000 students
  3. 15,00015,000 students
  4. 20,00020,000 students
Explanation: Round to easier numbers: 287 ≈ 300, 634 ≈ 600, 1,248 ≈ 1,200. Calculate: Elementary: 23 × 300 = 6,900; Middle: 8 × 600 = 4,800; High: 5 × 1,200 = 6,000. Total: 6,900 + 4,800 + 6,000 = 17,700 ≈ 18,000. Choice B uses the exact calculation of rounded numbers (17,700). Choice C underestimates high school enrollment significantly. Choice D overestimates by rounding student counts too high.

Question 13

A rectangular swimming pool is 48.248.2 feet long, 23.723.7 feet wide, and has an average depth of 5.85.8 feet. If one gallon equals 0.1340.134 cubic feet, approximately how many gallons does the pool hold?

  1. 50,00050,000 gallons
  2. 55,00055,000 gallons
  3. 40,00040,000 gallons
  4. 45,00045,000 gallons (correct answer)
Explanation: When you encounter a word problem involving volume and unit conversion, break it down into clear steps: calculate the volume first, then convert to the required units. To find the pool's volume, multiply length × width × depth: 48.2×23.7×5.8=6,622.17248.2 \times 23.7 \times 5.8 = 6,622.172 cubic feet. Since we need gallons, divide by the conversion factor: 6,622.172÷0.134=49,4186,622.172 ÷ 0.134 = 49,418 gallons. Rounding to the nearest thousand gives approximately 49,00049,000 gallons, which is closest to answer choice D) 45,00045,000 gallons. Let's examine why the other answers are incorrect. Choice A) 50,00050,000 gallons is too high—it likely comes from rounding errors or miscalculating the volume. Choice B) 55,00055,000 gallons is significantly too large and suggests a major calculation error, possibly multiplying by the conversion factor instead of dividing. Choice C) 40,00040,000 gallons is too low and might result from using incorrect dimensions or making an error in the conversion process. The key insight is recognizing that since one gallon equals 0.1340.134 cubic feet, you need to divide the cubic feet by 0.1340.134 to get gallons—not multiply. This is a common source of confusion in conversion problems. Study tip: In volume-to-capacity conversion problems, always identify what one unit of the desired measurement equals in terms of the given measurement, then set up your division or multiplication accordingly. Practice converting between cubic feet and gallons until the relationship becomes automatic.

Question 14

Which of the following expressions has the greatest approximate value?

  1. 41×1.941 \times 1.9
  2. 159÷2.1159 \div 2.1
  3. 13×243\frac{1}{3} \times 243
  4. 9.8×9.29.8 \times 9.2 (correct answer)
Explanation: Estimate the value of each expression: A) 41×1.9≈40×2=8041 \times 1.9 \approx 40 \times 2 = 80. B) 159÷2.1≈160÷2=80159 \div 2.1 \approx 160 \div 2 = 80. C) 13×243≈13×240=80\frac{1}{3} \times 243 \approx \frac{1}{3} \times 240 = 80. D) 9.8×9.2≈10×9=909.8 \times 9.2 \approx 10 \times 9 = 90. Comparing the approximate values, 90 is the greatest.

Question 15

Which of the following fractions is closest in value to 0.48?

  1. 12\frac{1}{2} (correct answer)
  2. 25\frac{2}{5}
  3. 14\frac{1}{4}
  4. 35\frac{3}{5}
Explanation: First, recognize that 0.48 is very close to 0.50. Now, convert the answer choices to decimals to compare. A) 14=0.25\frac{1}{4} = 0.25. B) 25=0.40\frac{2}{5} = 0.40. C) 12=0.50\frac{1}{2} = 0.50. D) 35=0.60\frac{3}{5} = 0.60. Comparing the decimals, 0.50 is the closest value to 0.48.

Question 16

Which of the following calculations results in a value closest to 20?

  1. 4.1+15.24.1 + 15.2 (correct answer)
  2. 82.1÷3.982.1 \div 3.9
  3. 3.9×4.93.9 \times 4.9
  4. 50.3−29.550.3 - 29.5
Explanation: To solve this, you can estimate each option or calculate precisely. A) 3.9×4.9≈4×5=203.9 \times 4.9 \approx 4 \times 5 = 20; exact is 19.11. B) 82.1÷3.9≈80÷4=2082.1 \div 3.9 \approx 80 \div 4 = 20; exact is ~21.05. C) 4.1+15.2≈4+15=194.1 + 15.2 \approx 4 + 15 = 19; exact is 19.3. D) 50.3−29.5≈50−30=2050.3 - 29.5 \approx 50 - 30 = 20; exact is 20.8. Comparing the exact values to 20: |19.11-20|=0.89; |21.05-20|=1.05; |19.3-20|=0.7; |20.8-20|=0.8. The smallest difference is 0.7, which corresponds to choice C.

Question 17

A painter estimates that a job will require 19.5 gallons of paint. The paint is sold in cans containing 1181\frac{1}{8} gallons. About how many cans of paint should the painter buy?

  1. 10
  2. 14
  3. 18 (correct answer)
  4. 22
Explanation: To estimate the number of cans, divide the total paint needed by the amount per can. Round 19.5 gallons to 20 gallons. The fraction 1181\frac{1}{8} is slightly more than 1. Dividing 20 by a number slightly more than 1 will give a result slightly less than 20. The most reasonable estimate is 18. Exact calculation: 19.5÷1.125≈17.3319.5 \div 1.125 \approx 17.33. Since the painter cannot buy a fraction of a can, 18 cans must be purchased.

Question 18

An assembly line produces 1,489 widgets in a 7.5-hour shift. Approximately how many widgets are produced per hour?

  1. 150
  2. 200 (correct answer)
  3. 225
  4. 250
Explanation: To estimate the rate, round the numbers to be compatible. Round 1,489 widgets to 1,500. To divide by 7.5, you can double both the dividend and divisor to eliminate the decimal: 1500÷7.5=3000÷151500 \div 7.5 = 3000 \div 15. This simplifies to 200 widgets per hour. The exact value is 1489÷7.5≈198.51489 \div 7.5 \approx 198.5, so 200 is an excellent estimate.

Question 19

The value of 1112+89\frac{11}{12} + \frac{8}{9} is closest to which whole number?

  1. 0
  2. 1
  3. 2 (correct answer)
  4. 3
Explanation: To estimate the sum, consider the value of each fraction. 1112\frac{11}{12} is very close to 1, because the numerator is almost equal to the denominator. Similarly, 89\frac{8}{9} is also very close to 1. Therefore, the sum is approximately 1+1=21 + 1 = 2.

Question 20

Which of the following is the best approximation of (49.75÷5.1)×3.8(49.75 \div 5.1) \times 3.8?

  1. 30
  2. 37
  3. 40 (correct answer)
  4. 48
Explanation: To approximate the value, round the numbers to the nearest compatible numbers. Round 49.75 to 50, 5.1 to 5, and 3.8 to 4. The expression becomes (50÷5)×4(50 \div 5) \times 4. Following the order of operations, this simplifies to 10×4=4010 \times 4 = 40.