Finite Mathematics Quiz: Checking Units And Reasonableness
10 questions · exam conditions
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Checking Units And ReasonablenessQuestion 1 of 10

A cargo drone flies from a distribution center to a delivery point 60 miles away and returns along the same path. The drone flies at 90 mph with a tailwind on the outbound trip and returns at 30 mph against a headwind. A student is asked to calculate the average speed for the entire round trip. Which of the following is the most reasonable answer?

60 mph
45 mph
2.67 hours
120 miles
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Finite Mathematics Quiz

Finite Mathematics Quiz: Checking Units And Reasonableness

Practice Checking Units And Reasonableness in Finite Mathematics 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 Checking Units And Reasonableness, giving you a quick way to practice the rules, question types, and explanations that matter most for Finite Mathematics.

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 cargo drone flies from a distribution center to a delivery point 60 miles away and returns along the same path. The drone flies at 90 mph with a tailwind on the outbound trip and returns at 30 mph against a headwind. A student is asked to calculate the average speed for the entire round trip. Which of the following is the most reasonable answer?

  1. 60 mph
  2. 45 mph (correct answer)
  3. 2.67 hours
  4. 120 miles
Explanation: The correct answer is the average speed, which must have units of miles per hour. Average speed is total distance divided by total time. The outbound trip takes 60 miles/90 mph=2/360 \text{ miles} / 90 \text{ mph} = 2/3 hours. The return trip takes 60 miles/30 mph=260 \text{ miles} / 30 \text{ mph} = 2 hours. The total distance is 120 miles and the total time is 2+2/3=8/32 + 2/3 = 8/3 hours. The average speed is 120 miles/(8/3 hours)=360/8=45120 \text{ miles} / (8/3 \text{ hours}) = 360/8 = 45 mph. This value is reasonably between the two speeds.

Question 2

Pipe A can fill a swimming pool in 12 hours, and Pipe B can fill the same pool in 8 hours. Pipe C can drain the pool completely in 4 hours. If the pool is empty and all three pipes are opened simultaneously, a student calculates the time it will take to fill the pool. Which of the following outcomes is the most reasonable?

  1. The pool will be filled in approximately 5.3 hours.
  2. The pool will never be completely filled. (correct answer)
  3. The pool will be filled in 24 hours.
  4. The pool will be filled in approximately 2.7 hours.
Explanation: To determine the outcome, we must compare the combined filling rate to the drainage rate. The rates are: Pipe A fills at 1/121/12 pool/hour, Pipe B fills at 1/81/8 pool/hour, and Pipe C drains at 1/41/4 pool/hour. The combined filling rate is 1/12+1/8=2/24+3/24=5/241/12 + 1/8 = 2/24 + 3/24 = 5/24 pool/hour. The drainage rate is 1/4=6/241/4 = 6/24 pool/hour. Since the drainage rate (6/246/24) is greater than the combined filling rate (5/245/24), water is removed faster than it is added. Therefore, the pool will never be completely filled.

Question 3

The weights of five puppies in a litter are recorded as 410 g, 450 g, 390 g, 430 g, and 4200 g. A supervisor notes that the last measurement is an obvious error and that the correct weight for that puppy was 470 g. Which of the following is the most reasonable value for the corrected mean weight of the litter?

  1. 1176 g
  2. 420 g
  3. 430 g (correct answer)
  4. 2150 g
Explanation: The original data contains a significant outlier (4200 g) that unreasonably skews the mean. To find the corrected mean, replace the erroneous value with the correct one and recalculate. The corrected set of weights is 410, 450, 390, 430, and 470 g. The sum of these weights is 410+450+390+430+470=2150410 + 450 + 390 + 430 + 470 = 2150 g. The corrected mean is the sum divided by the number of puppies: 2150/5=4302150 / 5 = 430 g. This value is centered within the range of the individual puppy weights and is therefore a reasonable mean.

Question 4

A company manufactures solid steel ball bearings. It plans to introduce a new, larger model with double the weight (and thus double the volume). Assuming the cost of the protective coating is directly proportional to the surface area, and the original coating costs $0.32 per bearing, what is the most reasonable cost to coat the new, larger bearing?

  1. $0.64
  2. $0.40
  3. $1.28
  4. $0.51 (correct answer)
Explanation: This problem tests your understanding of how geometric scaling affects different measurements - a key concept in finite mathematics applications. When a sphere doubles in volume, you need to find how its surface area changes. Since volume scales with the cube of linear dimensions and surface area scales with the square, there's a specific relationship. If volume doubles, then the linear scale factor is 23≈1.26\sqrt[3]{2} \approx 1.26. The surface area then increases by this factor squared: (23)2=43≈1.587(\sqrt[3]{2})^2 = \sqrt[3]{4} \approx 1.587. Therefore, the new coating cost is $0.32×1.587=$0.508\$0.32 \times 1.587 = \$0.508, which rounds to $0.51. Let's examine why the other answers represent common mistakes: A) $0.64 assumes surface area doubles when volume doubles, but this incorrectly applies linear scaling to area measurements. B) 0.40mightresultfromusinganincorrectscalingfactorof1.25(0.40 might result from using an incorrect scaling factor of 1.25 ( \0.32 \times 1.25 ), possibly from approximating the cube root relationship poorly. C) 1.28 applies the volume scaling directly to cost ($$\0.32 \times 4 = $1.28$$), incorrectly assuming that doubling volume means quadrupling surface area. The key insight is recognizing that when volume changes by a factor, surface area changes by that factor raised to the 23\frac{2}{3} power. For finite mathematics problems involving geometric scaling, always identify what measurement you're given (volume, area, or length) and what you need to find, then apply the appropriate scaling relationship rather than assuming direct proportionality.

Question 5

A doctor prescribes a drug with a dosage of 15 mg per kg of body weight. The drug is supplied as a liquid with a concentration of 5.0 grams per liter. For a patient weighing 176 pounds, which is the most reasonable volume of the liquid drug to administer? (Use the conversion 1 kg ≈ 2.2 lbs).

  1. 48 mL
  2. 1.2 mL
  3. 240 mL (correct answer)
  4. 240 L
Explanation: This is a multi-step unit conversion problem that tests your ability to work systematically through dosage calculations. When you encounter medical dosage problems, always identify what units you're given, what units you need, and plan your conversion pathway before calculating. First, convert the patient's weight from pounds to kilograms: 176 lbs×1 kg2.2 lbs=80 kg176 \text{ lbs} \times \frac{1 \text{ kg}}{2.2 \text{ lbs}} = 80 \text{ kg} Next, calculate the total drug dose needed: 80 kg×15mgkg=1200 mg80 \text{ kg} \times 15 \frac{\text{mg}}{\text{kg}} = 1200 \text{ mg} Now convert this to grams since the concentration is given in grams per liter: 1200 mg=1.2 g1200 \text{ mg} = 1.2 \text{ g} Finally, use the concentration to find the volume needed: 1.2 g5.0 g/L=0.24 L=240 mL\frac{1.2 \text{ g}}{5.0 \text{ g/L}} = 0.24 \text{ L} = 240 \text{ mL} Answer C (240 mL) is correct. Answer A (48 mL) likely results from an error in the weight conversion or forgetting to convert mg to grams. Answer B (1.2 mL) represents the mass in grams rather than the volume, showing confusion between mass and volume units. Answer D (240 L) makes the same calculation error as C but fails to convert liters to milliliters—this volume would be enormous and clearly unreasonable for a single dose. Strategy tip: In dosage problems, always check if your final answer passes the "reasonableness test." A few hundred milliliters is typical for liquid medications, while liters would be excessive.

Question 6

The weekly profit PP, in thousands of dollars, for a company is modeled by the function P(x)=−2x2+80x−300P(x) = -2x^2 + 80x - 300, where xx is the number of units produced, in hundreds. A manager correctly calculates the production level that maximizes profit. Which of the following values is the most plausible maximum weekly profit?

  1. 2,000 units
  2. $500,000 (correct answer)
  3. $1,600,000
  4. $20,000
Explanation: The maximum profit occurs at the vertex of the parabola. The x-coordinate of the vertex is x=−b/(2a)=−80/(2(−2))=20x = -b/(2a) = -80/(2(-2)) = 20. Since xx is in hundreds of units, this corresponds to 2,000 units. The maximum profit is P(20)=−2(20)2+80(20)−300=−800+1600−300=500P(20) = -2(20)^2 + 80(20) - 300 = -800 + 1600 - 300 = 500. Since PP is in thousands of dollars, the maximum profit is $500 \times $1,000 = $500,000. This is a monetary value, not a number of units, and is the result of the full calculation.

Question 7

An insurance company offers a one-year policy for a specific type of equipment. The policy premium is $250. Based on historical data, the company estimates the following probabilities for claims during the year: a 1% chance of a total loss claim of $10,000, a 5% chance of a partial damage claim of $2,000, and a 94% chance of no claim. Which of the following is a reasonable estimate for the company's expected profit per policy?

  1. $50 (correct answer)
  2. $200
  3. -$9,750
  4. 0.06
Explanation: The expected profit is the premium minus the expected payout. The expected payout is calculated by multiplying each claim amount by its probability and summing the results: E(\text{Payout}) = (0.01)(\10,000) + (0.05)($2,000) + (0.94)($0) = $100 + $100 + $0 = $200.Theexpectedprofitisthen. The expected profit is then E(Profit\text{Profit}) = \text{Premium} - E(Payout\text{Payout}) = $250 - $200 = $50. This is a reasonable positive profit for the insurer.

Question 8

Water is pumped into a vertical cylindrical tank with a radius of 4 meters at a constant rate of 2π2\pi cubic meters per minute. An analyst is calculating the rate at which the water level is rising. Which of the following is a reasonable value for this rate?

  1. 0.1250.125 meters per minute (correct answer)
  2. 2π2\pi cubic meters per minute
  3. 16π16\pi square meters
  4. 0.250.25 meters per minute
Explanation: The question asks for the rate the water level is rising, which must have units of length per time. The volume VV of water in the tank is V=πr2hV = \pi r^2 h. Taking the derivative with respect to time gives dV/dt=πr2(dh/dt)dV/dt = \pi r^2 (dh/dt). We are given dV/dt=2πdV/dt = 2\pi m³/min and r=4r=4 m. Substituting these values gives 2π=π(42)(dh/dt)2\pi = \pi (4^2) (dh/dt), so 2π=16π(dh/dt)2\pi = 16\pi (dh/dt). Solving for dh/dtdh/dt gives dh/dt=2π/(16π)=1/8=0.125dh/dt = 2\pi / (16\pi) = 1/8 = 0.125 m/min.

Question 9

An alloy is created by mixing 100 cm³ of Metal A with 300 cm³ of Metal B. Metal A has a density of 8 g/cm³ and Metal B has a density of 12 g/cm³. A scientist calculates the density of the resulting alloy. Which of the following is the most reasonable density for the alloy? (Assume the final volume is the sum of the initial volumes).

  1. 10 g/cm³
  2. 4400 g
  3. 12.5 g/cm³
  4. 11 g/cm³ (correct answer)
Explanation: When you encounter density problems involving mixtures, you need to find the weighted average density based on the masses and total volume of the components. First, calculate the mass of each metal using mass=density×volume\text{mass} = \text{density} \times \text{volume}:
  • Metal A: 8 g/cm³×100 cm³=800 g8 \text{ g/cm³} \times 100 \text{ cm³} = 800 \text{ g}
  • Metal B: 12 g/cm³×300 cm³=3600 g12 \text{ g/cm³} \times 300 \text{ cm³} = 3600 \text{ g}
The total mass is 800+3600=4400 g800 + 3600 = 4400 \text{ g}, and the total volume is 100+300=400 cm³100 + 300 = 400 \text{ cm³}. Therefore, the alloy's density is 4400 g400 cm³=11 g/cm³\frac{4400 \text{ g}}{400 \text{ cm³}} = 11 \text{ g/cm³}, making D correct. Choice A (10 g/cm³) represents a simple arithmetic average of the two densities, ignoring that Metal B contributes three times more volume than Metal A. Choice B (4400 g) gives you the total mass rather than density—this catches students who forget to divide by volume. Choice C (12.5 g/cm³) is higher than either individual metal's density, which is impossible since the alloy density must fall between the component densities. Remember that in mixture problems, the resulting density will always be between the individual densities, weighted toward whichever component contributes more mass. Since Metal B has both higher density and greater volume, the alloy density should be closer to 12 g/cm³ than to 8 g/cm³.

Question 10

A lab technician attempts to create 100 mL of an 80% acid solution using two available stock solutions: a 20% acid solution and a 70% acid solution. Which statement correctly identifies a fundamental flaw in the plan based on a reasonableness check, even before any calculations are performed?

  1. The task is impossible because the target concentration of 80% is higher than the concentration of either stock solution. (correct answer)
  2. The calculation would show that the required amount of the 70% solution is more than the total desired volume of 100 mL.
  3. The task is impossible because solving the system of equations results in a negative volume for the 20% solution.
  4. The total amount of acid required, 80 mL, cannot be achieved with the given stock solutions in a 100 mL total volume.
Explanation: When mixing two solutions of different concentrations, the resulting concentration must lie strictly between the concentrations of the two initial solutions. In this case, any mixture of a 20% solution and a 70% solution must have a final concentration between 20% and 70%. The target concentration of 80% is outside this range, so the plan is fundamentally impossible. This reasonableness check can be done without setting up or solving equations.