ISAT - International Student Admissions Quantitative Reasoning with Units Questions and Answers — Questions and Answers
Question 1: A solid rectangular block of aluminum has dimensions of 10 cm, 20 cm, and 50 cm. If the density of aluminum is 2.7 g/cm³, what is the mass of the block in kilograms?
- 2.7 kg
- 27 kg (Correct answer)
- 270 kg
- 27,000 kg
Correct answer: 27 kg
The volume of the rectangular block is calculated by multiplying its dimensions: Volume = 10 cm × 20 cm × 50 cm = 10,000 cm³. The mass is found using the formula Mass = Density × Volume. So, Mass = 2.7 g/cm³ × 10,000 cm³ = 27,000 grams. [9, 19] The question asks for the mass in kilograms. Since 1 kg = 1000 g, we convert grams to kilograms by dividing by 1000: 27,000 g / 1000 = 27 kg.
Question 2: A pump fills a tank at a rate of 50 Liters per minute. The tank has a small leak and loses water at a rate of 250 cubic centimeters per second. What is the net change in the volume of water in the tank over a period of 5 minutes, expressed in Liters?
- 175 L increase (Correct answer)
- 235 L increase
- 250 L increase
- 75 L decrease
Correct answer: 175 L increase
First, make the units consistent. The filling rate is 50 L/min. The leaking rate is 250 cm³/s. To convert the leaking rate to L/min: 250 cm³/s * (1 L / 1000 cm³) * (60 s / 1 min) = 15 L/min. Now calculate the total volume filled and leaked over 5 minutes. Volume filled = 50 L/min × 5 min = 250 L. Volume leaked = 15 L/min × 5 min = 75 L. The net change is the volume filled minus the volume leaked: 250 L - 75 L = 175 L increase.
Question 3: In physics, pressure is defined as force per unit area. The standard unit for pressure is the Pascal (Pa), and the standard unit for force is the Newton (N). Given that 1 Newton is equivalent to 1 kg·m/s², which of the following expressions correctly represents one Pascal in fundamental SI units?
- kg·m² / s²
- kg / (m·s)
- kg / (m·s²) (Correct answer)
- kg·m / s
Correct answer: kg / (m·s²)
Pressure is defined as Force divided by Area (P = F/A). The SI unit for Force (Newton) is kg·m/s². The SI unit for Area is m². Therefore, the unit for Pressure (Pascal) is (kg·m/s²) / m². When you simplify this fraction, one 'm' in the numerator cancels with one 'm' in the denominator, leaving kg / (m·s²).
Question 4: A medication is to be administered at a dosage of 20 milligrams per kilogram of body weight. The medication is available as a solution with a concentration of 50 mg per 2 mL. If a patient weighs 165 pounds, what volume of the solution, in milliliters, should be administered? (Use the approximation 1 kg ≈ 2.2 lbs).
- 30 mL
- 75 mL
- 150 mL
- 60 mL (Correct answer)
Correct answer: 60 mL
Step 1: Convert the patient's weight to kilograms. 165 lbs ÷ 2.2 lbs/kg = 75 kg. [3] Step 2: Calculate the total required dose of the medication. Dosage = 20 mg/kg × 75 kg = 1500 mg. [8] Step 3: Determine the volume of the solution needed. The concentration is 50 mg per 2 mL, which simplifies to 25 mg/mL. Volume = Total dose ÷ Concentration = 1500 mg ÷ 25 mg/mL = 60 mL.
Question 5: A household appliance is rated at 1,500 watts. If the appliance is used for an average of 90 minutes per day, and the cost of electricity is $0.20 per kilowatt-hour (kWh), what is the approximate cost to operate the appliance for 30 days?
- $6.75
- $13.50 (Correct answer)
- $81.00
- $40.50
Correct answer: $13.50
First, convert the power from watts to kilowatts: 1,500 W = 1.5 kW. Next, convert the daily usage time from minutes to hours: 90 minutes = 1.5 hours. Now, calculate the daily energy consumption in kilowatt-hours (kWh): Energy = Power × Time = 1.5 kW × 1.5 hours = 2.25 kWh per day. Over 30 days, the total energy consumption is: 2.25 kWh/day × 30 days = 67.5 kWh. Finally, calculate the total cost: Total Cost = Total Energy × Cost per kWh = 67.5 kWh × $0.20/kWh = $13.50. [13, 10]
Question 6: A satellite travels in a circular orbit at a constant speed of 17,000 miles per hour. If the circumference of its orbit is 26,400 miles, how many minutes does it take for the satellite to complete exactly 4 orbits? (Round to the nearest minute).
- 93 minutes
- 155 minutes
- 272 minutes
- 373 minutes (Correct answer)
Correct answer: 373 minutes
The total distance for 4 orbits is the circumference of one orbit multiplied by 4: 26,400 miles/orbit × 4 orbits = 105,600 miles. To find the time it takes, use the formula Time = Distance / Speed. Time = 105,600 miles / 17,000 miles per hour ≈ 6.212 hours. The question asks for the time in minutes, so convert hours to minutes: 6.212 hours × 60 minutes/hour ≈ 372.7 minutes. Rounding to the nearest minute gives 373 minutes.
ISAT - International Student Admissions Quantitative Reasoning with Units Questions and Answers
A solid rectangular block of aluminum has dimensions of 10 cm, 20 cm, and 50 cm.
If the density of aluminum is 2.7 g/cm³, what is the mass of the block in kilograms?