ISAT - International Student Admissions Quantitative Reasoning with Units 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?

Accepted Answer

27 kg

Answer

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?

Accepted Answer

175 L increase

Answer

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?

Accepted Answer

kg / (m·s²)

Answer

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).

Accepted Answer

60 mL

Answer

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?

Accepted Answer

$13.50

Answer

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]

ISAT - International Student Admissions Test Practice Test

ISAT - International Student Admissions Test Practice Test

ISAT - International Student Admissions Quantitative Reasoning with Units Questions and Answers