NFSI Mathematical and Numeric Reasoning Questions and Answers

Question 1

An engine must lay a supply line to a hydrant that is 475 feet away. The engine carries supply hose in 50-foot sections. What is the minimum number of sections the crew must deploy to reach the hydrant?

Accepted Answer

10 sections

Answer

To determine the number of sections, divide the total distance by the length of one section: 475 feet / 50 feet/section = 9.5 sections. Since it's impossible to deploy half a section, the crew must use 10 full sections to ensure the hose reaches the hydrant.

Question 2

A firefighter begins an operation with a full 4,500 psi SCBA cylinder. After 10 minutes of strenuous work, the cylinder's pressure is 3,000 psi. Assuming a constant rate of air consumption, what was the total estimated working air time available from the full cylinder?

Accepted Answer

30 minutes

Answer

First, calculate the amount of air consumed: 4,500 psi - 3,000 psi = 1,500 psi. This consumption occurred over 10 minutes, establishing a rate of 150 psi per minute (1,500 psi / 10 min). To find the total time the full cylinder would last at this rate, divide the total pressure by the consumption rate: 4,500 psi / 150 psi/min = 30 minutes.

Question 3

A fire engine's water tank has a capacity of 750 gallons. If water weighs approximately 8.34 pounds per gallon, what is the total weight of the water in the tank when it is completely full?

Accepted Answer

6,255 lbs

Answer

To find the total weight of the water, multiply the volume of the water in gallons by the weight of one gallon: 750 gallons * 8.34 lbs/gallon = 6,255 lbs.

Question 4

A pump operator needs to supply water to a nozzle at the top of a 5-story building. The required nozzle pressure is 100 psi. There is a pressure loss of 25 psi due to friction in the hose. Additionally, the department calculates a pressure loss of 5 psi for each story of elevation. What is the required pump discharge pressure (PDP)?

Accepted Answer

150 psi

Answer

The total pump discharge pressure (PDP) is the sum of all pressures that must be overcome. This includes Nozzle Pressure (100 psi), Friction Loss (25 psi), and Elevation Loss (5 stories * 5 psi/story = 25 psi). Therefore, the calculation is: 100 + 25 + 25 = 150 psi.

Question 5

A fire crew is preparing to use a 3% foam concentrate to extinguish a flammable liquid fire. They estimate they will need to apply a total of 200 gallons of the finished foam solution. How many gallons of foam concentrate must be mixed with water to create the solution?

Accepted Answer

6 gallons

Answer

A 3% foam solution means that 3% of the total solution's volume is foam concentrate. To calculate the required amount, convert the percentage to a decimal (3% = 0.03) and multiply it by the total volume of the solution: 200 gallons * 0.03 = 6 gallons of foam concentrate.

NFSI - National Firefighter Selection Inventory Practice Test

NFSI - National Firefighter Selection Inventory Practice Test

NFSI Mathematical and Numeric Reasoning Questions and Answers