NATE Math
A technician calculates the bill for a service call to be a total of $269.60. The sales tax rate is 5%. How much is the sales tax for the bill? A: $13.48 B: $14.67 C: $26.96 D: $283.08
A: $13.48 269.60 X .05 = $13.48
The velocity in fpm is equal to the square root of the velocity pressure times the factor 4005. A technician measures a velocity pressure of .25. What is the square root of .25? A: 0.5 B: 0.05 C: 0.025 D: 0.625
A: 0.5
A duct that has a circumference of 31.416" has a diameter of: A: 10" B: 11" C: 12" D: 16.5"
A: 10" Cir = 31.416/Pi Cir = 31.416/3.1416 = 10
How many pounds of water can be heated by 6 degrees with the addition of 72 btu? A: 0.833 B: 12 C: 432 D: 72
B: 12 btu = lbs/wtr X DT lbs/wtr = btu/DT lbs/wtr = 72/6 = 12
Code restricts filling refrigerant cylinders to more than 80% of their total capacity. How many pounds of refrigerant are allowed in a 150 pound capacity cylinder? A: 100 lbs B: 120 lbs C: 125 lbs D: 130 lbs
B: 120 lbs
A clamp-on ammeter reads 20 amperes on a purely resistive circuit and the voltage is 120 volts. What is the wattage in kW? A: 2 kW B: 2.4 kW C: 24 kW D: 240 kW
B: 2.4 kW P = EI P = 120 x 20 = 2400 convert to kW div by 1000 2400/1000 = 2.4
A technician needs to calculate the compression ratio for a system operating with a high side pressure of 200 psig. In order to compute the ratio, the pressure must first be converted to psia. What is the psia equivalent for 200 psig? A: 185 psia B: 215 psia C: 230 psia D: 300 psia
B: 215 psia PSIA = PSIG + 15
The saturation temperature of an evaporator is 40 degrees F. The evaporator uses an external equalized thermostatic expansion valve. The temperature measured at the sensing bulb is 50 degrees F, and the temperature measured 20' away and 6 inches from the compressor's suction service valve is 65° F. What is the superheat of the thermostatic expansion valve? A: 10 degrees B: 15 degrees C: 20 degrees D: 50 degrees
A: 10 degrees
How much heat in btu is required to raise the temperature of a full 30 gallons of water in a water heater from 50 degrees to 100 degrees F? A: 12,495 B: 13,680 C: 15,000 D: 20,000
A: 12,495 (30 x 8.33) x 50 = 12,495
Water weighs 8.33 lbs per gallon, there are 7.5 gallons per cubic foot and one cubic foot of water weighs 62.4 pounds. What is the weight of the water in the tank in problem 20? Assume the tank is full. A: 17,634.24 lbs B: 16,746 lbs C: 8,333 lbs D: 62,400 lbs
A: 17,634.24 lbs wtr wght per cf X 282.6 62.4 X 282.6 = 17,634.24
An evaporator has 1600 CFM of airflow across it and is removing 30,000 btuh of heat. What is the temperature drop of the air across the evaporator? A: 17.36 B: 18.75 C: 19.25 D: 20.5
A: 17.36 BTUH = TD x 1600 x 1.08 30,000 = TD x 1728 TD = 30,000/1728 = 17.36 In reality this formula only works with heating systems. To get a true btuh for an a/c, moisture content of the air must be considered. Without going into the 4 formulas involved, 1.5 in place of 1.08 works good in the field for a/c. Providing indoor temp is between 75 & 85 and around 50% humidity.
A 120 to 24 volt step down control transformer has a VA rating of 48 watts. What is the maximum amperage the transformer should be allowed to draw on the 24 volt side? A: 2 amps B: 2.5 amps C: 5 amps D: 5.5 amps
A: 2 amps 48 = VA 48 = 24 X A A = 48/24 A = 2
How many gallons of water can the tank in problems 20 and 21 hold? A: 2,116.95 gallons B: 2,351.23 gallons C: 833.333 gallons D: None of these is correct
A: 2,116.95 gallons 17634.24lbs/8.33 = 2,116.95 gallons or 282.6 cubic feet X 7.5 = 2119.5 Due to repeating decimals these answers are off a little
The specific heat of air is .24 btu/lb/degree. The density of air is .075 lbs/cubic foot. In the equation, Btuh = 1.08 x CFM x TD, where does the factor 1.08 come from? A: It converts minutes to hours, cubic feet to pounds and includes the specific heat of air. B: It converts minutes to hours, pounds to cubic feet and specific heat to temperature difference. C: It converts cubic feet to cubic inches, specific heat to temperature difference and hours to minutes. D: It is a number used to average out the values and give an approximate answer for the equation.
A: It converts minutes to hours, cubic feet to pounds and includes the specific heat of air.
A motor has a power factor of .69, a voltage rating of 230 volts, 3-phase and an efficiency rating of 88% with an SF rating of 1.15. Which of these ratings relates to the phase angle between the current and the voltage? A: Power factor B: Voltage C: Phase D: SF
A: Power factor
A furnace manufacturer is offering a 20% discount off their normal wholesale price to dealers. If the normal wholesale price is $400.00 what is the discounted price for the furnace? A: $300.00 B: $320.00 C: $325.00 D: $380.00
B: $320.00
A technician has used 50 feet of four conductor thermostat wire from a 500 foot roll. What is the value of the remainder of the wire on the roll if the cost of the wire is 10 cents per foot? A: $25 B: $45 C: $50 D: $55
B: $45
A technician pulls 156 inches of thermostat wire through a crawl space. How many feet of thermostat wire did he pull? A: 15.5 feet B: 13 feet C: 18 feet D: 18.5 feet
B: 13 feet
Electric resistance heaters give off 3.42 btu per watt. How much heat in btuh will an electric resistance space heater give off if it draws 20 amps at 230 volts? A: 12,732 B: 15,732 C: 16,000 D: 18,230
B: 15,732 Power (watts) = Amps x Voltage (20 x 230) x 3.42 = 15,732
What is the size of a supply duct that passes 800 cfm of air at 600 fpm velocity? A: 133 square inches B: 192 square inches C: 239 square inches D: 414 square inches
B: 192 square inches cfm = sqins x fpm 800 = sqft x 600 sqft = 800/600 = 1.333 convert to sqins X 144 1.333 x 144 = 191.9
Assuming a normal comfort cooling application, the average cfm per ton is 400. How many cfm should a 5-ton comfort cooling air conditioning system move through its air system if the system utilizes a 7.5 hp motor at 230 volts, 3-phase and uses a centrifugal blower with a belt drive? A: 1,000 cfm B: 2,000 cfm C: 2,500 cfm D: 3,000 cfm
B: 2,000 cfm
The square root of 25 is: A: 8 B: 5 C: 2.5 D: 12
B: 5 category20quiz:
A hot water heating coil has an actual output of 40,000 btuh and has a water temperature differential of 10 degrees between the supply and return pipes. What is the water flow rate in gpm through the coil? A: 6 gpm B: 8 gpm C: 10 gpm D: 12 gpm
B: 8 gpm btuh = (8.33 x 60mins) x gpm x DT gpm = btuh/((8.33 x 60) x DT)) gpm = 40,000/((500) x 10)) gpm = 40,000/5,000 gpm = 8
How many degrees are in a quarter of a circle? A: 180 B: 90 C: 60 D: 45
B: 90
The number on the top of a fraction is called: A: Quotient B: Numerator C: Denominator D: Divisor
B: Numerator
A technician purchases a gallon of POE oil for $120. The technician uses one quart of the oil on a job. The profit mark-up to be applied is 2 times the cost. How much is the marked up cost of the quart of oil? A: $15.00 B: $30.00 C: $60.00 D: $120.00
C: $60.00
A technician clocked a furnace as using 40 cubic feet of natural gas in 60 minutes. How many cubic feet did the furnace use per minute? A: .5 cubic feet per minute B: 5.5 cubic feet per minute C: .66 cubic feet per minute D: 6.6 cubic feet per minute
C: .66 cubic feet per minute
A technician is using a U-tube manometer to measure a pressure differential. One side of the U-tube water level is at .75". The opposite side of the U-tube reads .75". What is the pressure differential in inches? A: .75" B: 1.25" C: 1.5" D: 1.75"
C: 1.5"
Acme Heating's new service van used 18 gallons of fuel and traveled 200 miles. What is the gas mileage for the new van? A: 8 mpg B: 10 mpg C: 11 mpg D: 12 mpg
C: 11 mpg
One ton of cooling is at a rate of 12,000 btuh. How many btu per day is this? Use a 24-hour day as a normal day. A: 200 B: 200,000 C: 288,000 D: 300,000
C: 288,000
Using the internal volume from the previous if the density of air is .075 lbs per cubic foot, what is the weight of the air in the building? A: 37.5 lbs B: 375. lbs C: 3,750 lbs D: 37,750 lbs
C: 3,750 lbs 50,000 x .075 = 3,750 lbs
A compressor operates with a high side pressure of 100 psig and a low side pressure of 10 psig. What is the compression ratio for the compressor? A: 10:01 B: 8:01 C: 4.6:1 D: 2.5:1
C: 4.6:1 (100 + 15)/(10 + 15) = CR converts psig to psia 115/25 = 4.6
A duct measures 24" high by 36" wide. How many square feet of duct area are there? A: 3 square feet B: 4 square feet C: 6 square feet D: 8 square feet
C: 6 square feet (24 x 36)/144 = 6
The volume of a theatre is 100,000 cubic feet. Standard air has a volume of 13.33 cubic feet per pound and a density of .075 lbs per cubic foot. What is the weight of the air in the theater? A: 750 lbs B: 133.3 lbs C: 7,500 lbs D: 13,300 lbs
C: 7,500 lbs 100,000 x .075 = 7,500 lbs or 100,000/13.33 = 7,500 lbs
A heating system has an input of 100,000 btuh with an output of 75,000 btuh. What is its efficiency in percent? A: 100% B: 80% C: 75% D: 70%
C: 75% Output/Input X 100 = % 75,000/100,000 X 100 = % .75 X 100 = 75%
A boiler with an input of 120,000 btuh and which has an output of 102,000 btuh has a numerical efficiency of: A: 75% B: 80% C: 85% D: 90%
C: 85% (102,000/120,000) x 100
A motor operating a blower has a belt drive system. The motor pulley is 6 inches in diameter and operates at 1800 rpm. The blower pulley diameter is 12 inches. What is the rpm of the blower? A: 3600 rpm B: 1800 rpm C: 900 rpm D: 800 rpm
C: 900 rpm RPM blower = (6 X 1800)/12 RPM blower = 10800/12 RPM blower = 900 rpm
Convert minus 40 degrees Fahrenheit to Centigrade: A: 40 B: 20 C: -20 D: -40
D: -40 .56 x (F - 32) = C .56 x (-40 -32) = C .56 x (-72) = C -40.32 = C
The U value of a wall is the reciprocal of the R value. A wall with an R value of 10 has just had enough insulation added to increase the R value by 5. What is the new U value of the wall to two decimal places? A: 15 B: 5 C: 0.66 D: 0.06
D: 0.06 1/15 = .06
A typical frame wall is constructed of the following materials where the individual R values for each material is known. i. Outside air film R = .17 ii. Wood siding R = .85 iii. Sheathing R = 2.06 iv. Air space R = .97 v. Plaster board R = .41 vi. Inside air film R = .68 The U value for this wall is: A: 5.14 B: 4.27 C: 0.27 D: 0.19
D: 0.19 1 --------------------------------------- = U value R1 + R2 + R3 + R4 + R5 + R6
A technician measures an air velocity of 400 fpm through a duct that measures 24-inches square. What is the airflow quantity in CFM? A: 400 cfm B: 600 cfm C: 800 cfm D: 1,600 cfm
D: 1,600 cfm cfm = ((24 x 24)/144) x 400 cfm = (576/144) x 400 cfm = 4 x 400 = 1,600
What is the volume of a cylindrical water tank that is 6 feet in diameter and 10 feet tall? A: 826.2 cubic feet B: 826.2 cubic inches C: 600 cubic inches D: 282.6 cubic feet
D: 282.6 cubic feet V = R(sq) X 3.14 X H V = 3(sq) X 3.14 X 10 V = 9 X 3.14 X 10 = 282.6
The decimal equivalent of the mixed fraction 3 7⁄8 is: A: 3.125 B: 3.375 C: 3.75 D: 3.875
D: 3.875 7/8 = .875 + 3 = 3.875
Air balancing reports generally round off all cfm air flow rates to the nearest 5 cfm. An airflow measurement of 348.3 cfm will then be rounded off to which of the following? A: 340 cfm B: 345 cfm C: 348 cfm D: 350 cfm
D: 350 cfm
Increasing a duct diameter from 4 inches to 8 inches will increase its area by: A: 2 times B: 2.5 times C: 3 times D: 4 times
D: 4 times Area = R(sq) X 3.14 Area = 2sq x 3.14 = 12.56 Area = 4sq x 3.14 = 50.24 50.24/12.56 = 4
The internal dimensions of a building are 10 feet high, 100 feet long and 50 feet wide. How many cubic feet of air are contained in the building? A: 500 cubic feet B: 750 cubic feet C: 5000 cubic feet D: 50,000 cubic feet
D: 50,000 cubic feet Cubic ft = W x L x H Cubic ft = 50 x 100 x 10 Cubic ft = 50,000
A 5-ton air conditioning system has a btuh capacity of: A: 40,000 B: 45,000 C: 50,000 D: 60,000
D: 60,000
It took two installers 10 hours total to install a new air conditioning system in the first of several homes going into a new tract. Every home is identical so the rest of the installations will be identical. If the two installers can reduce their installation time by 10%, how many hours should it take them per install? A: 6 hours B: 7 hours C: 8 hours D: 9 hours
D: 9 hours
There are 746 watts per horsepower. How many horsepower are there per watt? A: 0.746 B: 7.46 C: 74.6 D: none of these
D: none of these
The number on the bottom of a fraction is called:
Denominator
