Free TEAS 7 Math Practice Test 10 — 30 Questions With Full Explanations

Question 1. Numbers & Algebra easy

A courier truck averages 18 miles per gallon. How many gallons of fuel are needed for a 270-mile delivery route?

• A. 15 (correct)
• B. 12
• C. 18
• D. 20

Explanation: The route needs 270 miles divided by 18 miles per gallon, which is 15 gallons. 12 gallons covers only 216 miles, 18 gallons covers 324 miles, and 20 gallons covers 360 miles, so 15 is the only exact amount.

Question 2. Numbers & Algebra easy

A warehouse worker earns $17.25 per hour and works 32 hours this week. What is the gross pay for the week?

• A. $544.00
• B. $552.00 (correct)
• C. $560.00
• D. $536.00

Explanation: Gross pay is the hourly rate times hours worked: 32 x $17.25 = $552.00. $544.00 uses a $17.00 rate, $560.00 uses a $17.50 rate, and $536.00 uses a $16.75 rate, so none match the real rate.

Question 3. Numbers & Algebra easy

A muffin recipe uses 1.5 cups of oats to make 12 muffins. At the same ratio, how many cups of oats are needed for 30 muffins?

• A. 4.5
• B. 3.25
• C. 3.75 (correct)
• D. 4.0

Explanation: Scaling from 12 to 30 muffins is a factor of 30/12 = 2.5. Multiplying the oats by that factor gives 1.5 x 2.5 = 3.75 cups. 4.5 cups corresponds to 36 muffins, 4.0 cups to 32, and 3.25 cups to 26.

Question 4. Numbers & Algebra medium

A savings bond earns 4% simple interest per year. If $1,250 is deposited, what is the total value after 3 years?

• A. $1,500.00
• B. $1,390.00
• C. $1,410.00
• D. $1,400.00 (correct)

Explanation: Simple interest for 3 years is 4% x $1,250 x 3 = $150. Adding this to the deposit gives a total of $1,250 + $150 = $1,400.00. $1,500 would require $250 of interest, which is 3 years at about 6.7%.

Question 5. Numbers & Algebra medium

An order calls for 1.2 mg of a medication that is available as 0.4 mg per 1 mL. How many milliliters should be drawn up?

• A. 3 (correct)
• B. 2
• C. 4
• D. 2.5

Explanation: The dose needed is 1.2 mg, and each milliliter provides 0.4 mg, so the volume is 1.2 / 0.4 = 3 mL. Two milliliters would provide only 0.8 mg, and 4 mL would provide 1.6 mg, which is more than ordered.

Question 6. Numbers & Algebra medium

A freight shipment is made up of 24 cartons, and each carton weighs 38.5 lb. What is the total weight of the shipment?

• A. 912 lb
• B. 924 lb (correct)
• C. 930 lb
• D. 918 lb

Explanation: Total weight is the number of cartons times the weight of each carton: 24 x 38.5 = 924 lb. 912 lb would need each carton to weigh 38.0 lb, and 930 lb would require 38.75 lb per carton.

Question 7. Numbers & Algebra medium

An inventory total is reduced by 15%, and the new total is 68 units. What was the original total?

• A. 77
• B. 82
• C. 80 (correct)
• D. 75

Explanation: After a 15% reduction the new total is 85% of the original, so 0.85 x original = 68. Dividing gives 68 / 0.85 = 80 units. Checking: a 15% cut of 80 removes 12 units, leaving 68.

Question 8. Numbers & Algebra medium

A case of 24 bottles of disinfectant costs $54.00. At the same unit price, what would a case of 40 bottles cost?

• A. $86.00
• B. $96.00
• C. $94.00
• D. $90.00 (correct)

Explanation: The unit price is $54.00 / 24 = $2.25 per bottle. A case of 40 bottles would then cost 40 x $2.25 = $90.00. $96.00 would mean $2.40 per bottle and $86.00 would mean $2.15 per bottle.

Question 9. Numbers & Algebra medium

Solve for x: 3(2x - 5) = 2(x + 5) + 11.

• A. 9 (correct)
• B. 7
• C. 11
• D. 8

Explanation: Expand both sides: 6x - 15 = 2x + 10 + 11, which simplifies to 6x - 15 = 2x + 21. Moving terms gives 4x = 36, so x = 9. Checking: 3(18 - 5) = 39 and 2(14) + 11 = 39, so both sides match.

Question 10. Numbers & Algebra medium

A department's overtime budget is $3,600. Each overtime hour costs $45. How many overtime hours does the budget cover?

• A. 75
• B. 80 (correct)
• C. 90
• D. 85

Explanation: Divide the budget by the cost per hour: $3,600 / $45 = 80 overtime hours. At $45 per hour, 75 hours would cost $3,375 and 90 hours would cost $4,050, which exceeds the budget.

Question 11. Numbers & Algebra medium

A delivery truck uses 12.5 gallons of fuel to travel 287.5 miles. What is the truck's fuel economy in miles per gallon?

• A. 25
• B. 21
• C. 23 (correct)
• D. 24

Explanation: Fuel economy is distance divided by fuel used: 287.5 / 12.5 = 23 miles per gallon. At 25 mpg the same fuel would cover 312.5 miles, and at 21 mpg it would cover only 262.5 miles.

Question 12. Numbers & Algebra hard

A nurse is 7 years older than twice her intern's age. The sum of their ages is 46. How old is the intern?

• A. 12
• B. 15
• C. 11
• D. 13 (correct)

Explanation: Let the intern's age be x. The nurse's age is 2x + 7, and the sum is x + (2x + 7) = 46, so 3x = 39 and x = 13. Then the nurse is 33, and 13 + 33 = 46, which confirms the answer.

Question 13. Numbers & Algebra hard

Machine A labels 90 vials per hour and machine B labels 60 vials per hour. Working together, how many minutes will it take to label 450 vials?

• A. 180 (correct)
• B. 150
• C. 120
• D. 200

Explanation: Together the machines label 90 + 60 = 150 vials per hour. At that combined rate, 450 vials take 450 / 150 = 3 hours, which equals 180 minutes. 150 minutes is only 375 vials at the combined rate.

Question 14. Numbers & Algebra hard

A clinic pays $3,060 for equipment after receiving a 15% discount. What was the original price before the discount?

• A. $3,500.00
• B. $3,600.00 (correct)
• C. $3,520.00
• D. $3,650.00

Explanation: After a 15% discount the clinic paid 85% of the original price, so 0.85 x original = $3,060. Dividing gives $3,060 / 0.85 = $3,600.00. A 15% discount on $3,600 removes $540, leaving exactly $3,060.

Question 15. Numbers & Algebra hard

A tank holds 600 L of fluid and is currently 25% full. How many liters must be added to bring the level up to 75%?

• A. 250
• B. 450
• C. 300 (correct)
• D. 350

Explanation: The level must rise from 25% to 75%, a change of 50% of the tank. Half of 600 L is 300 L, so 300 liters must be added. Adding 250 L would only reach about 66.7%, and 450 L would overflow past 75%.

Question 16. Numbers & Algebra hard

Which value is equal to (2.4 x 10^3) + (6 x 10^2)?

• A. 3.0 x 10^2
• B. 3.0 x 10^4
• C. 2.46 x 10^3
• D. 3.0 x 10^3 (correct)

Explanation: Write both terms in standard form: 2.4 x 10^3 = 2,400 and 6 x 10^2 = 600. Adding them gives 3,000, which in scientific notation is 3.0 x 10^3. 3.0 x 10^2 equals only 300, far too small.

Question 17. Measurement & Data easy

A service van carries 2.5 gallons of reserve fuel for a long route. How many pints of reserve fuel is that? (1 gallon = 8 pints)

• A. 20 (correct)
• B. 16
• C. 24
• D. 18

Explanation: Each gallon equals 8 pints, so 2.5 gallons equals 2.5 x 8 = 20 pints. Sixteen pints would be only 2 gallons, and 24 pints would be 3 gallons, so 20 pints is the correct conversion.

Question 18. Measurement & Data easy

A loading crew starts a job at 7:30 AM and finishes at 11:45 AM. How many minutes does the job take?

• A. 225
• B. 255 (correct)
• C. 240
• D. 270

Explanation: From 7:30 to 11:30 is 4 hours, which is 240 minutes, and the remaining quarter hour adds 15 minutes for a total of 255 minutes. 240 minutes ignores the extra quarter hour, and 270 minutes would be 4.5 hours.

Question 19. Measurement & Data easy

Four fuel stops on a trip used 8.5, 6.0, 7.5, and 10.0 gallons. What is the mean amount of fuel used per stop?

• A. 7.5
• B. 8.5
• C. 8.0 (correct)
• D. 7.0

Explanation: Add the four amounts: 8.5 + 6.0 + 7.5 + 10.0 = 32.0 gallons. Dividing by the number of stops gives 32.0 / 4 = 8.0 gallons per stop. The value 8.5 is just the largest single reading, not the mean.

Question 20. Measurement & Data medium

Weekly shipping volumes for seven weeks were 62, 48, 55, 71, 58, 64, and 49 packages. What is the median volume?

• A. 62
• B. 55
• C. 64
• D. 58 (correct)

Explanation: Sort the volumes: 48, 49, 55, 58, 62, 64, 71. With seven values the median is the fourth, which is 58 packages. The values 62, 55, and 64 are above or below the middle of the sorted list.

Question 21. Measurement & Data medium

A fire station's response coverage is a circular area with a radius of 5 km. Using 3.14 for pi, what is the area of the coverage zone?

• A. 78.5 km^2 (correct)
• B. 31.4 km^2
• C. 25.0 km^2
• D. 157.0 km^2

Explanation: The area of a circle is pi times the radius squared: 3.14 x 5 x 5 = 78.5 square kilometers. The value 31.4 uses the radius once instead of squaring it, and 25.0 is just the radius squared with no pi factor.

Question 22. Measurement & Data medium

An overnight courier shipped 35 packages on Monday, 42 on Tuesday, 38 on Wednesday, 45 on Thursday, and 40 on Friday. How many more packages were shipped on Thursday than on Monday?

• A. 7
• B. 10 (correct)
• C. 5
• D. 8

Explanation: Thursday's total was 45 packages and Monday's was 35, so the difference is 45 - 35 = 10 packages. Seven is the difference between Tuesday and Monday, and 5 is the difference between Friday and Monday.

Question 23. Measurement & Data medium

A warehouse received 200 units, and 8 were damaged in transit. What percent of the units were damaged?

• A. 8%
• B. 2%
• C. 4% (correct)
• D. 6%

Explanation: The damaged portion is 8 out of 200, which is 8 / 200 = 0.04, or 4%. Since 200 is twice 100, the fraction is half of 8%, which confirms 4% rather than 8% for the whole shipment.

Question 24. Measurement & Data medium

A cooler holds 6 juice boxes and 4 water bottles. One drink is chosen at random. What is the probability that it is a water bottle?

• A. 3/5
• B. 1/2
• C. 1/4
• D. 2/5 (correct)

Explanation: There are 10 drinks total, and 4 of them are water bottles, so the probability is 4/10, which reduces to 2/5. The value 3/5 would be the probability of choosing a juice box instead of water.

Question 25. Measurement & Data medium

On a hiking trail map, 1 inch represents 6 miles. A trail measures 3.25 inches on the map. How many miles long is the trail?

• A. 19.5 (correct)
• B. 21.0
• C. 18.0
• D. 16.25

Explanation: Each inch on the map is 6 real miles, so 3.25 inches equals 3.25 x 6 = 19.5 miles. The value 16.25 incorrectly multiplies 3.25 by 5, and 21.0 would require 3.5 inches on the map.

Question 26. Measurement & Data medium

A cargo box measures 1.2 m by 0.8 m by 0.5 m. What is the volume of the box in cubic meters?

• A. 0.58
• B. 0.48 (correct)
• C. 0.4
• D. 0.52

Explanation: Volume of a rectangular box is length times width times height: 1.2 x 0.8 x 0.5 = 0.48 cubic meters. The value 0.4 ignores the third dimension, and 0.58 does not come from any product of the three sides.

Question 27. Measurement & Data hard

A triangular roof gable has a base of 10 m and a height of 4 m. The house has two identical gables. What is the total area of the two gables?

• A. 20
• B. 80
• C. 40 (correct)
• D. 60

Explanation: One triangle has area (1/2) x base x height = (1/2) x 10 x 4 = 20 square meters. With two identical gables, the total area is 2 x 20 = 40 square meters. The value 20 counts only a single gable.

Question 28. Measurement & Data hard

A cylindrical fuel tank has a radius of 1.5 m and a height of 2 m. Using 3.14 for pi, what is the capacity of the tank in liters? (1 m^3 = 1,000 L)

• A. 1,413
• B. 141,300
• C. 7,065
• D. 14,130 (correct)

Explanation: Volume is pi x radius squared x height: 3.14 x 1.5 x 1.5 x 2 = 14.13 cubic meters. Since 1 cubic meter is 1,000 liters, the capacity is 14.13 x 1,000 = 14,130 liters. The value 1,413 is off by a factor of ten.

Question 29. Measurement & Data hard

A contractor charges $100 per hour plus $305 for parts. The total bill for a job was $1,005. How many hours did the job take?

• A. 7 (correct)
• B. 6
• C. 8
• D. 9

Explanation: Subtract the parts cost from the total: $1,005 - $305 = $700 for labor. At $100 per hour, that labor covers $700 / $100 = 7 hours. Six hours would total only $905, and 8 hours would total $1,105.

Question 30. Measurement & Data hard

A flight departs New York at 3:00 PM Eastern Time and lands in Chicago 2 hours later. Chicago is on Central Time, which is 1 hour behind Eastern Time. What is the local arrival time in Chicago?

• A. 5:00 PM
• B. 4:00 PM (correct)
• C. 3:00 PM
• D. 6:00 PM

Explanation: The flight arrives at 3:00 PM + 2 hours = 5:00 PM Eastern Time. Converting to Central Time, which is 1 hour earlier, gives 4:00 PM local time in Chicago. The value 5:00 PM is the Eastern Time arrival before conversion.