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

Question 1. Numbers & Algebra easy

At a community blood drive, 3/8 of the 240 donors who registered were first-time donors. How many of the registered donors were first-time donors?

• A. 90 (correct)
• B. 80
• C. 96
• D. 72

Explanation: Multiply 240 donors by 3/8: 240 x 3/8 = 90. First-time donors made up three of every eight people who registered, so 90 of the 240 registered donors were first-time donors.

Question 2. Numbers & Algebra easy

Which decimal is equal to 3/25?

• A. 0.15
• B. 0.12 (correct)
• C. 0.32
• D. 0.75

Explanation: Divide 3 by 25 to convert the fraction: 3 / 25 = 0.12. Since 3/25 is under 1/4 (0.25), options such as 0.32 and 0.75 are too large, so 0.12 is correct.

Question 3. Numbers & Algebra easy

If y - 12.5 = 9.75, what is the value of y?

• A. 21.75
• B. 22.5
• C. 22.25 (correct)
• D. 20.25

Explanation: Add 12.5 to both sides to isolate y: y = 9.75 + 12.5, so y = 22.25. Checking, 22.25 - 12.5 = 9.75, which matches the equation, so 22.25 is the value of y.

Question 4. Numbers & Algebra easy

Evaluate: 15 - (8 - 3) x 2.

• A. 13
• B. 1
• C. 8
• D. 5 (correct)

Explanation: Work inside the parentheses first: 8 - 3 = 5. Then multiply: 5 x 2 = 10. Finally subtract: 15 - 10 = 5. Following order of operations gives 5, not the values from skipping parentheses.

Question 5. Numbers & Algebra medium

In January a clinic saw 400 patients; in February it saw 460. By what percent did patient visits increase?

• A. 15% (correct)
• B. 12%
• C. 18%
• D. 6%

Explanation: Find the increase first: 460 - 400 = 60 visits. Then divide the increase by the original amount: 60 / 400 = 0.15, which is 15%. Percent increase compares the change to the starting value, not to the new value.

Question 6. Numbers & Algebra medium

Solve for x: 4(x - 3) = 2x + 6.

• A. 6
• B. 9 (correct)
• C. 12
• D. 3

Explanation: Distribute on the left: 4x - 12 = 2x + 6. Subtract 2x from both sides: 2x - 12 = 6. Add 12: 2x = 18. Divide by 2: x = 9. Check: 4(9 - 3) = 24 and 2(9) + 6 = 24, so x = 9.

Question 7. Numbers & Algebra medium

A pharmacy buys a carton of 60 syringes for $42.00 and sells each syringe for $1.10. What is the profit on the whole carton?

• A. $18
• B. $22
• C. $24 (correct)
• D. $28

Explanation: Total selling price is 60 x $1.10 = $66.00. Subtract the purchase cost: $66.00 - $42.00 = $24.00. The profit is the difference between the revenue from all 60 syringes and the cost of the carton.

Question 8. Numbers & Algebra medium

A gardener plants a 480-square-foot plot: 1/3 with tomatoes, 1/4 with peppers, and the rest with herbs. How many square feet are planted with herbs?

• A. 160
• B. 140
• C. 120
• D. 200 (correct)

Explanation: Tomatoes take 1/3 of 480 = 160 sq ft, and peppers take 1/4 of 480 = 120 sq ft. Together that is 280 sq ft, so herbs fill 480 - 280 = 200 sq ft. The herb area is the leftover portion of the plot.

Question 9. Numbers & Algebra medium

A technician earns $18.50 per hour and works 38.5 hours in a week. What is the gross pay for the week before deductions?

• A. $712.25 (correct)
• B. $711.50
• C. $708.75
• D. $703.00

Explanation: Multiply the hourly rate by the hours worked: $18.50 x 38.5 = $712.25. The technician earns $18.50 for each of the 38.5 hours, so gross pay is 38.5 times the hourly rate, which is $712.25 before any deductions.

Question 10. Numbers & Algebra medium

The product of 4 x 10^5 and 3 x 10^-3 is equal to which of the following?

• A. 120
• B. 1200 (correct)
• C. 12000
• D. 12

Explanation: Multiply the coefficients: 4 x 3 = 12, and add the exponents of 10: 5 + (-3) = 2, giving 12 x 10^2. Since 12 x 100 = 1,200, the product is 1,200. Getting 120 would mean subtracting exponents instead of adding them.

Question 11. Numbers & Algebra medium

A commuter drives 45 mph for 2 hours and then 60 mph for 1 hour. What is the average speed for the whole trip in mph?

• A. 52.5
• B. 47.5
• C. 50 (correct)
• D. 55

Explanation: Total distance is 45 x 2 = 90 miles plus 60 x 1 = 60 miles, giving 150 miles over 3 hours. Average speed is 150 / 3 = 50 mph. A plain average of 45 and 60 gives 52.5 but ignores the longer time at the lower speed.

Question 12. Numbers & Algebra hard

A town's population grows by 10% in year one and then by 10% again in year two, starting from 5,000. What is the population after two years?

• A. 6000
• B. 6100
• C. 5500
• D. 6050 (correct)

Explanation: After the first year the population is 5,000 x 1.10 = 5,500. After the second year it is 5,500 x 1.10 = 6,050. Each 10% increase applies to the new population, so growth compounds instead of adding a flat 1,000.

Question 13. Numbers & Algebra hard

A student has $60 to spend on supplies. Pens cost $2.50 each and one notebook costs $14. If the student buys exactly one notebook, how many pens can be bought at most?

• A. 18 (correct)
• B. 19
• C. 17
• D. 16

Explanation: After buying the notebook, the student has $60 - $14 = $46 left. Each pen costs $2.50, so $46 / $2.50 = 18.4. Only whole pens can be bought, so the maximum is 18 pens; a 19th pen would cost more than the remaining money.

Question 14. Numbers & Algebra hard

The sum of a mother's age and her daughter's age is 60. The mother is 4 times as old as the daughter. How old is the daughter?

• A. 15
• B. 12 (correct)
• C. 20
• D. 48

Explanation: Let d be the daughter's age. The mother's age is 4d, and d + 4d = 60, so 5d = 60 and d = 12. The daughter is 12 and the mother is 48, which gives a sum of 60 and a mother four times as old as the daughter.

Question 15. Numbers & Algebra hard

A tank is 1/3 full of water. After 40 liters are added, it is 7/9 full. What is the capacity of the tank in liters?

• A. 120
• B. 75
• C. 90 (correct)
• D. 60

Explanation: Let the tank hold x liters. Since 1/3 = 3/9, adding 40 L changes the fill from 3x/9 to 7x/9, so 40 = 4x/9. Multiply by 9 and divide by 4: x = 90. Check: 90/3 + 40 = 70, and 7/9 of 90 is 70, so 90 is correct.

Question 16. Numbers & Algebra hard

The price of a procedure after a 6% sales tax was $318.00. What was the price before tax?

• A. $298.92
• B. $312
• C. $288
• D. $300 (correct)

Explanation: The tax multiplies the price by 1.06, so $318 = 1.06 x p. Dividing: p = 318 / 1.06 = 300. Checking, 300 x 0.06 = 18 in tax and 300 + 18 = 318, which confirms the price before tax was $300.

Question 17. Measurement & Data easy

A wheelchair ramp measures 2.5 meters. How many centimeters is that? (1 m = 100 cm)

• A. 250 (correct)
• B. 25
• C. 2500
• D. 0.25

Explanation: Multiply meters by 100 to convert to centimeters: 2.5 x 100 = 250. Since one meter is 100 centimeters, a 2.5-meter ramp is 250 centimeters; a value like 25 cm would be only a quarter of a meter.

Question 18. Measurement & Data easy

A procedure begins at 10:40 AM and lasts 1 hour 25 minutes. What time does it end?

• A. 11:05 AM
• B. 12:05 PM (correct)
• C. 1:05 PM
• D. 12:15 PM

Explanation: Add the duration to the start time: 10:40 AM plus 1 hour is 11:40 AM, then add 25 more minutes, which gives 12:05 PM. The procedure crosses the noon hour, so the end time is 12:05 PM, not an AM time.

Question 19. Measurement & Data medium

The table shows walk-in visits at an eye clinic over four days: Day Visits Monday 14 Tuesday 18 Wednesday 12 Thursday 16 What is the mean number of walk-in visits per day?

• A. 14
• B. 16
• C. 15 (correct)
• D. 13

Explanation: Add the four daily counts: 14 + 18 + 12 + 16 = 60 visits. Divide by the number of days, 4, to find the mean: 60 / 4 = 15. The mean walk-in count is 15 visits per day across the four recorded days.

Question 20. Measurement & Data medium

A clinic's parking log for one day shows 24 staff cars, 36 patient cars, and 20 visitor cars. What percent of the cars were patient cars?

• A. 40%
• B. 50%
• C. 36%
• D. 45% (correct)

Explanation: The total number of cars is 24 + 36 + 20 = 80. Patient cars make up 36 / 80 = 0.45, which is 45%. To get a percentage from a table, divide the category count by the total and multiply by 100.

Question 21. Measurement & Data medium

A cube-shaped storage block has edges of 5 cm. What is its volume in cubic centimeters?

• A. 125 (correct)
• B. 25
• C. 100
• D. 150

Explanation: The volume of a cube is the side length cubed: 5 cm x 5 cm x 5 cm = 125 cubic centimeters. Using 5 x 5 = 25 would give only the area of one face, so 125 cubic cm accounts for length, width, and height.

Question 22. Measurement & Data medium

A thermometer shows 36.5 degrees C. Using the formula F = (9/5)C + 32, what is the reading in degrees F?

• A. 98.6
• B. 97.7 (correct)
• C. 96.8
• D. 99.1

Explanation: Substitute into F = (9/5)C + 32: (9/5) x 36.5 = 65.7, then add 32, giving 97.7 degrees F. The familiar body temperature 98.6 comes from 37 degrees C, not from the 36.5 shown on this thermometer.

Question 23. Measurement & Data medium

A pump delivers 45 drops per minute, and 15 drops equal 1 mL. How many mL are delivered in 20 minutes?

• A. 75
• B. 45
• C. 60 (correct)
• D. 90

Explanation: In 20 minutes the pump delivers 45 x 20 = 900 drops. Since 15 drops equal 1 mL, divide: 900 / 15 = 60 mL. This is a two-step conversion: first find the total drops, then convert drops to milliliters.

Question 24. Measurement & Data medium

A staff training video runs 3 hours and 15 minutes. How many seconds is the video?

• A. 10800
• B. 11850
• C. 11500
• D. 11700 (correct)

Explanation: Each hour has 3,600 seconds, so 3 hours is 10,800 seconds, and 15 minutes is 15 x 60 = 900 seconds. Adding gives 10,800 + 900 = 11,700 seconds total for the video.

Question 25. Measurement & Data medium

The frequency table shows how many clinic visits patients reported last year: Visits 0 1 2 3 4 Patients 8 12 15 10 5 What is the total number of visits reported?

• A. 92 (correct)
• B. 90
• C. 88
• D. 95

Explanation: Multiply each visit count by its frequency: 1 x 12 = 12, 2 x 15 = 30, 3 x 10 = 30, and 4 x 5 = 20. Adding these products gives 12 + 30 + 30 + 20 = 92 visits. Frequencies must weight the counts.

Question 26. Measurement & Data medium

A roll of medical tape is 1.6 m long and is cut into strips of 20 cm each. How many strips can be cut from the roll?

• A. 16
• B. 8 (correct)
• C. 10
• D. 12

Explanation: Convert the roll length to centimeters: 1.6 m = 160 cm. Divide by the strip length: 160 / 20 = 8 strips. Converting to matching units first prevents the wrong answers that come from dividing 1.6 by 20 directly.

Question 27. Measurement & Data hard

A round fountain with radius 3 m is centered in a circular plaza of radius 5 m. Using 3.14 for pi, what is the area of the plaza that is not covered by the fountain?

• A. 78.5
• B. 28.26
• C. 50.24 (correct)
• D. 62.8

Explanation: Find the plaza area: 3.14 x 5^2 = 78.5 sq m, and the fountain area: 3.14 x 3^2 = 28.26 sq m. Subtract the fountain from the plaza: 78.5 - 28.26 = 50.24 sq m. The uncovered ring is the difference of the two circle areas.

Question 28. Measurement & Data hard

A container holds 3.75 L of saline. If 3/5 of it is used, how many milliliters remain?

• A. 2250
• B. 1250
• C. 1000
• D. 1500 (correct)

Explanation: If 3/5 of the container is used, then 2/5 remains: 2/5 of 3.75 L = 1.5 L. Convert liters to milliliters: 1.5 x 1,000 = 1,500 mL. The 2,250 option is the amount used, not the amount remaining.

Question 29. Measurement & Data hard

A paper cup is shaped like a cone with a radius of 3 cm and a height of 4 cm. Using 3.14 for pi, what is the volume of the cup in cubic centimeters? (Volume of a cone = 1/3 x pi x r^2 x h)

• A. 37.68 (correct)
• B. 113.04
• C. 50.24
• D. 75.36

Explanation: The volume of a cone is 1/3 x pi x r^2 x h. With r = 3, r^2 = 9, so pi x r^2 x h = 3.14 x 9 x 4 = 113.04, and one third of that is 37.68 cubic cm. Forgetting to divide by 3 gives 113.04, the most common error.

Question 30. Measurement & Data hard

A rectangular pool is 8 m by 5 m with a uniform depth of 1.5 m. How many liters does it hold? (1 cubic meter = 1,000 L)

• A. 6000
• B. 60000 (correct)
• C. 600
• D. 600000

Explanation: The volume of the pool is 8 x 5 x 1.5 = 60 cubic meters. Since 1 cubic meter holds 1,000 liters, the pool holds 60 x 1,000 = 60,000 liters. Forgetting the cubic-meter-to-liter conversion gives the smaller answers.