Free TEAS 7 Math Practice Test 6 — 30 Questions With Full Explanations

Question 1. Numbers & Algebra easy

A bakery produces 72 loaves of bread each morning, and 5/8 are sold before noon. How many loaves are sold before noon?

• A. 36
• B. 40
• C. 45 (correct)
• D. 27

Explanation: 5/8 of 72 is found by dividing 72 by the denominator 8, giving 9 loaves per eighth, then multiplying by the numerator 5: 9 x 5 = 45. The distractors come from 3/8 (27), half (36), and 5/9 (40).

Question 2. Numbers & Algebra easy

A warehouse ships 240 packages in a day, and 15% of them go by overnight courier. How many packages go by overnight courier?

• A. 24
• B. 36 (correct)
• C. 45
• D. 60

Explanation: 15% of 240 means 0.15 x 240 = 36 packages. 24 is 10% of 240, 45 is 18.75% of 240, and 60 is 25%. Converting the percent to a decimal before multiplying, then checking that the answer is smaller than 240, avoids the common decimal-place slips.

Question 3. Numbers & Algebra easy

Evaluate: 7 x 4 - 18 / 3 + 5.

• A. 27 (correct)
• B. 33
• C. 15
• D. 21

Explanation: Order of operations requires multiplication and division before addition and subtraction: 7 x 4 = 28 and 18 / 3 = 6, so 28 - 6 + 5 = 27. 33 adds 6 and 5 before subtracting, 15 drops the 18 / 3 term, and 21 multiplies 7 by 3 instead of 4.

Question 4. Numbers & Algebra medium

A juice bar makes 120 smoothies in a day. Of these, 3/5 contain fruit, and 1/6 of the fruit smoothies also contain protein powder. How many smoothies contain protein powder?

• A. 20
• B. 24
• C. 36
• D. 12 (correct)

Explanation: Work the compound fraction in two steps: 3/5 of 120 is 72 fruit smoothies, then 1/6 of 72 is 72 / 6 = 12 smoothies with protein powder. 20 uses only 1/6 of 120, 24 uses 1/5 of 120, and 36 multiplies 120 by 3/10. Splitting the two fractions keeps the arithmetic manageable.

Question 5. Numbers & Algebra medium

A clinic starts the week with 150 bottles of hand sanitizer and ends the week with 96. What is the percent decrease?

• A. 36% (correct)
• B. 56%
• C. 64%
• D. 26%

Explanation: Percent decrease divides the change by the original amount: (150 - 96) / 150 = 54 / 150 = 0.36 = 36%. 56% divides by the ending value 96 instead (the classic wrong-base error), 64% reports what fraction of the original remains, and 26% is an arithmetic slip. Always use the starting value as the base.

Question 6. Numbers & Algebra medium

On a ward, the ratio of registered nurses to licensed practical nurses is 4:3. If the ward has 21 licensed practical nurses, how many registered nurses are on the ward?

• A. 24
• B. 28 (correct)
• C. 32
• D. 16

Explanation: Each part of the 4:3 ratio is worth 21 / 3 = 7 staff members, so the registered nurse count is 4 x 7 = 28. 16 scales the ratio by the LPN count incorrectly, 24 adds the 3 parts to 21, and 32 adds 11. Setting each part equal to 21 / 3 and scaling by the RN portion 4 gives 28.

Question 7. Numbers & Algebra medium

A 12-pack of gauze rolls costs $7.80, and a 20-pack of the same rolls costs $12.40. Which statement about the cost per roll is correct?

• A. The 12-pack is cheaper by $0.03 per roll
• B. The 20-pack is cheaper by $0.05 per roll
• C. Both packs cost the same per roll
• D. The 20-pack is cheaper by $0.03 per roll (correct)

Explanation: Unit price is total cost divided by count: $7.80 / 12 = $0.65 and $12.40 / 20 = $0.62 per roll, so the 20-pack beats the 12-pack by $0.03 per roll. Subtracting the pack prices ($4.60) or comparing totals instead of per-roll costs leads to wrong conclusions. Compare unit costs whenever package sizes differ.

Question 8. Numbers & Algebra medium

If x = 6 and y = 3, what is the value of 2xy - y^2?

• A. 27 (correct)
• B. 33
• C. 45
• D. 36

Explanation: Substitute the values first: 2xy = 2 x 6 x 3 = 36 and y^2 = 3^2 = 9, so the expression is 36 - 9 = 27. 33 subtracts y (3) instead of y^2 (9), 45 adds the 9, and 36 omits the subtraction entirely. Substituting both values before applying order of operations is the reliable method.

Question 9. Numbers & Algebra medium

A 300 mL IV bag holds a 1.5% solution. How many mL of the active ingredient are in the bag?

• A. 45
• B. 15
• C. 4.5 (correct)
• D. 1.5

Explanation: A 1.5% solution contains 1.5 mL of active ingredient per 100 mL, so a 300 mL bag holds 3 x 1.5 = 4.5 mL; equivalently, 0.015 x 300 = 4.5. 45 is a decimal-place slip, 15 confuses the percent value with a count, and 1.5 uses only one of the three 100-mL units.

Question 10. Numbers & Algebra medium

Five less than three times a number is 40. What is the number?

• A. 12
• B. 20
• C. 13.33
• D. 15 (correct)

Explanation: Translate the words into 3n - 5 = 40. Adding 5 to both sides gives 3n = 45, then dividing by 3 gives n = 15. 12 comes from misreading five as four, 13.33 divides 40 by 3 without first adding 5, and 20 is 40 divided by 2. Checking by substitution (3 x 15 - 5 = 40) confirms the solution.

Question 11. Numbers & Algebra medium

A courier charges $3.50 per package plus a flat $12 pickup fee. A clinic pays $47 for one delivery run. How many packages are in the run?

• A. 8
• B. 10 (correct)
• C. 13
• D. 16

Explanation: Subtract the flat pickup fee before dividing: 47 - 12 = $35, then 35 / 3.50 = 10 packages. 13 divides the full $47 by $3.50 without removing the fee, and 8 or 16 come from mishandling the $12. Setting up the equation 3.50p + 12 = 47 and solving for p keeps the order straight.

Question 12. Numbers & Algebra hard

The sum of three consecutive even integers is 84. What is the largest of the three integers?

• A. 30 (correct)
• B. 28
• C. 32
• D. 26

Explanation: Consecutive even integers differ by 2. The middle of the three is 84 / 3 = 28, so the set is 26, 28, and 30, making the largest 30. 26 is the smallest, 28 is the middle value, and 32 comes from adding 4 to the middle instead of 2. Dividing the sum by 3 locates the center value.

Question 13. Numbers & Algebra hard

Evaluate: 5 - 2 x 3^2 + 8 / (-4).

• A. 1
• B. -9
• C. -15 (correct)
• D. -23

Explanation: Apply the rules in order: 3^2 = 9, then 2 x 9 = 18, and 8 / (-4) = -2. The expression becomes 5 - 18 + (-2) = -15. 1 treats 8 / (-4) as +2, -9 forgets the final -2 term, and -23 adds 18 to -5 instead of subtracting. Sign errors at the last step are common with negative divisors.

Question 14. Numbers & Algebra hard

Tickets for a fundraiser cost $9 for adults and $5 for children. A total of 80 tickets were sold for $600. How many adult tickets were sold?

• A. 30
• B. 40
• C. 45
• D. 50 (correct)

Explanation: With a adult and c child tickets, a + c = 80 and 9a + 5c = 600. Substituting c = 80 - a gives 9a + 400 - 5a = 600, so 4a = 200 and a = 50 adult tickets. 30 is the child count, 40 assumes an average price of $7.50, and 45 does not satisfy the $600 total when checked.

Question 15. Numbers & Algebra hard

A savings account earns 3% simple interest per year. How many years will it take for $2,000 to earn $360 in simple interest?

• A. 5
• B. 6 (correct)
• C. 8
• D. 12

Explanation: Simple interest is I = P x r x t, so 360 = 2000 x 0.03 x t = 60t and t = 360 / 60 = 6 years. 5, 8, and 12 divide 360 by incorrect yearly amounts such as 72, 45, or 30. Computing the annual interest (2000 x 0.03 = $60) first, then dividing the total interest by it, gives the number of years.

Question 16. Numbers & Algebra hard

What is the value of (2.5 x 10^3) / (5 x 10^-2)?

• A. 50,000 (correct)
• B. 5,000
• C. 500,000
• D. 0.5

Explanation: Divide the coefficients and subtract the exponents: 2.5 / 5 = 0.5 and 10^3 / 10^-2 = 10^5, giving 0.5 x 10^5 = 5 x 10^4 = 50,000. 5,000 drops one power of ten, 500,000 adds one, and 0.5 ignores the powers of ten. Writing the numbers out as 2500 / 0.05 confirms 50,000.

Question 17. Measurement & Data easy

A patient weighs 72 kg. Using the conversion 1 kg = 2.2 lb, what is the weight in pounds?

• A. 32.7
• B. 144
• C. 158.4 (correct)
• D. 176

Explanation: Multiply by the conversion factor: 72 kg x 2.2 lb/kg = 158.4 lb. 32.7 divides 72 by 2.2 instead of multiplying, 144 uses the rough 2 lb/kg factor, and 176 adds 72 and 104. A sanity check helps: since 2.2 lb is a bit more than double 1 kg, 72 kg should be a bit more than 144 lb.

Question 18. Measurement & Data easy

Five medication refill requests take 6, 9, 8, 11, and 6 minutes to process. What is the mean processing time in minutes?

• A. 9
• B. 8 (correct)
• C. 7
• D. 10

Explanation: The mean is the sum divided by the count: (6 + 9 + 8 + 11 + 6) / 5 = 40 / 5 = 8 minutes. 9, 7, and 10 come from miscounting the total as 45, 35, or 50 before dividing. Adding the five times carefully, then dividing by the number of requests, gives the correct average processing time.

Question 19. Measurement & Data easy

A bar chart shows oranges sold at a market stall: Monday 30, Tuesday 25, Wednesday 35, Thursday 30. What is the total number of oranges sold over the four days?

• A. 110
• B. 130
• C. 115
• D. 120 (correct)

Explanation: The total is the sum of the four daily bar values: 30 + 25 + 35 + 30 = 120 oranges. 110 leaves out Thursday, 130 double-counts one day, and 115 misreads Wednesday as 30. Reading each bar's height accurately before adding prevents table-reading errors.

Question 20. Measurement & Data medium

A storage room floor measures 8.5 m by 6 m. What is the area of the floor in square meters?

• A. 51 (correct)
• B. 29
• C. 102
• D. 42.5

Explanation: Area of a rectangle is length times width: 8.5 x 6 = 51 square meters. 29 is the sum of the sides (perimeter), 102 doubles the area as if counting four sides, and 42.5 multiplies 8.5 by 5. Remembering that area multiplies just two dimensions while perimeter adds all four separates the correct value.

Question 21. Measurement & Data medium

Eight lab turnaround times in minutes are 28, 42, 35, 51, 39, 46, 33, and 40. What is the median turnaround time?

• A. 39.25
• B. 39
• C. 39.5 (correct)
• D. 40

Explanation: With an even number of values, the median is the average of the two middle ones after sorting: 28, 33, 35, 39, 40, 42, 46, 51, so (39 + 40) / 2 = 39.5 minutes. 39.25 is the mean of the set, while 39 and 40 are each only one middle value. Sorting first, then splitting the list in half, avoids choosing by original order.

Question 22. Measurement & Data medium

A jar holds 6 red, 5 yellow, and 9 blue beads. One bead is drawn at random. What is the probability that it is yellow or blue?

• A. 3/10
• B. 7/10 (correct)
• C. 1/4
• D. 1/2

Explanation: There are 6 + 5 + 9 = 20 beads total, and 5 + 9 = 14 that are yellow or blue, so the probability is 14 / 20 = 7 / 10. 3/10 is the red fraction (6/20), 1/4 is yellow only (5/20), and 1/2 comes from miscounting the favorable beads as 10 of 20. Adding only the favorable outcomes and dividing by the total gives the probability.

Question 23. Measurement & Data medium

A department spent $1,240 on lab supplies out of a $6,200 monthly supply budget. What percent of the budget was spent?

• A. 25%
• B. 12.4%
• C. 40%
• D. 20% (correct)

Explanation: Percent is part divided by whole: 1240 / 6200 = 0.20 = 20%. 25% would require spending 1550, 40% would be 2480, and 12.4% treats the dollar amount as if it were already a percent. Dividing the money spent by the total budget, then converting the decimal to a percent, yields 20%.

Question 24. Measurement & Data medium

A patient's temperature is graphed at four hourly readings: 99.2, 99.0, 98.8, and 98.6 degrees F. If the temperature drops at a steady rate, how many degrees does it fall each hour?

• A. 0.2 (correct)
• B. 0.15
• C. 0.3
• D. 0.6

Explanation: The temperature fell from 99.2 to 98.6 over the three hour-long intervals, a total drop of 0.6 degrees, so the rate is 0.6 / 3 = 0.2 degree per hour. 0.6 is the whole change, and 0.3 divides by 2 intervals instead of 3. Dividing the total change by the number of intervals between readings gives the per-hour rate.

Question 25. Measurement & Data medium

On a map with a scale of 1 inch = 25 miles, two towns are 3.5 inches apart. How far apart are the towns in miles?

• A. 7.14
• B. 71.4
• C. 87.5 (correct)
• D. 97.5

Explanation: Each inch on the map represents 25 miles, so 3.5 inches is 3.5 x 25 = 87.5 miles. 7.14 divides 25 by 3.5, inverting the scale, 71.4 misreads 3.5 as 2.86, and 97.5 adds 25 to 72.5. Multiplying the measured distance by the scale factor always converts map units to ground units.

Question 26. Measurement & Data medium

A jug contains 0.75 gallon of cleaning fluid. How many fluid ounces is that? (1 gallon = 128 fluid ounces)

• A. 64
• B. 96 (correct)
• C. 84
• D. 110

Explanation: Multiply gallons by the conversion factor: 0.75 x 128 = 96 fluid ounces, which is three quarters of 128. 64 is half a gallon, 84 subtracts 12 instead of taking three quarters, and 110 approximates instead of computing. Recognizing 0.75 as 3/4 makes 128 x 3 / 4 = 96 the quickest path.

Question 27. Measurement & Data hard

An architect's drawing uses a scale of 1 cm = 3 ft. A room measures 5 cm by 4 cm on the drawing. What is the actual floor area of the room in square feet?

• A. 60
• B. 27
• C. 90
• D. 180 (correct)

Explanation: Convert each plan dimension using the scale: 5 cm = 15 ft and 4 cm = 12 ft, so the actual area is 15 x 12 = 180 sq ft. 60 multiplies the drawing's area (20 sq cm) by 3 instead of 9, the square of the scale, and 90 applies the scale to only one dimension before multiplying. Convert both sides first, then compute area.

Question 28. Measurement & Data hard

The mean of six measurements is 34. If one measurement of 58 is removed, what is the new mean of the remaining five measurements?

• A. 29.2 (correct)
• B. 27.4
• C. 30.8
• D. 28.6

Explanation: Rebuild the total from the old mean: 6 x 34 = 204, then remove the value of 58, leaving 146 for five measurements, so the new mean is 146 / 5 = 29.2. 27.4 divides 146 by 6, the old count, and the other options come from subtracting 58 before multiplying. Update both the total and the count, then divide.

Question 29. Measurement & Data hard

A rectangular garden is 12 m by 8 m and contains a circular pond with a radius of 2 m. Using 3.14 for pi, what is the area of the garden left for planting, in square meters?

• A. 88.88
• B. 84.56
• C. 83.44 (correct)
• D. 80.84

Explanation: The garden area is 12 x 8 = 96 sq m, and the pond is pi x r^2 = 3.14 x 2^2 = 12.56 sq m. Subtracting gives 96 - 12.56 = 83.44 sq m left for planting. 88.88 uses half the pond area, 84.56 uses 2.86 as pi, and 80.84 treats the radius as 2.2. Compute each area before subtracting.

Question 30. Measurement & Data hard

A bag holds 5 red and 3 blue tokens. Two tokens are drawn one after another without replacement. What is the probability that both tokens are red?

• A. 5/8
• B. 5/14 (correct)
• C. 25/64
• D. 15/56

Explanation: Without replacement, the first draw has 5 red of 8 tokens and the second has 4 red of 7 remaining, so P(both red) = 5/8 x 4/7 = 20/56 = 5/14. 5/8 is only the first draw, 25/64 assumes replacement (5/8 x 5/8), and 15/56 is red then blue. Adjusting the second probability for the removed token is the key step.