Free TEAS 7 Math Practice Test 3 — 30 Questions With Full Explanations

Question 1. Numbers & Algebra easy

A lab runs 36 tests in a batch, and 5/9 of them pass quality control. How many tests pass?

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

Explanation: Multiply the batch size by the fraction that passed: 36 x 5/9 = 20 tests. The 16 option computed the 4/9 that failed, answering the wrong group, the 18 option used half the batch, and the 24 option used 2/3 of the batch instead of 5/9.

Question 2. Numbers & Algebra easy

Which list shows the decimals 0.42, 0.405, and 0.5 arranged from smallest to largest?

• A. 0.5, 0.42, 0.405
• B. 0.405, 0.42, 0.5 (correct)
• C. 0.42, 0.405, 0.5
• D. 0.42, 0.5, 0.405

Explanation: Compare tenths first: 0.405 and 0.42 both start with 4 tenths, and 0.405 is smaller because its hundredths digit is 0 versus 2, so the order is 0.405, 0.42, 0.5. The other lists either assumed 0.42 is smaller than 0.405 or reversed the correct order.

Question 3. Numbers & Algebra easy

18 is what percent of 60?

• A. 0.3%
• B. 30% (correct)
• C. 33.3%
• D. 3%

Explanation: Divide the part by the whole and multiply by 100: 18 / 60 = 0.30, so 18 is 30% of 60. The 3% option misplaced the decimal one place, the 0.3% option moved it two places, and the 33.3% option confused 18/60 with one-third.

Question 4. Numbers & Algebra easy

Evaluate the expression: 18 - 6 / 3 + 5.

• A. 9
• B. 17
• C. 16
• D. 21 (correct)

Explanation: Division comes first: 6 / 3 = 2, then 18 - 2 = 16, and finally 16 + 5 = 21. The 9 option worked strictly left to right, the 17 option skipped the division entirely (18 - 6 + 5), and the 16 option stopped after the subtraction step.

Question 5. Numbers & Algebra medium

A tank holds 90 L of water, and a procedure drains 1/3 of the tank. How many liters remain in the tank?

• A. 60 (correct)
• B. 30
• C. 27
• D. 45

Explanation: Draining 1/3 leaves 2/3, so multiply 90 by 2/3 to get 60 L. The 30 option answered the amount drained rather than what remains, the 45 option used half the tank, and the 27 option multiplied by 0.3 instead of the fraction 1/3.

Question 6. Numbers & Algebra medium

A total of 3.6 L of solution is divided equally among 8 tubes. How many liters go into each tube?

• A. 0.045
• B. 4.5
• C. 0.45 (correct)
• D. 0.9

Explanation: Divide the total by the number of tubes: 3.6 / 8 = 0.45 L per tube. The 4.5 option misplaced the decimal a full place to the right, the 0.045 option moved it the wrong way, and the 0.9 option divided by 4 tubes instead of 8.

Question 7. Numbers & Algebra medium

A pharmacy technician earns $48,000 per year and receives a 7.5% raise. What is the new annual salary?

• A. 44400
• B. 50400
• C. 3600
• D. 51600 (correct)

Explanation: Multiply the salary by 1.075: $48,000 x 1.075 = $51,600. The $44,400 option subtracted 7.5% instead of adding it, the $3,600 option reported only the raise amount, and the $50,400 option used a 5% raise instead of 7.5%.

Question 8. Numbers & Algebra medium

A medication label reads 50 mg per 2 mL. An order calls for 75 mg. How many milliliters should be given?

• A. 150
• B. 3 (correct)
• C. 2
• D. 1.5

Explanation: The dose is 75 / 50 = 1.5 times the label amount, so multiply the label volume by 1.5: 2 x 1.5 = 3 mL. The 1.5 option stopped at the ratio without multiplying by the volume, the 2 option used the label volume directly, and the 150 option multiplied 75 by 2.

Question 9. Numbers & Algebra medium

Evaluate the expression: 5 + 3 x (10 - 6)^2 / 4.

• A. 17 (correct)
• B. 32
• C. 48
• D. 23

Explanation: Work inside the parentheses first: 10 - 6 = 4, then square it to get 16, then 3 x 16 = 48, then 48 / 4 = 12, and finally 5 + 12 = 17. The 23 option ignored the square and the division, the 32 option added 5 and 3 before multiplying, and the 48 option stopped at the product 3 x 16.

Question 10. Numbers & Algebra medium

Solve for x: 7x + 2 = 5x + 16.

• A. 7 (correct)
• B. 14
• C. 16
• D. 3.5

Explanation: Subtract 5x from both sides to get 2x + 2 = 16, subtract 2 to get 2x = 14, then divide by 2: x = 7. The 14 option stopped at the value of 2x, the 3.5 option divided 14 by 4 instead of 2, and the 16 option used the constant from the right side alone.

Question 11. Numbers & Algebra medium

For every 3 boxes of gloves a supply room orders, it receives 2 boxes of masks. If 24 boxes of masks arrive, how many boxes of gloves were ordered?

• A. 16
• B. 24
• C. 18
• D. 36 (correct)

Explanation: The ratio of gloves to masks is 3:2, so order gloves = 24 x 3/2 = 36 boxes. The 16 option applied the ratio backward (24 x 2/3), the 18 option used 3/4 of 24, and the 24 option assumed a one-to-one ratio.

Question 12. Numbers & Algebra medium

A meal delivery bill comes to $85 before an 18% tip. What is the total including the tip?

• A. 15.30
• B. 98.60
• C. 103.70
• D. 100.30 (correct)

Explanation: Multiply the bill by 1.18: $85 x 1.18 = $100.30. The $98.60 option used a 16% tip, the $103.70 option used 22%, and the $15.30 option reported only the tip amount without adding it to the bill.

Question 13. Numbers & Algebra medium

If x = 4 and y = 2, what is the value of 3x^2 - y^2?

• A. 12
• B. 46
• C. 44 (correct)
• D. 40

Explanation: Square each variable first: x^2 = 16 and y^2 = 4, so 3 x 16 - 4 = 48 - 4 = 44. The 40 option treated y^2 as x times y (subtracting 8), the 46 option used y = 2 instead of y^2 = 4, and the 12 option multiplied 3 x 4 and ignored the squares.

Question 14. Numbers & Algebra hard

A number is increased by 20% and the result is 42. What was the original number?

• A. 33.6
• B. 50.4
• C. 22
• D. 35 (correct)

Explanation: The result equals 120% of the original, so divide 42 by 1.20 to get 35. The 50.4 option multiplied 42 by 1.2, the 33.6 option subtracted 20% of 42 instead, and the 22 option subtracted 20 from 42 as if 20 were a count.

Question 15. Numbers & Algebra hard

A rectangle's length is 4 cm more than twice its width, and its area is 70 sq cm. What is the width of the rectangle?

• A. 5 (correct)
• B. 10
• C. 7
• D. 14

Explanation: If the width is w, the length is 2w + 4, so w(2w + 4) = 70, which gives 2w^2 + 4w - 70 = 0, or w = 5. The 7 option used the positive version of the negative root, the 10 option answered twice the width, and the 14 option reported the length instead.

Question 16. Numbers & Algebra hard

Pump A can fill a tank in 6 hours working alone, and pump B can fill the same tank in 3 hours. How long will it take to fill the tank if both pumps work together?

• A. 6
• B. 2 (correct)
• C. 9
• D. 4.5

Explanation: Add the rates: pump A fills 1/6 of the tank per hour and pump B fills 1/3, for a combined rate of 1/6 + 1/3 = 1/2 tank per hour, so the tank fills in 2 hours. The 4.5 option averaged the two times, the 9 option added them, and the 6 option used only the slower pump.

Question 17. Measurement & Data easy

A fluid bag holds 2.5 L. How many milliliters does it hold? (1 L = 1,000 mL)

• A. 25000
• B. 250
• C. 2500 (correct)
• D. 25

Explanation: Multiply liters by 1,000: 2.5 x 1,000 = 2,500 mL. The 250 option multiplied by 100, the 25 option multiplied by 10, and the 25,000 option multiplied by 10,000, each a decimal-place slip in the conversion factor.

Question 18. Measurement & Data easy

Five patient heights are recorded as 152, 148, 160, 156, and 158 cm. What is the median height?

• A. 156 (correct)
• B. 158
• C. 154.8
• D. 152

Explanation: Order the heights as 148, 152, 156, 158, 160; the middle of the five values is 156 cm. The 154.8 option is the mean instead, and the 158 and 152 options are individual data values mistaken for the middle.

Question 19. Measurement & Data medium

A square garden has a side length of 6.5 m. What is its perimeter?

• A. 24
• B. 42.25
• C. 13
• D. 26 (correct)

Explanation: A square has four equal sides, so the perimeter is 4 x 6.5 = 26 m. The 42.25 option computed the area instead, the 13 option added just two sides, and the 24 option used a side length of 6 m by misreading 6.5.

Question 20. Measurement & Data medium

A triangular banner has a base of 12 cm and a height of 7 cm. What is its area?

• A. 19
• B. 21
• C. 42 (correct)
• D. 84

Explanation: Area of a triangle is one-half base times height: 0.5 x 12 x 7 = 42 sq cm. The 84 option forgot to halve the product, the 21 option halved it twice, and the 19 option added the base and height instead of multiplying them.

Question 21. Measurement & Data hard

A rectangular aquarium measures 60 cm by 30 cm by 40 cm. What is its capacity in liters? (1 L = 1,000 cu cm)

• A. 7200
• B. 7.2
• C. 720
• D. 72 (correct)

Explanation: First find the volume in cubic cm: 60 x 30 x 40 = 72,000, then divide by 1,000 to convert to liters, giving 72 L. The 720 option divided by 100, the 7.2 option divided by 10,000, and the 7,200 option divided by only 10.

Question 22. Measurement & Data medium

A clinic's weekly patient totals were 45, 52, 47, 56, and 50. What was the mean number of patients seen per week?

• A. 49
• B. 52
• C. 51
• D. 50 (correct)

Explanation: Add the five weekly totals (45 + 52 + 47 + 56 + 50 = 250) and divide by 5 to get a mean of 50. The 49 and 51 options come from small addition slips on the total, and the 52 option is one of the data values rather than the average.

Question 23. Measurement & Data hard

A monthly budget is $2,400, and a pie chart shows rent at 40% of the budget. If next month's rent rises by 15%, what will the new rent be?

• A. 960
• B. 1104 (correct)
• C. 1128
• D. 1140

Explanation: Current rent is 40% of 2,400, or 960 dollars, and a 15% increase makes it 960 x 1.15 = $1,104. The 960 option reported the old rent without applying the increase, the 1,128 option used 47% of the budget, and the 1,140 option applied the increase to the whole budget instead of to the rent.

Question 24. Measurement & Data medium

One card is drawn at random from a standard 52-card deck. What is the probability that it is a heart?

• A. 1/13
• B. 1/2
• C. 1/4 (correct)
• D. 1/52

Explanation: There are 13 hearts in a 52-card deck, and 13/52 reduces to 1/4. The 1/13 option is the probability of drawing one specific rank, the 1/2 option confused hearts with the red suits, and the 1/52 option is the chance of drawing one particular card.

Question 25. Measurement & Data medium

A supplement packet contains 1,800 mg of powder. How many grams is that? (1 g = 1,000 mg)

• A. 18
• B. 1.8 (correct)
• C. 180
• D. 0.18

Explanation: Divide milligrams by 1,000 to convert to grams: 1,800 / 1,000 = 1.8 g. The 180 option divided by 10, the 18 option divided by 100, and the 0.18 option divided by 10,000, each a decimal-place error in the conversion.

Question 26. Measurement & Data medium

Five lab values are 4.2, 5.1, 3.9, 6.0, and 4.8. What is the range of these values?

• A. 6.0
• B. 2.1 (correct)
• C. 1.8
• D. 4.8

Explanation: Range is the largest value minus the smallest: 6.0 - 3.9 = 2.1. The 4.8 option is the mean of the five values, the 1.8 option subtracted 4.2 from 6.0, and the 6.0 option is simply the maximum value.

Question 27. Measurement & Data hard

A rectangular room that is 10 m by 6 m has a 2 m by 2 m storage niche cut out of one corner. What is the floor area of the remaining space?

• A. 56 (correct)
• B. 58
• C. 52
• D. 60

Explanation: The room's area is 10 x 6 = 60 sq m, and the niche is 2 x 2 = 4 sq m, so the remaining area is 60 - 4 = 56 sq m. The 58 option subtracted the niche's side length instead of its area, the 52 option subtracted the niche's perimeter, and the 60 option forgot to subtract at all.

Question 28. Measurement & Data hard

The range of a set of measurements is 23, and the smallest measurement is 9. What is the largest measurement in the set?

• A. 14
• B. 23
• C. 20.5
• D. 32 (correct)

Explanation: Range equals largest minus smallest, so the largest is 9 + 23 = 32. The 14 option subtracted the range from the smallest value instead of adding, the 23 option answered with the range itself, and the 20.5 option reported the average of 9 and 32.

Question 29. Measurement & Data hard

A fair coin is flipped and a fair six-sided die is rolled. What is the probability that the coin lands heads AND the die shows a 4?

• A. 1/6
• B. 1/12 (correct)
• C. 2/3
• D. 7/12

Explanation: Multiply the independent probabilities: 1/2 for heads times 1/6 for rolling a 4 gives 1/12. The 2/3 option added the two probabilities, the 7/12 option computed the probability of either event occurring, and the 1/6 option ignored the coin flip entirely.

Question 30. Measurement & Data hard

A production table shows: 0 hours produces 0 units, 2 hours produce 16 units, 4 hours produce 32 units, and 6 hours produce 48 units. At this steady rate, how many units are produced in 5 hours?

• A. 36
• B. 40 (correct)
• C. 32
• D. 44

Explanation: The rate is 16 units per 2 hours, or 8 units per hour, so 5 hours produce 5 x 8 = 40 units. The 32 option read the 4-hour row without interpolating, the 44 option overestimated the 5-hour point, and the 36 option underestimated it.