TEAS 7 Math Practice Test

25 practice questions

Choose an answer, then check it under Show answer.

1. Question 1 of 25Medium

   A hospital's monthly budget for medications is $30,000. In January, they spent 15% of the budget on antibiotics, 40% of the remaining on cardiovascular drugs, and then $9,800 on other medications. How much money is left in the budget at the end of January?

   1. AA. $3,700
   2. BB. $5,500
   3. CC. $7,000
   4. DD. $4,500
   Show answer to question 1

   Answer: B. $5,500

   Start: $30,000. Antibiotics: 15% of $30,000 = $4,500. Remaining: $30,000 − $4,500 = $25,500. Cardiovascular: 40% of $25,500 = $10,200. Remaining: $25,500 − $10,200 = $15,300. Other: $9,800. Left: $15,300 − $9,800 = $5,500.

   Why the other options are wrong

   • AThis results from subtracting 40% of the original budget instead of the remaining amount after antibiotics, leading to an incorrect leftover of $3,700.
   • CAfter antibiotics and cardiovascular drugs, $15,300 remains. Subtracting the stated $9,800 expense leaves $5,500, not $7,000.
   • D$4,500 is the amount spent on antibiotics, not the amount left after all medication expenses.

2. Question 2 of 25Easy

   A clinic records the number of pediatric vaccinations administered daily. A bar graph displays the following counts from Monday to Friday: Monday, 45; Tuesday, 60; Wednesday, 50; Thursday, 75; and Friday, 40. What is the difference between the day with the highest number of vaccinations and the day with the lowest number of vaccinations?

   1. AA. 25
   2. BB. 35
   3. CC. 20
   4. DD. 30
   Show answer to question 2

   Answer: B. 35

   The day with the highest count is Thursday with 75 vaccinations, and the day with the lowest count is Friday with 40 vaccinations. Subtracting 40 from 75 yields 35. The value 30 is incorrect because it subtracts the Monday count (45) from the highest value rather than the lowest value.

   Why the other options are wrong

   • ASubtracting Wednesday’s count from Thursday’s gives 75 − 50 = 25, but Wednesday does not have the lowest count.
   • CSubtracting Friday’s count from Tuesday’s gives 60 − 40 = 20, but Tuesday does not have the highest count.
   • DSubtracting Monday’s count from Thursday’s gives 75 − 45 = 30, but Monday does not have the lowest count.

3. Question 3 of 25Medium

   Solve for x: (2/3)x − 1/2 = 5/6

   1. AA. 2
   2. BB. 3/2
   3. CC. 1
   4. DD. 5/2
   Show answer to question 3

   Answer: A. 2

   Add 1/2 to both sides: (2/3)x = 5/6 + 1/2 = 5/6 + 3/6 = 8/6 = 4/3. Multiply both sides by the reciprocal 3/2: x = (4/3) × (3/2) = 12/6 = 2.

   Why the other options are wrong

   • BSubstituting x = 3/2 gives (2/3) × (3/2) − 1/2 = 1/2, not 5/6.
   • CSubstituting x = 1 gives (2/3) × 1 − 1/2 = 1/6, not 5/6.
   • DSubstituting x = 5/2 gives (2/3) × (5/2) − 1/2 = 7/6, not 5/6.

4. Question 4 of 25Hard

   A medical supply store sells a box of gloves for $24. After applying a 20% discount, the store still makes a 25% profit based on the cost. What was the cost of the box?

   1. AA. $18.00
   2. BB. $16.00
   3. CC. $15.36
   4. DD. $14.40
   Show answer to question 4

   Answer: C. $15.36

   Sale price after 20% discount = $24 × 0.80 = $19.20. This sale price gives a 25% profit on cost, so $19.20 = cost × 1.25. Cost = $19.20 ÷ 1.25 = $15.36.

   Why the other options are wrong

   • A$18.00 = $24 × 0.75. This ignores the 20% discount and incorrectly subtracts 25% from the original price instead of dividing the discounted sale price by 1.25.
   • B$16.00 results from mistakenly dividing $19.20 by 1.2 instead of 1.25.
   • D$14.40 is $19.20 × 0.75, which incorrectly subtracts 25% from the sale price rather than representing cost plus profit.

5. Question 5 of 25Easy

   A nurse monitors an intravenous infusion of 450 mL of saline that runs at a constant rate over 3 hours. What is the unit rate of the infusion in milliliters per hour?

   1. AA. 225 mL/hr
   2. BB. 150 mL/hr
   3. CC. 175 mL/hr
   4. DD. 135 mL/hr
   Show answer to question 5

   Answer: B. 150 mL/hr

   To determine the unit rate, divide the total volume of 450 mL by the 3 hours of administration, which yields 150 mL/hr. The value of 225 mL/hr is incorrect because it results from dividing by 2 hours instead of 3.

6. Question 6 of 25Easy

   A line graph records a patient's monthly oral fluid intake in liters: January (45 L), February (52 L), March (48 L), April (62 L), and May (55 L). Between which two consecutive months did the fluid intake show the greatest decrease?

   1. AA. February to March
   2. BB. March to April
   3. CC. January to February
   4. DD. April to May
   Show answer to question 6

   Answer: D. April to May

   Fluid intake decreased during two intervals: February to March (a decrease of 4 liters) and April to May (a decrease of 7 liters). The decrease from April to May is the larger drop. February to March is incorrect because that decrease was only 4 liters, which is smaller than the 7-liter decline between April and May.

   Why the other options are wrong

   • AChoosing the smaller decrease overlooks the larger drop: 52 minus 48 = 4 L, compared with 62 minus 55 = 7 L from April to May.
   • BThis confuses the largest increase with the greatest decrease: 62 minus 48 = 14 L, so intake rose from March to April.
   • CThis confuses an increase with a decrease: 52 minus 45 = 7 L, so intake rose from January to February.

7. Question 7 of 25Hard

   A hospital heliport is built in the shape of a right trapezoid. The two parallel bases measure 16 meters and 28 meters, and the perpendicular side measures 9 meters. What is the perimeter of the heliport in meters?

   1. AA. 53
   2. BB. 65
   3. CC. 198
   4. DD. 68
   Show answer to question 7

   Answer: D. 68

   The slanted side forms the hypotenuse of a right triangle with legs of 9 meters (the height) and 12 meters (the difference between the bases: 28 − 16). Using the Pythagorean theorem, the square root of (9 squared plus 12 squared) is the square root of 225, which equals 15 meters. Adding all four outer boundary sides gives 16 + 28 + 9 + 15 = 68 meters. The value 65 meters is incorrect because it incorrectly adds the base difference of 12 meters instead of the slanted hypotenuse, and 198 square meters is the area of the trapezoid.

   Why the other options are wrong

   • AAdding only the two bases and the perpendicular side gives 16 + 28 + 9 = 53 meters, omitting the 15 meter slanted side from the perimeter.
   • BUsing the base difference as the slanted side gives 16 + 28 + 9 + (28 − 16) = 65 meters. The 12 meter difference is a horizontal distance, not the slanted side’s length.
   • CCalculating (16 + 28) × 9 ÷ 2 = 198 finds the trapezoid’s area in square meters, not its perimeter in meters.

8. Question 8 of 25Medium

   A rectangular hallway in a clinic is 45 feet long and 8 feet wide. A square supply closet with sides measuring 6 feet is installed in one corner, taking up part of the floor space. What is the remaining floor area of the hallway?

   1. AA. 354 sq ft
   2. BB. 324 sq ft
   3. CC. 396 sq ft
   4. DD. 336 sq ft
   Show answer to question 8

   Answer: B. 324 sq ft

   The initial area of the hallway is 45 feet multiplied by 8 feet, which equals 360 square feet. The area taken by the square closet is 6 feet multiplied by 6 feet, which equals 36 square feet; subtracting 36 from 360 leaves 324 square feet. The value of 336 square feet incorrectly subtracts the perimeter of the closet rather than its area.

   Why the other options are wrong

   • ASubtracting the closet's side length instead of its area gives 45 × 8 − 6 = 354. This incorrectly subtracts feet from square feet.
   • CAdding the closet's area instead of subtracting it gives 45 × 8 + 6 × 6 = 396. The closet reduces the available floor area.
   • DSubtracting the closet's perimeter instead of its area gives 45 × 8 − 4 × 6 = 336. Floor space requires subtracting the closet's area, not its perimeter.

9. Question 9 of 25Easy

   Out of 96 patients screened at a community health clinic, 72 were determined to need follow-up care. What fraction of the screened patients needed follow-up care, expressed in lowest terms?

   1. AA. 6/8
   2. BB. 3/4
   3. CC. 2/3
   4. DD. 7/9
   Show answer to question 9

   Answer: B. 3/4

   The initial ratio of screened patients needing follow-up care is 72/96. Dividing both the numerator and denominator by their greatest common factor of 24 simplifies the fraction to 3/4. The option 6/8 is equivalent to 72/96, but it is not in lowest terms because both values still share a common factor of 2.

   Why the other options are wrong

   • ADividing 72 and 96 by 12 gives 6/8, which is equivalent but not in lowest terms because 6 and 8 still share a factor of 2.
   • CSubtracting 24 from both numbers gives 48/72 = 2/3, but simplifying requires dividing both numbers by the same nonzero factor, not subtracting the same amount.
   • DDropping the ones digits changes 72/96 to 7/9, but deleting digits is not a valid way to simplify a fraction.

10. Question 10 of 25Medium

    Solve the inequality for x: 4 − 2(3x − 5) ≥ −4x + 22

    1. AA. x ≥ 4
    2. BB. x ≤ 4
    3. CC. x ≤ −4
    4. DD. x ≥ −4
    Show answer to question 10

    Answer: C. x ≤ −4

    Distributing and combining constants yields −6x + 14 ≥ −4x + 22, which simplifies to −2x ≥ 8 after moving variable and constant terms. Dividing both sides by −2 requires flipping the inequality direction, resulting in x ≤ −4. The option x ≥ −4 is incorrect because it fails to reverse the inequality symbol after division by −2.

    Why the other options are wrong

    • AThis result combines two errors: incorrectly calculating 8 ÷ (−2) as 4 and failing to reverse the inequality when dividing −2x ≥ 8 by −2.
    • BThis result reverses the inequality correctly but makes a sign error in division, incorrectly calculating 8 ÷ (−2) as 4 instead of −4.
    • DThis result comes from dividing −2x ≥ 8 by −2 without reversing the inequality sign. Dividing by a negative number changes ≥ to ≤.

11. Question 11 of 25Hard

    A patient weighs 176 lb. The order is for 5 mg/kg of a medication. The vial contains 500 mg of powder. After reconstitution with 1.8 mL of sterile water, the concentration is 250 mg/mL. How many mL should the nurse administer? (Round to the nearest tenth.)

    1. AA. 1.6 mL
    2. BB. 2.0 mL
    3. CC. 1.8 mL
    4. DD. 1.2 mL
    Show answer to question 11

    Answer: A. 1.6 mL

    Convert weight: 176 lb ÷ 2.2 = 80 kg. Dose required: 5 mg/kg × 80 kg = 400 mg. Concentration is 250 mg/mL. Volume = 400 mg / 250 mg/mL = 1.6 mL.

    Why the other options are wrong

    • B2.0 mL would provide 500 mg, which exceeds the required 400 mg.
    • C1.8 mL is the volume of diluent added, not the dose volume.
    • D1.2 mL would provide 300 mg, which is less than the required dose.

12. Question 12 of 25Medium

    Solve for \(y\): \[-\frac{4}{9}y = 20\]

    1. AA. \(\frac{80}{9}\)
    2. BB. \(−\frac{80}{9}\)
    3. CC. −45
    4. DD. 45
    Show answer to question 12

    Answer: C. −45

    Multiplying both sides by the reciprocal of the coefficient, \(−\frac{9}{4}\), yields \(y = 20 × \left(−\frac{9}{4}\right) = −45\). Omitting the negative sign during computation leads to the distractor \(45\).

    Why the other options are wrong

    • AIgnoring the negative sign and multiplying by \(\frac{4}{9}\) instead of the reciprocal gives \(20 × \frac{4}{9} = \frac{80}{9}\). Isolating \(y\) requires multiplying by \(−\frac{9}{4}\).
    • BMultiplying by the coefficient instead of its reciprocal gives \(20 × \left(−\frac{4}{9}\right) = −\frac{80}{9}\). The required multiplier is \(−\frac{9}{4}\), not \(−\frac{4}{9}\).
    • DDropping the negative sign from the reciprocal gives \(20 × \frac{9}{4} = 45\). The reciprocal must be negative, so \(y\) must be negative.

13. Question 13 of 25Medium

    A hospital's patient satisfaction score rose from 72 percent to 90 percent. What is the percent increase relative to the original score, rounded to the nearest whole percent?

    1. AA. 18 percent
    2. BB. 20 percent
    3. CC. 80 percent
    4. DD. 25 percent
    Show answer to question 13

    Answer: D. 25 percent

    Percent increase = (new − original) ÷ original × 100 = (90 − 72) ÷ 72 × 100 = 18 ÷ 72 × 100 = 25 percent.

    Why the other options are wrong

    • A18 is the change in percentage points, not the percent increase relative to 72.
    • B20 percent divides the change by the new score (18 ÷ 90) instead of the original score.
    • C80 percent is the original score as a fraction of the new one (72 ÷ 90).

14. Question 14 of 25Medium

    A circular sign has a diameter of 12 cm. Using 3.14 for π, what is the area of the sign?

    1. AA. 36.00 sq cm
    2. BB. 144.00 sq cm
    3. CC. 37.68 sq cm
    4. DD. 113.04 sq cm
    Show answer to question 14

    Answer: D. 113.04 sq cm

    To find the area, first divide the diameter by 2 to obtain a radius of 6 cm, then apply the formula πr². The calculation 3.14 × 36 equals 113.04 square cm. The value 37.68 represents the circumference of the sign.

15. Question 15 of 25Hard

    A nurse needs to prepare 20 liters of an 18% saline solution. She has a 10% saline solution and a 30% saline solution. How many liters of the 10% solution should she mix with the 30% solution to obtain the desired mixture?

    1. AA. 10
    2. BB. 8
    3. CC. 12
    4. DD. 15
    Show answer to question 15

    Answer: C. 12

    Let x = liters of 10% solution, then (20 − x) = liters of 30% solution. Equation: 0.10x + 0.30(20 − x) = 0.18 × 20 → 0.10x + 6 − 0.30x = 3.6 → −0.20x = −2.4 → x = 12.

    Why the other options are wrong

    • A10 liters results from assuming an equal mix (10 of each), which gives 20% average, not 18%.
    • B8 liters would be the amount of 30% solution (20 − 12 = 8), not the 10% solution.
    • DMixing 15 liters of the 10% solution with 5 liters of the 30% solution gives (0.10 × 15 + 0.30 × 5) ÷ 20 = 0.15, or 15%, not 18%.

16. Question 16 of 25Medium

    A study of 200 patients found that 60 had high blood pressure, 80 had high cholesterol, and 30 had both conditions. If a patient is randomly selected from the study, what is the probability they have neither high blood pressure nor high cholesterol?

    1. AA. 0.45
    2. BB. 0.60
    3. CC. 0.50
    4. DD. 0.55
    Show answer to question 16

    Answer: A. 0.45

    Number with either condition = 60 + 80 − 30 = 110. Number with neither = 200 − 110 = 90. Probability = 90/200 = 0.45.

    Why the other options are wrong

    • B0.60 is the proportion without high cholesterol (120/200), which still includes 30 patients with high blood pressure.
    • C0.50 would mean 100 patients have neither condition, but 200 − 110 = 90.
    • D0.55 is the proportion with at least one condition (110/200), not the proportion with neither.

17. Question 17 of 25Easy

    A public health researcher creates a scatter plot comparing weekly aerobic exercise in hours along the horizontal axis to resting heart rate in beats per minute along the vertical axis. The plotted data points generally slope downward from left to right. Which of the following conclusions is best supported by this scatter plot?

    1. AA. There is no correlation between weekly exercise hours and resting heart rate.
    2. BB. There is an undefined correlation between weekly exercise hours and resting heart rate.
    3. CC. There is a negative correlation between weekly exercise hours and resting heart rate.
    4. DD. There is a positive correlation between weekly exercise hours and resting heart rate.
    Show answer to question 17

    Answer: C. There is a negative correlation between weekly exercise hours and resting heart rate.

    A downward slope from left to right demonstrates that higher values on the horizontal axis correspond to lower values on the vertical axis, which defines a negative correlation. A positive correlation would be represented by points sloping upward from left to right, where both variables increase together.

    Why the other options are wrong

    • AThis confuses a downward trend with no trend. The points show that resting heart rate generally decreases as weekly exercise hours increase, indicating a correlation.
    • BThis incorrectly treats a recognizable downward trend as undefined. The direction of the plotted points clearly identifies a negative correlation.
    • DThis reverses the direction of the relationship. A positive correlation would show resting heart rate generally increasing as weekly exercise hours increase, producing an upward trend.

18. Question 18 of 25Hard

    An organization has a total budget of $1,260 to assemble and deliver hygiene kits. It sets aside 12% of that budget for delivery and can use only the remaining money for kits. Each adult kit costs $4.50, and each child kit costs $3.20. Adult kits and child kits must be assembled in a ratio of 3:2. What is the greatest total number of complete kits the organization can assemble?

    1. AA. 275 kits
    2. BB. 280 kits
    3. CC. 315 kits
    4. DD. 278 kits
    Show answer to question 18

    Answer: A. 275 kits

    After reserving delivery costs, the available amount is $1,260 × (1 − 0.12) = $1,108.80. Each group of 3 adult kits and 2 child kits contains 5 kits and costs (3 × $4.50) + (2 × $3.20) = $19.90. Since 55 × $19.90 = $1,094.50 but 56 × $19.90 = $1,114.40 > $1,108.80, the maximum is 55 × 5 = 275 kits.

    Why the other options are wrong

    • BTreats delivery as 12% of kit costs instead of 12% of the total budget, incorrectly allowing 56 groups and giving 280 kits.
    • CIgnores the delivery allocation and uses the entire $1,260 for kits, allowing 63 groups of 5, or 315 kits.
    • DDivides $1,108.80 by the weighted average cost of $3.98 per kit and rounds down to 278, ignoring that the 3:2 ratio requires a multiple of 5 kits.

19. Question 19 of 25Medium

    A clinic tracks its average patient wait time across four consecutive quarters: Quarter | Average Wait Time (minutes) Quarter 1 | 40 Quarter 2 | 50 Quarter 3 | 45 Quarter 4 | 36 What is the percent decrease in average wait time from Quarter 2 to Quarter 4?

    1. AA. 35%
    2. BB. 28%
    3. CC. 39%
    4. DD. 14%
    Show answer to question 19

    Answer: B. 28%

    The percent decrease is calculated by dividing the absolute change by the original value: (50 − 36) ÷ 50 = 14 ÷ 50 = 0.28, or 28%. The value 39% incorrectly uses the final Quarter 4 value as the denominator instead of the baseline Quarter 2 value.

    Why the other options are wrong

    • AUsing Quarter 1's value as the denominator gives 14 ÷ 40 × 100 = 35%, but the baseline must be Quarter 2's 50 minutes.
    • CDividing by Quarter 4's value gives 14 ÷ 36 × 100 ≈ 39%. Percent decrease uses the original value, 50 minutes, not the final value.
    • DSubtracting 36 from 50 gives 14 minutes, not 14%. Reporting the difference as a percentage skips dividing by the original 50 minutes and multiplying by 100.

20. Question 20 of 25Medium

    A clinic purchases an otoscope set with an original list price of $240.00. The medical supply company provides a 15% discount, and a 6% sales tax is then applied to the discounted price. What is the final total cost of the otoscope set?

    1. AA. $216.24
    2. BB. $218.40
    3. CC. $204.00
    4. DD. $225.60
    Show answer to question 20

    Answer: A. $216.24

    The 15% discount reduces the price by $36.00 to $204.00, and adding the 6% tax on this discounted amount ($12.24) yields a final total of $216.24. The total of $218.40 is incorrect because it applies the sales tax to the original $240.00 price rather than the discounted amount.

    Why the other options are wrong

    • BApplying tax to the original price instead of the discounted price gives $204.00 + ($240.00 × 0.06) = $218.40. Tax must be calculated on $204.00.
    • CStopping after the discount gives $240.00 × 0.85 = $204.00. This omits the required 6% sales tax.
    • DIgnoring the 15% discount and treating the 6% tax as a discount gives $240.00 × 0.94 = $225.60. The discount must be applied first, then tax must be added.

21. Question 21 of 25Easy

    A physical therapist records that a patient completed 3 5/8 miles on a stationary bicycle during a rehabilitation session. Which of the following represents this distance as a decimal?

    1. AA. 3.625
    2. BB. 3.850
    3. CC. 3.750
    4. DD. 3.58
    Show answer to question 21

    Answer: A. 3.625

    To convert the mixed number 3 5/8 to a decimal, convert the fractional portion 5/8 by dividing 5 by 8, which equals 0.625, and add the whole number 3 to obtain 3.625. The value 3.58 is an incorrect literal concatenation of the numerator and denominator rather than a true division.

    Why the other options are wrong

    • BReversing the fraction’s digits and treating them as hundredths gives 3 + 85/100 = 3.850, but a fraction must be converted by dividing its numerator by its denominator.
    • CMistaking 5/8 for 3/4 gives 3 + (3 ÷ 4) = 3.750, but these fractions are not equivalent.
    • DPlacing the numerator and denominator directly after the decimal point gives 3 + 0.58 = 3.58, but writing fraction digits together does not perform the required division, 5 ÷ 8.

22. Question 22 of 25Hard

    A clinic courtyard starts as an 840 cm by 600 cm rectangle. A rectangular recess, 320 cm wide and 250 cm deep, is removed from the middle of one 840-cm side, creating a U-shaped courtyard. Edging is needed along the entire resulting boundary except for a 90-cm entrance on the opposite side. Each roll contains 2.5 m of edging, and pieces can be cut and joined without waste. What is the minimum number of rolls needed?

    1. AA. 12 rolls
    2. BB. 13 rolls
    3. CC. 16 rolls
    4. DD. 14 rolls
    Show answer to question 22

    Answer: D. 14 rolls

    The recess replaces a 320-cm boundary segment with another 320-cm segment plus two 250-cm sides, increasing the perimeter by 500 cm. The required edging length is 2 × (840 + 600) + 2 × 250 − 90 = 3,290 cm = 32.9 m. Since 32.9 ÷ 2.5 = 13.16, at least 14 rolls must be purchased.

    Why the other options are wrong

    • AIgnores the two sides added by the recess, calculating (28.8 − 0.9) ÷ 2.5 = 11.16 and rounding up to 12 rolls.
    • BRounds 13.16 down to 13 rolls, which would provide only 32.5 m of the required 32.9 m.
    • CAdds 2 × 320 cm for the recess's width, although its back edge replaces an equal-width original boundary segment, producing an inflated requirement of 39.3 m.

23. Question 23 of 25Medium

    A receipt for clinical equipment shows a total of $282.10, which includes an 8.5% sales tax. What was the pre-tax price of the equipment?

    1. AA. $260.00
    2. BB. $273.60
    3. CC. $258.12
    4. DD. $262.50
    Show answer to question 23

    Answer: A. $260.00

    Because the total includes the original price plus 8.5% tax, $282.10 equals 108.5% (or 1.085 times) the pre-tax price. Dividing $282.10 by 1.085 gives the correct pre-tax price of $260.00. The value $258.12 is incorrect because it mistakenly subtracts 8.5% of the total amount instead of dividing by 1.085.

    Why the other options are wrong

    • BSubtracting $8.50 gives $282.10 minus $8.50 = $273.60, incorrectly treating an 8.5% tax rate as a fixed dollar amount.
    • CCalculating $282.10 × (1 minus 0.085) = $258.1215, rounded to $258.12, incorrectly subtracts 8.5% of the total. Sales tax is calculated on the pre-tax price, not the total.
    • DSubtracting an incorrect tax amount gives $282.10 minus $19.60 = $262.50. However, 8.5% tax on $262.50 would round to $22.31, not $19.60.

24. Question 24 of 25Easy

    A nurse records the number of patient visits per day: 3, 5, 5, 7, 8, 9, 12. What is the median number of visits?

    1. AA. 7
    2. BB. 6
    3. CC. 8
    4. DD. 5
    Show answer to question 24

    Answer: A. 7

    The data set is already ordered: 3, 5, 5, 7, 8, 9, 12. With 7 numbers, the median is the 4th value, which is 7.

    Why the other options are wrong

    • B6 is the average of the 3rd and 4th values (5 and 7), but with 7 values, the median is the 4th value alone.
    • C8 is the 5th value, not the middle (4th) value.
    • D5 is the mode, not the median.

25. Question 25 of 25Hard

    The first-time and returning participants initially registered for a workshop are in a ratio of 5:3. Then 20% of the first-time participants and 25% of the returning participants cancel. After 30 additional returning participants register, the ratio of first-time to returning participants is 4:3. How many participants were registered initially?

    1. AA. 280 participants
    2. BB. 400 participants
    3. CC. 200 participants
    4. DD. 320 participants
    Show answer to question 25

    Answer: D. 320 participants

    Let x represent one part of the original ratio, making the initial counts 5x and 3x. After the changes, the counts are 0.80 × 5x = 4x and (0.75 × 3x) + 30 = 2.25x + 30, so 4x ÷ (2.25x + 30) = 4 ÷ 3. Cross-multiplying gives 12x = 9x + 120, so x = 40 and the original total was (5 + 3) × 40 = 320 participants.

    Why the other options are wrong

    • AReports the final enrollment, 160 + 120 = 280, rather than the initial enrollment.
    • BApplies the 20% cancellation rate to both groups instead of applying 25% to returning participants, yielding an incorrect initial total of 400.
    • CReports only the original first-time participants, 5 × 40 = 200, instead of including both groups.

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