ACT Math Quiz: Word Problems

What this quiz covers

This quiz focuses on Word Problems, giving you a quick way to practice the rules, question types, and explanations that matter most for ACT Math.

How to use this quiz

Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

Question 1

1. 120
2. 180
3. 220 (correct answer)
4. 310

Explanation: The correct answer is C (220). Set up the equation: base fee + per-mile charge = total cost → 30 + 0.15m = 63 → 0.15m = 33 → m = 33 ÷ 0.15 = 220 miles. A (120) likely results from an arithmetic error when dividing 33 by 0.15, possibly misplacing a decimal. B (180) is another arithmetic error in the division. D (310) could result from failing to subtract the base fee, using the full $63 as the variable amount, then dividing incorrectly. The key step is subtracting the flat fee before dividing by the per-unit rate.

Question 2

1. 3
2. 7
3. 14
4. 21 (correct answer)

Explanation: This is a Greatest Common Factor (GCF) question embedded in a real-world context. Choice D (21) is correct — the GCF determines the maximum number of identical bags with no items left over. Factor both numbers: 42 = 2 × 3 × 7 and 63 = 3² × 7. GCF = 3 × 7 = 21. Check: 42 ÷ 21 = 2 pencils per bag; 63 ÷ 21 = 3 stickers per bag. No remainder either way. Choice A (3) identifies a common factor (3 divides both 42 and 63) but not the greatest one. Choice B (7) identifies another common factor but also not the greatest. Choice C (14) = 42 ÷ 3, which is not a factor of 63 (63 ÷ 14 = 4.5). Pro tip: "Greatest number of identical groups with nothing left over" always means GCF. List prime factors of both numbers and multiply all shared prime factors together. The GCF of 42 and 63 is not their product (2,646) divided by anything — it's the product of their shared factors only.

Question 3

1. $7$ groups (correct answer)
2. $24$ groups
3. $32$ groups
4. $112$ groups

Explanation: We need to find how many groups of 4 can be formed from 28 students. This requires division: number of groups = total students ÷ students per group. So we calculate 28 ÷ 4 = 7 groups. Choice D (112) incorrectly multiplies 28 × 4 instead of dividing.

Question 4

1. 40
2. 60
3. 80 (correct answer)
4. 100

Explanation: This is a mixture problem testing weighted average setup. Choice C (80 mL) is correct — let x = mL of Solution A. Set up the equation: acid contributed by A + acid contributed by B = acid in the final mixture: 0.20x + 0.50(40) = 0.30(x + 40). Simplify: 0.20x + 20 = 0.30x + 12. Solve: 8 = 0.10x → x = 80 mL. Choice A (40 mL) assumes equal volumes of both solutions, which would produce a 35% mixture (the average of 20% and 50%), not 30%. Choice B (60 mL) results from a setup or arithmetic error, possibly not distributing 0.30 across the full total volume on the right side. Choice D (100 mL) results from a sign or distribution error in solving the equation, perhaps writing 0.30(40) instead of 0.30(x + 40) for the right side. Pro tip: The mixture equation template is: %(A) × vol(A) + %(B) × vol(B) = %(mixture) × total volume. Always express the total volume as (vol A + vol B), and use the target percentage on the full mixture — not just one component.

Question 5

1. $690.00
2. $735.00 (correct answer)
3. $750.00
4. $1{,}035.00

Explanation: This is an arithmetic and rates question testing overtime pay calculations. Choice B ($735.00) is correct — regular pay for the first 40 hours: 40 × $15.00 = $600.00. Overtime hours: 46 − 40 = 6 hours. Overtime pay: 6 × $22.50 = $135.00. Total: $600 + $135 = $735.00. Choice A ($690.00) applies the regular $15.00 rate to all 46 hours, ignoring the overtime premium entirely: 46 × $15 = $690. Choice C ($750.00) results from a small arithmetic error in the overtime calculation — possibly computing 6 × $25 = $150 instead. Choice D ($1,035.00) applies the overtime rate of $22.50 to all 46 hours, as if the entire shift were overtime: 46 × $22.50 = $1,035. Pro tip: Always split overtime problems into two separate calculations — regular hours at base pay, overtime hours at the elevated rate — then add. Never apply one rate to the full total.

Question 6

1. 2
2. 2.4 (correct answer)
3. 5
4. 10

Explanation: This is a work rates question testing the combined rate method. Choice B (2.4 hours) is correct — convert each pump's time into a rate (fraction of the tank filled per hour): Pump A fills 1/4 of the tank per hour; Pump B fills 1/6 of the tank per hour. Working together, their rates add: 1/4 + 1/6 = 3/12 + 2/12 = 5/12 of the tank per hour. Time to fill one full tank = 1 ÷ (5/12) = 12/5 = 2.4 hours. Choice A (2.0 hours) comes from averaging the two times and halving: (4 + 6)/2 = 5, then 5/2 = 2.5... or simply assuming two pumps cut the faster pump's time in half: 4/2 = 2. Neither approach is valid — the combined time depends on both rates, not just the faster one. Choice C (5.0 hours) averages the two times directly: (4 + 6)/2 = 5 — a common intuition that produces a result slower than either pump alone, which should immediately signal an error. Choice D (10.0 hours) adds the two times together: 4 + 6 = 10 — the slowest possible wrong answer, producing a combined time slower than either pump working alone, which is impossible. Pro tip: The combined rate method always works for these problems — convert each time to a rate (1/time), add the rates, then take the reciprocal to get the combined time. The answer must always be LESS than the faster pump's time alone. If your answer is slower than either individual pump, you've made an error.

Question 7

1. $1{,}028
2. $1{,}200
3. $1{,}440 (correct answer)
4. $1{,}800

Explanation: This is a fractions and budget problem testing algebraic equation setup. Choice C ($1,440) is correct — spent fraction: 1/3 + 1/4 = 4/12 + 3/12 = 7/12. Remaining: 1 − 7/12 = 5/12. Set up: (5/12) × B = 600 → B = 600 × (12/5) = 600 × 2.4 = $1,440. Choice A ($1,028) divides $600 by the spent fraction instead of the remaining fraction: 600 ÷ (7/12) = 600 × (12/7) ≈ $1,028. Choice B ($1,200) treats the remaining fraction as 1/2 instead of 5/12: 600 × 2 = $1,200. Choice D ($1,800) treats the remaining fraction as 1/3: 600 × 3 = $1,800. Pro tip: When a fraction of a total is left over, the leftover fraction is (1 − sum of spent fractions). Here: 1 − (1/3 + 1/4) = 1 − 7/12 = 5/12. Then solve: (5/12) × Budget = 600 → Budget = 600 × (12/5) = 1,440. A quick check: 1/3 of 1,440 = 480, 1/4 of 1,440 = 360, 480 + 360 + 600 = 1,440 ✓.

Question 8

1. 500 ml
2. 600 ml (correct answer)
3. 550 ml
4. 650 ml

Explanation: This problem asks how much juice remains after pouring some out. We need to subtract the amount poured from the original amount. Juice remaining = 750 ml - 150 ml = 600 ml. Choice C (550 ml) might result from an arithmetic error in subtraction.

Question 9

1. $1.80 + 3.5$
2. $3.5 \div 1.80$
3. $1.80 \times 3.5$ (correct answer)
4. $1.80 - 3.5$

Explanation: We need to find the total cost of apples when Maya buys 3.5 pounds at $1.80 per pound. To find the total cost when we know the price per unit and the number of units, we multiply: total cost = (price per pound) × (number of pounds). This gives us $1.80 × 3.5, which represents the total cost in dollars. Choice A incorrectly adds the price and weight, which doesn't give a meaningful result.

Question 10

1. 10 miles (correct answer)
2. 25 miles
3. 600 miles
4. 0.44 miles

Explanation: We need to find the distance traveled when cycling at 15 mph for 40 minutes. First, convert 40 minutes to hours: 40 ÷ 60 = 2/3 hour. Using distance = speed × time: distance = 15 mph × (2/3) hour = 10 miles. Choice B (25 miles) would result from incorrectly using 40 as 1.67 hours instead of 2/3 hour.

Question 11

1. 800 meters
2. 1,200 meters (correct answer)
3. 4,000 meters
4. 133.3 meters

Explanation: We need to find the total distance when a runner completes 3 laps of a 400-meter track. The total distance is 3 laps × 400 meters per lap = 1,200 meters. Choice A (800 meters) would result from incorrectly using 2 laps instead of 3, or from adding 400 + 400 instead of multiplying by 3.

Question 12

1. $180 (correct answer)
2. $190
3. $195
4. $200

Explanation: This problem asks for the sale price after applying a percentage discount. We calculate the discount amount first: 10% of $200 = 0.10 × $200 = $20, then subtract from the original price: $200 - $20 = $180. Choice B would result from incorrectly calculating a 5% discount instead of 10%.

Question 13

1. 750 ml
2. 800 ml
3. 900 ml
4. 1000 ml (correct answer)

Explanation: This problem asks for the total volume when combining multiple identical containers. We multiply the volume per juice box by the number of boxes: total volume = 250 ml per box × 4 boxes. Calculating: 250 × 4 = 1000 ml. Choice C would result from incorrectly using 225 ml per box instead of 250 ml per box.

Question 14

1. $45
2. $50
3. $55
4. $60 (correct answer)

Explanation: This problem asks for the total cost of multiple identical items. We multiply the price per ticket by the number of tickets: total cost = $15 per ticket × 4 tickets. Calculating: $15 × 4 = $60. Choice B would result from incorrectly adding $15 + 4 instead of multiplying $15 × 4.

Question 15

1. 4 days
2. 5 days (correct answer)
3. 6 days
4. 7 days

Explanation: This problem asks how many days it will take to read the book. We need to divide the total pages by the pages read per day. Days needed = 250 pages ÷ 50 pages per day = 5 days. Choice A (4 days) might result from dividing incorrectly or using wrong numbers.

Question 16

1. $1.2(p + 3.5)$
2. $\dfrac{1.2}{p} + 3.5$
3. $1.2p + 3.5$ (correct answer)
4. $(1.2 + 3.5)p$

Explanation: We need to find the total cost when buying p pounds of apples at $1.20$ per pound plus a loaf of bread for $3.50$. The total cost is the cost of apples plus the cost of bread: Cost = $1.20 \times p + 3.50 = 1.2p + 3.5$. Choice A incorrectly groups the apple cost and bread cost together before multiplying by p, which would apply the bread cost per pound of apples.

Question 17

1. $x=7$
2. $x=8$ (correct answer)
3. $x=9$
4. $x=12$

Explanation: We need to find the number of classes (x) when the total cost is $57, with a $25 monthly fee plus $4 per class. The equation is: $25 + $4x = $57, so $4x = $57 - $25 = $32. Dividing both sides by 4 gives x = 32 ÷ 4 = 8 classes. Choice A (x = 7) would give a total of only $53, not $57.

Question 18

1. 12
2. 18
3. 24 (correct answer)
4. 36

Explanation: This least common multiple (LCM) problem requires finding the smallest number that is divisible by both 6 and 12. Since the customer must buy equal numbers of muffins and donuts, you need a common multiple: $LCM(6, 12) = 12$. This means 2 boxes of muffins (12 muffins) and 1 box of donuts (12 donuts), for a total of 24 baked goods. Strategy: When a problem involves "same number" of items packaged differently, think LCM immediately.

Question 19

1. 300 miles
2. 350 miles
3. 400 miles (correct answer)
4. 450 miles

Explanation: This problem asks how far the car can travel on 20 gallons. We need to find the rate (miles per gallon) first, then multiply by 20 gallons. Rate = 100 miles ÷ 5 gallons = 20 miles per gallon. Distance = 20 miles/gallon × 20 gallons = 400 miles. Choice A (300 miles) might result from using the wrong rate or making an arithmetic error.

Question 20

1. 50 mph
2. 55 mph
3. 60 mph (correct answer)
4. 65 mph

Explanation: This problem asks for the speed of the school bus. We need to use the formula: speed = distance ÷ time. Bus speed = 120 miles ÷ 2 hours = 60 mph. Choice B (55 mph) might result from an arithmetic error or misreading the problem.