19 Arithmetic Reasoning (AR) Practice Questions & Answers
Every Arithmetic Reasoning (AR) practice question from the ASVAB Practice Test, with the correct answer and a short explanation.
Start practice test →1. A car travels 300 miles in 5 hours at a constant speed. What is the car's average speed?
- A.65 mph
- B.60 mph✓ Answer
- C.55 mph
- D.50 mph
Average speed equals total distance divided by total time, so 300 miles ÷ 5 hours = 60 mph.
Source: ASVAB Arithmetic Reasoning — distance-rate-time (rate = distance ÷ time)Report a problem with this question
2. What is 20% of 80?
- A.14
- B.12
- C.16✓ Answer
- D.18
To find a percent of a number, convert the percent to a decimal and multiply: 0.20 × 80 = 16.
Source: ASVAB Arithmetic Reasoning — percentages (percent of a number)Report a problem with this question
3. The number 15 is what percent of 60?
- A.20%
- B.25%✓ Answer
- C.30%
- D.40%
To find what percent one number is of another, divide the part by the whole and multiply by 100: (15 ÷ 60) × 100 = 25%.
Source: ASVAB Arithmetic Reasoning — percentages (part/whole)Report a problem with this question
4. A student's five test scores are 82, 90, 78, 84, and 86. What is the average (mean) score?
- A.85
- B.82
- C.83
- D.84✓ Answer
The mean is the sum of the values divided by how many there are: (82+90+78+84+86) ÷ 5 = 420 ÷ 5 = 84.
Source: ASVAB Arithmetic Reasoning — averages/meansReport a problem with this question
5. What is 2/3 of 90?
- A.72
- B.54
- C.45
- D.60✓ Answer
Taking a fraction 'of' a number means multiplying: (2/3) × 90 = 180/3 = 60.
Source: ASVAB Arithmetic Reasoning — fractions in real-world contextsReport a problem with this question
6. Working alone, one pump can fill a tank in 4 hours and a second pump can fill the same tank in 6 hours. Working together, how long will they take to fill the tank?
- A.3.0 hours
- B.2.0 hours
- C.2.4 hours✓ Answer
- D.2.5 hours
Add the rates: 1/4 + 1/6 = 3/12 + 2/12 = 5/12 tank per hour, so the time is the reciprocal, 12/5 = 2.4 hours.
Source: ASVAB Arithmetic Reasoning — work-rate problems (combined rate)Report a problem with this question
7. A driver needs to travel 240 miles at an average speed of 60 miles per hour. How long will the trip take?
- A.3.5 hours
- B.3 hours
- C.4.5 hours
- D.4 hours✓ Answer
Time equals distance divided by rate: 240 miles ÷ 60 mph = 4 hours.
Source: ASVAB Arithmetic Reasoning — distance-rate-time (time = distance ÷ rate)Report a problem with this question
8. Two numbers are in the ratio 3:5 and their sum is 40. What is the larger number?
- A.20
- B.25✓ Answer
- C.24
- D.15
The ratio has 3 + 5 = 8 equal parts, so each part is 40 ÷ 8 = 5; the larger number is 5 parts, 5 × 5 = 25.
Source: ASVAB Arithmetic Reasoning — ratios and proportionsReport a problem with this question
9. A jacket originally priced at 60 units is marked down by 25%. What is the sale price?
- A.48 units
- B.42 units
- C.45 units✓ Answer
- D.40 units
A 25% discount leaves 75% of the price, so the sale price is 0.75 × 60 = 45 units.
Source: ASVAB Arithmetic Reasoning — percentages (discount)Report a problem with this question
10. It takes 5 identical workers 8 days to complete a job. Working at the same rate, how many days would 10 such workers take to complete the same job?
- A.4 days✓ Answer
- B.16 days
- C.10 days
- D.5 days
Workers and time are inversely proportional, so the total work is 5 × 8 = 40 worker-days; dividing by 10 workers gives 40 ÷ 10 = 4 days.
Source: ASVAB Arithmetic Reasoning — inverse proportion (work problems)Report a problem with this question
11. A principal of 800 units is invested at a simple annual interest rate of 5% for 3 years. How much interest is earned?
- A.150 units
- B.80 units
- C.120 units✓ Answer
- D.40 units
Simple interest is principal × rate × time: 800 × 0.05 × 3 = 120 units, because simple interest is computed only on the original principal each year.
Source: ASVAB Arithmetic Reasoning — simple interest (I = P·r·t)Report a problem with this question
12. If 12 pencils cost 36 units, how much do 5 pencils cost at the same rate?
- A.12 units
- B.15 units✓ Answer
- C.20 units
- D.18 units
Find the unit price first: 36 ÷ 12 = 3 units per pencil, then multiply by 5 to get 3 × 5 = 15 units.
Source: ASVAB Arithmetic Reasoning — proportions (unit rate)Report a problem with this question
13. A train covers 90 kilometers in 1.5 hours. What is its average speed in kilometers per hour?
- A.75 km/h
- B.55 km/h
- C.60 km/h✓ Answer
- D.45 km/h
Speed equals distance divided by time: 90 km ÷ 1.5 hours = 60 km/h.
Source: ASVAB Arithmetic Reasoning — distance-rate-timeReport a problem with this question
14. A recipe that serves 4 people requires 6 cups of flour. How many cups of flour are needed to serve 6 people, keeping the same proportions?
- A.10 cups
- B.8 cups
- C.9 cups✓ Answer
- D.7 cups
Set up a proportion: 6 cups ÷ 4 people = x ÷ 6 people, so x = (6/4) × 6 = 9 cups.
Source: ASVAB Arithmetic Reasoning — proportions (scaling)Report a problem with this question
15. A sum of 1,000 units is invested for 2 years at 10% interest compounded annually. What is the total value at the end of 2 years?
- A.1,200 units
- B.1,210 units✓ Answer
- C.1,100 units
- D.1,220 units
Compound interest adds each year's interest to the balance before the next year: 1,000 × 1.10 = 1,100 after year 1, then 1,100 × 1.10 = 1,210 after year 2.
Source: ASVAB Arithmetic Reasoning — compound interest conceptReport a problem with this question
16. How many feet are in 4 yards? (1 yard = 3 feet)
- A.7 feet
- B.15 feet
- C.12 feet✓ Answer
- D.9 feet
Multiply by the conversion factor: since 1 yard = 3 feet, 4 yards × 3 feet/yard = 12 feet.
Source: ASVAB Arithmetic Reasoning — unit conversion (yards to feet)Report a problem with this question
17. A shirt's price is increased by 20% and the new price is 72 units. What was the original price?
- A.58 units
- B.64 units
- C.52 units
- D.60 units✓ Answer
A 20% increase means the new price is 120% of the original, so the original is 72 ÷ 1.20 = 60 units.
Source: ASVAB Arithmetic Reasoning — percentages (reverse percent increase)Report a problem with this question
18. A cyclist rides 36 miles in 3 hours, rests, then rides another 24 miles in 2 hours. What is the cyclist's average speed for the entire ride (excluding rest)?
- A.13 mph
- B.15 mph
- C.11 mph
- D.12 mph✓ Answer
Average speed uses total distance over total time, not the average of the two speeds: (36 + 24) ÷ (3 + 2) = 60 ÷ 5 = 12 mph.
Source: ASVAB Arithmetic Reasoning — average speed over multiple legsReport a problem with this question
19. A 40-liter mixture is 25% acid. How many liters of acid does it contain?
- A.10 liters✓ Answer
- B.12 liters
- C.15 liters
- D.8 liters
The amount of acid is the percentage of the total: 0.25 × 40 = 10 liters.
Source: ASVAB Arithmetic Reasoning — percentages (mixture concentration)Report a problem with this question
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