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ASVAB Arithmetic Reasoning Practice Questions and Study Tips
Arithmetic Reasoning is the word-problem subtest. It is one of the four subtests that make up your AFQT score, so it directly affects whether you can enlist. You read a short real-world problem, decide what math it needs, and solve it without a calculator.
| Questions (paper ASVAB) | 30 |
|---|---|
| Time limit | 36 minutes |
| Abbreviation | AR |
| Counts toward AFQT? | Yes, it is one of the four AFQT subtests. |
The computer version of the ASVAB (CAT-ASVAB) has fewer questions and adjusts the difficulty to your answers, but it covers the same material.
What the Arithmetic Reasoning subtest covers
- Rates, speed, distance and time
- Percentages, discounts, tax and interest
- Ratios and proportions
- Averages
- Work problems (how long jobs take together)
- Unit conversions and simple geometry in word form
Arithmetic Reasoning practice questions
Try these 18 questions written in the ASVAB style. They cover every common problem type, from rates to ages. Work each one on scratch paper before you open the answer.
1. A recruit runs 3 miles in 24 minutes. At the same pace, how long will it take to run 5 miles?
- 32 minutes
- 36 minutes
- 40 minutes
- 45 minutes
Show answer
C. 40 minutes 24 ÷ 3 = 8 minutes per mile, and 8 × 5 = 40 minutes.
2. A pair of boots costs $60 and is on sale for 25% off. What is the sale price?
- $35
- $40
- $45
- $48
Show answer
C. $45 25% of $60 is $15, and $60 − $15 = $45.
3. A truck travels 150 miles on 5 gallons of fuel. How many gallons does it need for 420 miles?
- 12
- 14
- 16
- 18
Show answer
B. 14 150 ÷ 5 = 30 miles per gallon, and 420 ÷ 30 = 14 gallons.
4. The price of a uniform rises from $80 to $92. By what percent did the price increase?
- 12%
- 15%
- 18%
- 20%
Show answer
B. 15% The increase is $12. Divide by the original price: 12 ÷ 80 = 0.15, or 15%.
5. You put $1,200 in an account that pays 5% simple interest per year. How much interest do you earn in 3 years?
- $60
- $150
- $1,380
- $180
Show answer
D. $180 Interest = principal × rate × time = 1,200 × 0.05 × 3 = $180. ($1,380 is the total balance, not the interest.)
6. A recruit scored 82, 90 and 76 on three tests. What score does she need on the fourth test to average 85?
- 92
- 88
- 85
- 95
Show answer
A. 92 An average of 85 over 4 tests needs a total of 340. She has 82 + 90 + 76 = 248, so she needs 340 − 248 = 92.
Want to know where you stand? The free 25-question diagnostic covers all nine subtests and shows your weakest one. No account needed to start.
7. One crew can paint a barracks in 6 hours. A second crew can paint it in 3 hours. How long will it take if both crews work together?
- 4.5 hours
- 3 hours
- 2.5 hours
- 2 hours
Show answer
D. 2 hours Together they paint 1/6 + 1/3 = 1/2 of the barracks per hour, so the job takes 2 hours.
8. The ratio of enlisted soldiers to officers at a briefing is 9 to 2. If 44 people attend, how many are officers?
- 6
- 8
- 9
- 11
Show answer
B. 8 The ratio has 9 + 2 = 11 parts. 44 ÷ 11 = 4 people per part, and officers are 2 parts: 2 × 4 = 8.
9. A convoy drives at 45 miles per hour for 2 hours, then at 60 miles per hour for 3 hours. How far does it travel in total?
- 270 miles
- 255 miles
- 300 miles
- 225 miles
Show answer
A. 270 miles Distance = rate × time for each part: 45 × 2 = 90 and 60 × 3 = 180. 90 + 180 = 270 miles.
10. A driver goes 120 miles at 60 miles per hour, then returns the same 120 miles at 40 miles per hour. What is the average speed for the whole trip?
- 50 mph
- 52 mph
- 48 mph
- 45 mph
Show answer
C. 48 mph The trip takes 2 hours out and 3 hours back: 240 miles in 5 hours is 48 mph. Averaging 60 and 40 to get 50 is the trap.
11. A canteen holds 1.5 quarts. How many canteens can be filled from 3 gallons of water? (1 gallon = 4 quarts)
- 6
- 9
- 12
- 8
Show answer
D. 8 3 gallons is 3 × 4 = 12 quarts, and 12 ÷ 1.5 = 8 canteens.
12. A $200 jacket is marked 20% off. At the register you get another 10% off the sale price. What do you pay?
- $140
- $144
- $150
- $156
Show answer
B. $144 20% off leaves $160. 10% off $160 is $16, so you pay $144. Adding the discounts to get 30% off ($140) is the trap.
Want to know where you stand? The free 25-question diagnostic covers all nine subtests and shows your weakest one. No account needed to start.
13. A meal costs $24. Sales tax is 8%, and you leave a $4 tip. What is the total?
- $28.92
- $30.40
- $29.92
- $31.12
Show answer
C. $29.92 Tax is 0.08 × 24 = $1.92. $24 + $1.92 + $4 = $29.92.
14. A rectangular parade field is 120 yards long and 50 yards wide. How many yards of fence are needed to go around it?
- 340
- 170
- 6,000
- 600
Show answer
A. 340 Perimeter = 2 × (120 + 50) = 340 yards. (6,000 is the area.)
15. On a map, 1 inch represents 25 miles. Two bases are 3.5 inches apart on the map. How far apart are they?
- 75 miles
- 82.5 miles
- 92.5 miles
- 87.5 miles
Show answer
D. 87.5 miles 3.5 × 25 = 87.5 miles.
16. A platoon has 35 members, and 40% of them are women. How many members are men?
- 14
- 21
- 19
- 24
Show answer
B. 21 If 40% are women, 60% are men. 0.6 × 35 = 21. (14 is the number of women.)
17. A trainee spends 1/3 of her monthly pay on rent and 1/4 on food. She has $1,000 left. What is her monthly pay?
- $2,000
- $2,200
- $2,400
- $3,000
Show answer
C. $2,400 Rent and food take 1/3 + 1/4 = 7/12, so 5/12 is left. If 5/12 of her pay is $1,000, her pay is 1,000 × 12 ÷ 5 = $2,400.
18. Sam is three times as old as his sister. In 5 years he will be twice as old as she is. How old is his sister now?
- 4
- 6
- 5
- 8
Show answer
C. 5 Let her age be s. Then 3s + 5 = 2(s + 5), so 3s + 5 = 2s + 10 and s = 5. Check: Sam is 15; in 5 years, 20 is twice 10.
How to set up any word problem
- Find the question. Read the last sentence first and underline what it asks for, including the units.
- List what you know. Write the numbers with their labels: 45 mph, 2 hours, $1,200.
- Pick the pattern. Most problems are a percent, a ratio, a rate, an average or a work-together problem. Each has one formula.
- Solve and sanity-check. Ask whether the answer is sensible: a discount should lower the price, and two crews together should finish faster than either alone.
This takes a few seconds once it is a habit, and it prevents the most expensive mistake on the subtest: correctly solving the wrong problem.
Question types students miss most
- Average speed. Driving out at 60 mph and back at 40 mph is not an average of 50. Divide total distance by total time.
- Percent change. Always divide the change by the starting value, not the new one.
- Back-to-back discounts. 20% off and then 10% off is 28% off, not 30%. Apply them one at a time.
- Working together. Add the rates (1/6 + 1/3 of the job per hour), not the times.
- Fractions of what is left. When several fractions come out of one amount, add them first, then find what remains.
Common mistakes
- Answering a different question than the one asked, such as giving the number of women when it asks for men.
- Mixing units: minutes with hours, quarts with gallons, inches with feet. Convert before you calculate.
- Stopping one step early. Many answers include the value you get halfway through as a trap.
- Rushing the setup. Most wrong answers come from the equation, not the arithmetic.
Time strategy
The paper test gives you 36 minutes for 30 questions, about 72 seconds each. That is enough time if you don't get stuck. If a question takes more than 2 minutes, mark your best guess and move on. Wrong answers don't cost extra points on the paper test, so never leave a bubble blank.
On the computer test (CAT-ASVAB) you can't go back to a question, and running out of time with questions unanswered lowers your score, so answer every question even if you have to guess near the end.
A 7-day plan for Arithmetic Reasoning
- Day 1: Take the free diagnostic to get a baseline, then review fractions, decimals and percents by hand.
- Day 2: Percents: discounts, tax, percent change and simple interest.
- Day 3: Ratios and proportions, including map scales and recipes.
- Day 4: Rate problems: distance, speed, time and average speed.
- Day 5: Work-together and averages, including the missing-score type.
- Day 6: Mixed practice under a clock: 15 questions in 18 minutes.
- Day 7: Review every question you missed this week and redo it without looking at the solution.
Tips for the Arithmetic Reasoning subtest
- Write down what the question is actually asking before you start working.
- Many problems are a proportion in disguise. Set up two equal fractions and cross-multiply.
- Check that your answer makes sense. A sale price can't be higher than the original price.
- No calculator is allowed, so practice long division and percentages by hand. Keep the ASVAB formula sheet handy while you study.
Questions people ask
How many questions are on ASVAB Arithmetic Reasoning?
The paper ASVAB has 30 Arithmetic Reasoning questions with a 36-minute time limit. The computer version has fewer questions.
Does Arithmetic Reasoning count toward the AFQT?
Yes, it is one of the four AFQT subtests.
Can I use a calculator on ASVAB Arithmetic Reasoning?
No. Neither math subtest allows a calculator, so practice working problems by hand with scratch paper.
How can I get better at ASVAB word problems?
Learn the handful of problem types that repeat (percents, ratios, rates, averages and work-together), practice each until the setup is automatic, then mix them under a clock.
Free download: print the ASVAB formula sheet with every math formula you need to know by heart, since no calculator or formula sheet is allowed on test day.
Find your weakest subtest in about 20 minutes. The free 25-question diagnostic covers all nine ASVAB subtests. No card needed.
Take the free ASVAB diagnostic