A car travels at 55 miles per hour. How many miles will it travel in 3 hours and 30 minutes?

Correct answer: 192.5 miles. 3 hours 30 minutes = 3.5 hours. Distance = 55 × 3.5 = 192.5 miles.

A store marks up an item by 40% from its wholesale cost of $35. What is the retail selling price?

Correct answer: $49.00. Markup = 40% × $35 = $14. Retail price = $35 + $14 = $49.00.

A recipe calls for flour and sugar in a ratio of 5:2. If you use 20 cups of flour, how many cups of sugar are needed?

Correct answer: 8 cups. Set sugar/flour = 2/5, so sugar = (2/5) × 20 = 8 cups. Choice 4 cups uses the difference between ratio parts (5 − 2 = 3) and applies it loosely, then halves the answer. Choice 6 cups assumes the ratio means 2 cups of sugar for every 6 of flour, misreading the colon as a one-step gap rather than a multiplicative ratio. Choice 10 cups halves the 20 cups of flour, ignoring the 5:2 relationship and treating the ratio as if it were 2:1.

A soldier earns $2,400 per month and saves 15% of that amount. After 6 months, how much has the soldier saved?

Correct answer: $2,160. Monthly savings = 15% × $2,400 = $360. Over 6 months: $360 × 6 = $2,160.

A tank holds 500 gallons of water. It drains at a rate of 25 gallons per minute and fills at 10 gallons per minute simultaneously. Starting with a full tank, how many minutes will it take to empty?

Correct answer: 33 minutes. Net drain rate = 25 − 10 = 15 gal/min, so time = 500 ÷ 15 ≈ 33.3 minutes, which rounds to 33. Choice 20 minutes divides 500 by 25, using the drain rate alone and ignoring the simultaneous inflow. Choice 25 minutes splits the difference between the two rates without combining them into a net rate. Choice 50 minutes divides 500 by 10, using only the fill rate as if the tank were filling, the exact opposite of the scenario.

A platoon of 40 soldiers must carry 480 pounds of equipment equally. How many pounds does each soldier carry?

Correct answer: 12 pounds. Divide total load by soldiers: 480 ÷ 40 = 12 pounds each. Choice 10 pounds rounds 480 down to 400 to avoid the long division. Choice 14 pounds estimates between 10 and 16 without doing the division. Choice 16 pounds divides 480 by 30 instead of 40, miscounting the platoon size.

A shirt originally priced at $60 is on sale for 25% off. What is the sale price?

Correct answer: $45. Discount = 25% × $60 = $15. Sale price = $60 − $15 = $45.

Two workers can paint a room in 6 hours working together. If one worker can complete the job alone in 10 hours, how long would the second worker take alone?

Correct answer: 15 hours. Worker 2's rate = combined rate − Worker 1's rate = 1/6 − 1/10 = 5/30 − 3/30 = 2/30 = 1/15, so Worker 2 alone takes 15 hours. Choice 12 hours averages 6 and 10 incorrectly, splitting the difference between team and Worker 1 times. Choice 16 hours adds the two stated times (10 + 6) instead of subtracting rates. Choice 20 hours simply doubles 10, assuming Worker 2 is half as fast without using the combined-rate equation.

If 5 pens cost $3.75, what is the cost of 8 pens at the same price?

Correct answer: $6.00. Price per pen = $3.75 ÷ 5 = $0.75. Cost of 8 pens = 8 × $0.75 = $6.00.

A rectangular field is 120 yards long and 80 yards wide. What is its area in square yards?

Correct answer: 9,600. Area = length × width = 120 × 80 = 9,600 square yards. Choice 4,800 halves the answer, perhaps computing perimeter logic (2 × (120 + 80) = 400) and then estimating area from that. Choice 8,400 drops a hundreds digit during the multiplication, treating it as 12 × 7 instead of 12 × 8. Choice 10,400 adds an extra 800 from a stray carry during the multiplication.

A train leaves a station at 9:00 AM traveling at 60 mph. A second train leaves the same station at 10:00 AM traveling in the same direction at 90 mph. At what time does the second train catch up to the first?

Correct answer: 12:00 PM. Train 1's head start at 10:00 AM is 60 miles, closing rate = 90 − 60 = 30 mph, so catch-up = 60 ÷ 30 = 2 hours after 10:00 AM, which is 12:00 PM. Choice 11:00 AM uses 90 mph as the closing rate, forgetting that Train 1 keeps moving forward. Choice 12:30 PM adds a 30-minute buffer for unstated startup. Choice 1:00 PM divides 60 by 20 instead of 30, miscalculating the speed gap between the trains.

A map has a scale of 1 inch = 50 miles. Two cities are 3.5 inches apart on the map. What is the actual distance between them?

Correct answer: 175 miles. Actual distance = inches × scale = 3.5 × 50 = 175 miles. Choice 150 miles rounds 3.5 down to 3 inches before multiplying. Choice 200 miles rounds 3.5 up to 4 inches. Choice 225 miles adds an extra half-scale unit (4.5 × 50), reading the half-inch as a full step on top of the 4-inch round-up.

How many free Arithmetic Reasoning practice questions are here?

This page has 12 free ASVAB Arithmetic Reasoning questions, each with the correct answer and a full worked explanation. They're free to use with no account required.

Does Arithmetic Reasoning count toward my AFQT score?

Yes. Arithmetic Reasoning is one of the four AFQT subtests (AR, WK, PC, MK), so it directly affects your enlistment eligibility.

What does the Arithmetic Reasoning subtest cover?

Word problems that test your ability to solve real-world math situations. One of the 4 AFQT subtests, so it directly affects your enlistment eligibility. On the CAT-ASVAB it has 15 questions with about 39 minutes to answer them. Topics include: Word problems: rates, percentages, ratios, basic algebra.

Are these the same as the real ASVAB questions?

No. These are original practice questions calibrated to match the style and difficulty of the real ASVAB. The actual test is a secure exam, so no one publishes its live items. Practicing this format is the closest legitimate prep.

Free ASVAB Arithmetic Reasoning Practice Test

12 Arithmetic Reasoning (AR) practice questions, each with a worked explanation of the right answer.

Last updated May 2026

The ASVAB Arithmetic Reasoning (AR) subtest covers word problems: rates, percentages, ratios, basic algebra. On the computer-adaptive CAT-ASVAB it has 15 questions with about 39 minutes to answer. It is one of the four AFQT subtests, so it directly affects your enlistment eligibility. Work the 12 questions below, then read each explanation. Understanding why the answer is right is what raises your score.

Question 1· Arithmetic Reasoning
A car travels at 55 miles per hour. How many miles will it travel in 3 hours and 30 minutes?
- A.165 miles
- B.182.5 miles
- C.192.5 miles
- D.198 miles
Show answer & explanationHide answer
Correct answer: C. 192.5 miles
Why: 3 hours 30 minutes = 3.5 hours. Distance = 55 × 3.5 = 192.5 miles.
Question 2· Arithmetic Reasoning
A store marks up an item by 40% from its wholesale cost of $35. What is the retail selling price?
- A.$14.00
- B.$45.50
- C.$49.00
- D.$52.50
Show answer & explanationHide answer
Correct answer: C. $49.00
Why: Markup = 40% × $35 = $14. Retail price = $35 + $14 = $49.00.
Question 3· Arithmetic Reasoning
A recipe calls for flour and sugar in a ratio of 5:2. If you use 20 cups of flour, how many cups of sugar are needed?
- A.4 cups
- B.6 cups
- C.8 cups
- D.10 cups
Show answer & explanationHide answer
Correct answer: C. 8 cups
Why: Set sugar/flour = 2/5, so sugar = (2/5) × 20 = 8 cups. Choice 4 cups uses the difference between ratio parts (5 − 2 = 3) and applies it loosely, then halves the answer. Choice 6 cups assumes the ratio means 2 cups of sugar for every 6 of flour, misreading the colon as a one-step gap rather than a multiplicative ratio. Choice 10 cups halves the 20 cups of flour, ignoring the 5:2 relationship and treating the ratio as if it were 2:1.
Question 4· Arithmetic Reasoning
A soldier earns $2,400 per month and saves 15% of that amount. After 6 months, how much has the soldier saved?
- A.$1,440
- B.$2,160
- C.$2,400
- D.$3,600
Show answer & explanationHide answer
Correct answer: B. $2,160
Why: Monthly savings = 15% × $2,400 = $360. Over 6 months: $360 × 6 = $2,160.
Question 5· Arithmetic Reasoning
A tank holds 500 gallons of water. It drains at a rate of 25 gallons per minute and fills at 10 gallons per minute simultaneously. Starting with a full tank, how many minutes will it take to empty?
- A.20 minutes
- B.25 minutes
- C.33 minutes
- D.50 minutes
Show answer & explanationHide answer
Correct answer: C. 33 minutes
Why: Net drain rate = 25 − 10 = 15 gal/min, so time = 500 ÷ 15 ≈ 33.3 minutes, which rounds to 33. Choice 20 minutes divides 500 by 25, using the drain rate alone and ignoring the simultaneous inflow. Choice 25 minutes splits the difference between the two rates without combining them into a net rate. Choice 50 minutes divides 500 by 10, using only the fill rate as if the tank were filling, the exact opposite of the scenario.
Question 6· Arithmetic Reasoning
A platoon of 40 soldiers must carry 480 pounds of equipment equally. How many pounds does each soldier carry?
- A.10 pounds
- B.12 pounds
- C.14 pounds
- D.16 pounds
Show answer & explanationHide answer
Correct answer: B. 12 pounds
Why: Divide total load by soldiers: 480 ÷ 40 = 12 pounds each. Choice 10 pounds rounds 480 down to 400 to avoid the long division. Choice 14 pounds estimates between 10 and 16 without doing the division. Choice 16 pounds divides 480 by 30 instead of 40, miscounting the platoon size.
Question 7· Arithmetic Reasoning
A shirt originally priced at $60 is on sale for 25% off. What is the sale price?
- A.$15
- B.$40
- C.$45
- D.$50
Show answer & explanationHide answer
Correct answer: C. $45
Why: Discount = 25% × $60 = $15. Sale price = $60 − $15 = $45.
Question 8· Arithmetic Reasoning
Two workers can paint a room in 6 hours working together. If one worker can complete the job alone in 10 hours, how long would the second worker take alone?
- A.12 hours
- B.15 hours
- C.16 hours
- D.20 hours
Show answer & explanationHide answer
Correct answer: B. 15 hours
Why: Worker 2's rate = combined rate − Worker 1's rate = 1/6 − 1/10 = 5/30 − 3/30 = 2/30 = 1/15, so Worker 2 alone takes 15 hours. Choice 12 hours averages 6 and 10 incorrectly, splitting the difference between team and Worker 1 times. Choice 16 hours adds the two stated times (10 + 6) instead of subtracting rates. Choice 20 hours simply doubles 10, assuming Worker 2 is half as fast without using the combined-rate equation.
Question 9· Arithmetic Reasoning
If 5 pens cost $3.75, what is the cost of 8 pens at the same price?
- A.$5.00
- B.$5.60
- C.$6.00
- D.$6.25
Show answer & explanationHide answer
Correct answer: C. $6.00
Why: Price per pen = $3.75 ÷ 5 = $0.75. Cost of 8 pens = 8 × $0.75 = $6.00.
Question 10· Arithmetic Reasoning
A rectangular field is 120 yards long and 80 yards wide. What is its area in square yards?
- A.4,800
- B.8,400
- C.9,600
- D.10,400
Show answer & explanationHide answer
Correct answer: C. 9,600
Why: Area = length × width = 120 × 80 = 9,600 square yards. Choice 4,800 halves the answer, perhaps computing perimeter logic (2 × (120 + 80) = 400) and then estimating area from that. Choice 8,400 drops a hundreds digit during the multiplication, treating it as 12 × 7 instead of 12 × 8. Choice 10,400 adds an extra 800 from a stray carry during the multiplication.
Question 11· Arithmetic Reasoning
A train leaves a station at 9:00 AM traveling at 60 mph. A second train leaves the same station at 10:00 AM traveling in the same direction at 90 mph. At what time does the second train catch up to the first?
- A.11:00 AM
- B.12:00 PM
- C.12:30 PM
- D.1:00 PM
Show answer & explanationHide answer
Correct answer: B. 12:00 PM
Why: Train 1's head start at 10:00 AM is 60 miles, closing rate = 90 − 60 = 30 mph, so catch-up = 60 ÷ 30 = 2 hours after 10:00 AM, which is 12:00 PM. Choice 11:00 AM uses 90 mph as the closing rate, forgetting that Train 1 keeps moving forward. Choice 12:30 PM adds a 30-minute buffer for unstated startup. Choice 1:00 PM divides 60 by 20 instead of 30, miscalculating the speed gap between the trains.
Question 12· Arithmetic Reasoning
A map has a scale of 1 inch = 50 miles. Two cities are 3.5 inches apart on the map. What is the actual distance between them?
- A.150 miles
- B.175 miles
- C.200 miles
- D.225 miles
Show answer & explanationHide answer
Correct answer: B. 175 miles
Why: Actual distance = inches × scale = 3.5 × 50 = 175 miles. Choice 150 miles rounds 3.5 down to 3 inches before multiplying. Choice 200 miles rounds 3.5 up to 4 inches. Choice 225 miles adds an extra half-scale unit (4.5 × 50), reading the half-inch as a full step on top of the 4-inch round-up.

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What's on the ASVAB Arithmetic Reasoning subtest

Word problems that test your ability to solve real-world math situations. One of the 4 AFQT subtests, so it directly affects your enlistment eligibility.

Common topics you'll see:

Rate, time & distance problems
Percentage calculations
Ratio & proportion
Basic algebra word problems
Number sequences & patterns
Work rate problems
Profit, loss & discount
Geometry word problems
Consecutive integer problems
Mixed operations

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FAQ

How many free Arithmetic Reasoning practice questions are here?: This page has 12 free ASVAB Arithmetic Reasoning questions, each with the correct answer and a full worked explanation. They're free to use with no account required.
Does Arithmetic Reasoning count toward my AFQT score?: Yes. Arithmetic Reasoning is one of the four AFQT subtests (AR, WK, PC, MK), so it directly affects your enlistment eligibility.
What does the Arithmetic Reasoning subtest cover?: Word problems that test your ability to solve real-world math situations. One of the 4 AFQT subtests, so it directly affects your enlistment eligibility. On the CAT-ASVAB it has 15 questions with about 39 minutes to answer them. Topics include: Word problems: rates, percentages, ratios, basic algebra.
Are these the same as the real ASVAB questions?: No. These are original practice questions calibrated to match the style and difficulty of the real ASVAB. The actual test is a secure exam, so no one publishes its live items. Practicing this format is the closest legitimate prep.

Free practice tests for the other subtests

ASVAB score calculator for converting raw scores to AFQT and line scores
Score requirements by branch for army, navy, air force, marines, and coast guard