Free ASVAB Arithmetic Reasoning Practice Test
Arithmetic Reasoning (AR) tests whether you can turn a short word problem into the right calculation: percents, ratios, rates, averages, and money. On the computer-based CAT-ASVAB, Arithmetic Reasoning has 15 questions with a 55-minute time limit. AR is one of the four subtests that make up your AFQT score, so it directly affects whether you can enlist.
Below are 15 free Arithmetic Reasoning practice questions. Open "Show answer" under each one for the correct choice and an explanation.
Arithmetic Reasoning practice questions
Question 1
A jacket regularly priced at $80 is on sale for 25% off. What is the sale price?
- A.$20
- B.$55
- C.$60
- D.$64
Show answer
Correct answer: C. $60
25% of $80 is 0.25 × 80 = $20. The sale price is $80 − $20 = $60.
Question 2
A supply truck travels at a steady 52 miles per hour for 3.5 hours. How far does it travel?
- A.182 miles
- B.156 miles
- C.175 miles
- D.208 miles
Show answer
Correct answer: A. 182 miles
Distance = rate × time = 52 × 3.5 = 182 miles.
Question 3
A recipe uses 3 cups of flour for every 2 cups of sugar. If a mess hall cook uses 15 cups of flour, how many cups of sugar are needed?
- A.6 cups
- B.7.5 cups
- C.22.5 cups
- D.10 cups
Show answer
Correct answer: D. 10 cups
Set up the proportion 3/2 = 15/x. Then 3x = 30, so x = 10 cups of sugar.
Question 4
A recruit scored 82, 90, 76, and 88 on four fitness tests. What score does she need on the fifth test to average exactly 85?
- A.85
- B.89
- C.91
- D.87
Show answer
Correct answer: B. 89
An 85 average over 5 tests needs a total of 85 × 5 = 425. She has 82 + 90 + 76 + 88 = 336, so she needs 425 − 336 = 89.
Question 5
A hallway is 18 feet long. How long is it in yards?
- A.3 yards
- B.6 yards
- C.9 yards
- D.54 yards
Show answer
Correct answer: B. 6 yards
There are 3 feet in a yard, so 18 ÷ 3 = 6 yards.
Question 6
A water tank holds 240 gallons and is currently 3/8 full. How many more gallons are needed to fill it completely?
- A.90 gallons
- B.120 gallons
- C.160 gallons
- D.150 gallons
Show answer
Correct answer: D. 150 gallons
The tank is missing 1 − 3/8 = 5/8 of its capacity. 5/8 × 240 = 150 gallons.
Question 7
A recruiting office orders 14 boxes of pens with 24 pens in each box. After handing out 290 pens at a job fair, how many pens are left?
- A.46
- B.56
- C.36
- D.24
Show answer
Correct answer: A. 46
The office had 14 × 24 = 336 pens. 336 − 290 = 46 pens remain.
Question 8
A store buys a pair of boots for $50 and marks the price up 40%. During a sale, it takes 20% off the marked price. What is the sale price of the boots?
- A.$60
- B.$40
- C.$56
- D.$58
Show answer
Correct answer: C. $56
Marked price: $50 × 1.40 = $70. Sale price: $70 × 0.80 = $56.
Question 9
Two convoys leave the same base at 9:00 AM and drive in opposite directions, one at 45 mph and the other at 55 mph. At what time will they be 350 miles apart?
- A.12:00 PM
- B.1:00 PM
- C.3:30 PM
- D.12:30 PM
Show answer
Correct answer: D. 12:30 PM
Moving apart, their distance grows at 45 + 55 = 100 mph. 350 ÷ 100 = 3.5 hours, and 9:00 AM + 3.5 hours = 12:30 PM.
Question 10
Maria is 3 times as old as her son. In 12 years, she will be twice as old as her son. How old is Maria now?
- A.36
- B.24
- C.12
- D.48
Show answer
Correct answer: A. 36
Let the son be s, so Maria is 3s. Then 3s + 12 = 2(s + 12), which gives s = 12, so Maria is 3 × 12 = 36.
Question 11
On a map, 1 inch represents 15 miles. Two towns are 4 3/4 inches apart on the map. What is the actual distance between them?
- A.60 miles
- B.67.5 miles
- C.71.25 miles
- D.75 miles
Show answer
Correct answer: C. 71.25 miles
Multiply the map distance by the scale: 4.75 × 15 = 71.25 miles.
Question 12
Pump A can fill a reservoir in 6 hours, and Pump B can fill it in 3 hours. How long will it take to fill the reservoir if both pumps run together?
- A.4.5 hours
- B.2 hours
- C.3 hours
- D.1.5 hours
Show answer
Correct answer: B. 2 hours
Together they fill 1/6 + 1/3 = 1/2 of the reservoir per hour, so the job takes 1 ÷ 1/2 = 2 hours.
Question 13
A soldier deposits $2,400 in an account that pays 3.5% simple interest per year. How much interest will the account earn in 4 years?
- A.$336
- B.$84
- C.$2,736
- D.$350
Show answer
Correct answer: A. $336
Simple interest = principal × rate × time = $2,400 × 0.035 × 4 = $336.
Question 14
A drill sergeant has 84 recruits in one company and 60 in another. He wants to split each company into squads that are all the same size, with no recruits left over and no mixing of companies. What is the largest possible squad size?
- A.6
- B.4
- C.15
- D.12
Show answer
Correct answer: D. 12
The largest size that divides both 84 and 60 evenly is their greatest common factor. 84 = 12 × 7 and 60 = 12 × 5, so the answer is 12.
Question 15
A bag holds 5 red, 7 blue, and 8 green marbles. If one marble is drawn at random, what is the probability that it is blue?
- A.7/13
- B.1/3
- C.7/20
- D.13/20
Show answer
Correct answer: C. 7/20
There are 5 + 7 + 8 = 20 marbles, and 7 of them are blue, so the probability is 7/20.
Tips for ASVAB Arithmetic Reasoning
- Write down what the question asks for before you calculate — many wrong choices are the right answer to a different step.
- Estimate first. If your exact answer is far from your estimate, recheck the setup, not just the arithmetic.
- Learn the core patterns: percent change, distance = rate × time, combined work rates, and averages.
- You cannot use a calculator on the ASVAB, so practice long division and fraction arithmetic by hand.
Keep practicing
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