20 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.

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1. A pump moves 84 gallons of water in 6 minutes. At that same rate, how many gallons will it move in 20 minutes?
- A.252 gallons
- B.336 gallons
- C.240 gallons
- D.280 gallons✓ Answer
Rate problems are solved by finding the unit rate first, then multiplying by the new amount of time. Here the unit rate is 84 ÷ 6 = 14 gallons per minute, so in 20 minutes the pump moves 14 × 20 = 280 gallons. Multiplying 84 by a whole number of 6-minute blocks fails because 20 is not a multiple of 6, which is why the unit-rate step matters.
Source: officialasvab.com — Arithmetic Reasoning subtest ("ability to solve arithmetic word problems"); unit-rate principle: rate = quantity ÷ time, then quantity = rate × timeReport a problem with this question
2. One store sells a 4-pound bag of rice for $9.60. Another store sells a 6-pound bag of the same rice for $13.50. How much less per pound does the cheaper bag cost?
- A.$0.15✓ Answer
- B.$1.15
- C.$0.25
- D.$3.90
A "better buy" comparison requires reducing both packages to the same unit before comparing: $9.60 ÷ 4 = $2.40 per pound and $13.50 ÷ 6 = $2.25 per pound. The 6-pound bag is cheaper by $2.40 − $2.25 = $0.15 per pound. Comparing the sticker prices ($13.50 − $9.60 = $3.90) is meaningless because the bags hold different amounts.
Source: officialasvab.com — Arithmetic Reasoning subtest; unit-price rule: unit price = total price ÷ number of unitsReport a problem with this question
3. A truck travels 350 miles on 25 gallons of fuel. At the same rate of fuel use, how many gallons are needed to travel 476 miles?
- A.28 gallons
- B.34 gallons✓ Answer
- C.36 gallons
- D.19 gallons
Set up the fuel-use rate as miles per gallon: 350 ÷ 25 = 14 miles per gallon. Gallons needed is then distance ÷ rate, so 476 ÷ 14 = 34 gallons. Dividing 476 by 25 instead (giving about 19) inverts the relationship — 25 is a quantity of gallons, not a rate.
Source: officialasvab.com — Arithmetic Reasoning subtest; proportional reasoning with rates (a/b = c/d solved by cross-multiplication)Report a problem with this question
4. A group of 187 people must be transported by bus. Each bus seats 45 people. What is the smallest number of buses needed so that everyone gets a seat?
- A.3
- B.5✓ Answer
- C.6
- D.4
Dividing gives 187 ÷ 45 = 4 with a remainder of 7, and a remainder of people still needs transportation, so the quotient must be rounded UP. Four buses seat only 180 people, leaving 7 without a seat, so 5 buses are required. "How many containers are needed" problems always round up; "how many complete items can be made" problems round down.
Source: officialasvab.com — Arithmetic Reasoning subtest; remainder-interpretation rule for capacity problems (round the quotient up)Report a problem with this question
5. In a training company of 480 recruits, 1 out of every 6 recruits is assigned to the motor pool. How many recruits are NOT assigned to the motor pool?
- A.80
- B.384
- C.400✓ Answer
- D.96
"One out of every 6" means the motor pool group is 1/6 of the total: 480 ÷ 6 = 80 recruits. The question asks for the complement, so subtract: 480 − 80 = 400 recruits are not assigned there. The classic trap is answering 80, which is the part that was given rather than the part that was asked for.
Source: officialasvab.com — Arithmetic Reasoning subtest; part-to-whole ratio rule and complement (whole − part)Report a problem with this question
6. A construction crew mixes gravel and sand in a 3 to 5 ratio by weight to produce 400 pounds of mix. How many pounds of sand are in the mix?
- A.250 pounds✓ Answer
- B.240 pounds
- C.150 pounds
- D.200 pounds
A ratio of 3 to 5 means the mix is divided into 3 + 5 = 8 equal parts, so one part weighs 400 ÷ 8 = 50 pounds. Sand is 5 parts, giving 5 × 50 = 250 pounds (gravel is 3 × 50 = 150 pounds, and the two correctly total 400). Splitting the total in half would only be correct if the ratio were 1 to 1.
Source: officialasvab.com — Arithmetic Reasoning subtest; ratio rule: each part = total ÷ (sum of ratio terms)Report a problem with this question
7. On a map, 1 inch represents 25 miles. Two supply depots are 3.5 inches apart on the map. What is the actual distance between them?
- A.87.5 miles✓ Answer
- B.75 miles
- C.92.5 miles
- D.62.5 miles
A map scale is a proportion: 1 inch / 25 miles = 3.5 inches / d miles. Cross-multiplying gives d = 3.5 × 25 = 87.5 miles. A useful check is that 3 inches would be 75 miles and 4 inches would be 100 miles, so the answer must fall between those two values.
Source: officialasvab.com — Arithmetic Reasoning subtest; map-scale proportion solved by cross-multiplication (a/b = c/d → ad = bc)Report a problem with this question
8. A machine purchased for $8,000 loses 10% of its value each year. What is the machine worth at the end of 2 years?
- A.$6,500
- B.$6,400
- C.$7,200
- D.$6,480✓ Answer
Losing 10% leaves 90% of the value, so each year the value is multiplied by 0.90 rather than having a fixed dollar amount subtracted. After one year: $8,000 × 0.90 = $7,200; after two years: $7,200 × 0.90 = $6,480. Subtracting 10% of the ORIGINAL price twice gives $6,400, which is wrong because the second year's loss is based on the reduced value.
Source: officialasvab.com — Arithmetic Reasoning subtest; depreciation rule: new value = original × (1 − rate), applied once per periodReport a problem with this question
9. A jacket regularly priced at $240 is marked down 25%. A clerk then takes an additional 10% off the sale price. What is the final price?
- A.$162✓ Answer
- B.$156
- C.$180
- D.$168
Successive discounts multiply; they do not add. The first markdown leaves 75%: $240 × 0.75 = $180, and the second leaves 90% of that: $180 × 0.90 = $162. Adding the percents to get a single 35% discount would give $156, which is too low because the 10% is taken on $180, not on $240.
Source: officialasvab.com — Arithmetic Reasoning subtest; successive-discount rule: final = original × (1 − r1) × (1 − r2)Report a problem with this question
10. A tool is on sale for $63 after a 30% discount. What was the price before the discount?
- A.$81.90
- B.$93
- C.$70
- D.$90✓ Answer
After a 30% discount the sale price represents 70% of the original, so original × 0.70 = $63 and the original is found by DIVIDING: $63 ÷ 0.70 = $90. Checking confirms it: 30% of $90 is $27, and $90 − $27 = $63. Multiplying $63 by 1.30 instead gives $81.90, a common error because the 30% would then be taken on the smaller sale price.
Source: officialasvab.com — Arithmetic Reasoning subtest; working backward from a discounted price: original = sale price ÷ (1 − rate)Report a problem with this question
11. A salesperson earns a 4% commission on everything sold. If total sales for the month were $18,500, how much commission was earned?
- A.$460
- B.$740✓ Answer
- C.$700
- D.$1,850
Commission equals the commission rate written as a decimal times total sales: 0.04 × $18,500 = $740. A quick mental check is that 1% of $18,500 is $185, and 4 × $185 = $740. The choice $1,850 is 10% of sales, the error made by shifting the decimal point one place instead of two.
Source: officialasvab.com — Arithmetic Reasoning subtest; commission rule: commission = rate (as a decimal) × total salesReport a problem with this question
12. A driver travels 120 miles to a job site at an average speed of 60 mph and returns over the same 120 miles at an average speed of 40 mph. What was the average speed for the entire round trip?
- A.50 mph
- B.45 mph
- C.52 mph
- D.48 mph✓ Answer
Average speed is always total distance divided by total time, never the average of the two speeds. The outbound leg takes 120 ÷ 60 = 2 hours and the return takes 120 ÷ 40 = 3 hours, for 240 miles in 5 hours: 240 ÷ 5 = 48 mph. The answer is below 50 mph because more time is spent traveling at the slower speed.
Source: officialasvab.com — Arithmetic Reasoning subtest; average-speed rule: average speed = total distance ÷ total time (d = r × t)Report a problem with this question
13. A truck leaves a depot traveling at a steady 45 mph. One hour later a car leaves the same depot on the same road traveling at a steady 60 mph. How long after the car leaves will it catch up to the truck?
- A.1.5 hours
- B.2 hours
- C.4 hours
- D.3 hours✓ Answer
In the hour of head start the truck covers 45 × 1 = 45 miles, so the car begins 45 miles behind. Because both move in the same direction, the gap closes at the DIFFERENCE of the speeds, 60 − 45 = 15 mph, so the catch-up time is 45 ÷ 15 = 3 hours. Using the sum of the speeds would be correct only if the two vehicles were approaching each other.
Source: officialasvab.com — Arithmetic Reasoning subtest; same-direction overtake rule: time = head-start distance ÷ (faster rate − slower rate)Report a problem with this question
14. Working alone, one worker can unload a truck in 6 hours. A second worker can unload the same truck alone in 12 hours. Working together at those rates, how long will it take them to unload one truck?
- A.3 hours
- B.9 hours
- C.4 hours✓ Answer
- D.5 hours
Work problems are solved by adding rates, not times: the first worker does 1/6 of the truck per hour and the second does 1/12, so together they do 1/6 + 1/12 = 3/12 = 1/4 of the truck per hour. Completing 1 truck therefore takes 4 hours. Averaging the two times to get 9 hours is wrong because two workers must always finish faster than the faster one alone.
Source: officialasvab.com — Arithmetic Reasoning subtest; combined-work rule: 1/t = 1/a + 1/b, so t = ab ÷ (a + b)Report a problem with this question
15. Four identical machines running together complete an order in 90 minutes. If only 3 of those machines are available and they run at the same rate, how long will the same order take?
- A.120 minutes✓ Answer
- B.67.5 minutes
- C.90 minutes
- D.135 minutes
Machines and time are INVERSELY proportional: fewer machines means more time, so the total machine-minutes stay constant. The job requires 4 × 90 = 360 machine-minutes, so with 3 machines it takes 360 ÷ 3 = 120 minutes. Scaling directly (90 × 3/4 = 67.5) is the common error, since it would mean removing a machine makes the work go faster.
Source: officialasvab.com — Arithmetic Reasoning subtest; inverse proportion / man-hours rule: workers × time = constantReport a problem with this question
16. A worker is paid $18 per hour for the first 40 hours in a week and time-and-a-half for every hour beyond 40. If the worker puts in 46 hours, what is the gross pay for the week?
- A.$828
- B.$882✓ Answer
- C.$720
- D.$1,242
Overtime pay must be split into two separate calculations because the two blocks of hours are paid at different rates. Regular pay is 40 × $18 = $720, the overtime rate is 1.5 × $18 = $27, and the 6 overtime hours pay 6 × $27 = $162, so the total is $720 + $162 = $882. Multiplying all 46 hours by $18 gives $828 and ignores the overtime premium entirely.
Source: officialasvab.com — Arithmetic Reasoning subtest; overtime pay rule: gross = (regular hours × rate) + (overtime hours × 1.5 × rate)Report a problem with this question
17. A person deposits $2,400 in an account that pays 5% simple annual interest. How much interest will the deposit earn in 6 months?
- A.$240
- B.$120
- C.$60✓ Answer
- D.$30
Simple interest is I = P × r × t with the rate as a decimal and the time in YEARS, so 6 months must be entered as 0.5 rather than 6. That gives $2,400 × 0.05 × 0.5 = $60. Forgetting to convert the months leaves the full-year figure of $120, which is exactly twice the correct amount.
Source: officialasvab.com — Arithmetic Reasoning subtest; simple-interest formula I = P × r × t (t expressed in years)Report a problem with this question
18. A student has an average score of 82 on the first 4 tests of a course. What score is needed on the fifth test to raise the average for all 5 tests to 85?
- A.91
- B.88
- C.97✓ Answer
- D.94
Because the mean equals the sum divided by the count, work with sums rather than averages. The 5 tests must total 85 × 5 = 425 points, while the first 4 have already produced 82 × 4 = 328 points, so the fifth score must be 425 − 328 = 97. Simply adding the 3-point gap to 82 gives 85 and ignores that one test has to make up the shortfall on all four earlier tests.
Source: officialasvab.com — Arithmetic Reasoning subtest; mean rule: required sum = mean × count, then subtract the known valuesReport a problem with this question
19. A person starts the month with $720. She spends 1/3 of it on rent, then spends 1/4 of what is left on groceries. How much money does she have left after both expenses?
- A.$420
- B.$240
- C.$480
- D.$360✓ Answer
The second fraction applies to the REMAINDER, not to the original amount, so the steps must be done in order. Rent is 720 ÷ 3 = $240, leaving $480; groceries are 1/4 of $480 = $120, leaving $480 − $120 = $360. Stopping at $480 answers the money left after rent only, which is the most common error on "then he spent part of what was left" problems.
Source: officialasvab.com — Arithmetic Reasoning subtest; sequential fraction-of-remainder rule (each fraction applies to the current remaining amount)Report a problem with this question
20. A room measures 18 feet by 12 feet. Carpet costs $21 per square yard. What is the cost to carpet the entire room?
- A.$4,536
- B.$480
- C.$1,512
- D.$504✓ Answer
First find the area in square feet: 18 × 12 = 216 square feet. Because the price is quoted per square YARD, convert using 1 square yard = 3 ft × 3 ft = 9 square feet, so 216 ÷ 9 = 24 square yards, and the cost is 24 × $21 = $504. Dividing by 3 instead of 9 gives $1,512 — area units must be converted with the SQUARE of the linear factor.
Source: officialasvab.com — Arithmetic Reasoning subtest; rectangle area A = l × w with square-unit conversion (1 yd² = 9 ft²)Report a problem with this question

Practice questions modeled on the ASVAB content domains. Not affiliated with or endorsed by the U.S. Department of Defense, USMEPCOM, or any branch of the U.S. Armed Forces. Study the official practice materials at officialasvab.com. Official ASVAB →

1. A pump moves 84 gallons of water in 6 minutes. At that same rate, how many gallons will it move in 20 minutes?

2. One store sells a 4-pound bag of rice for $9.60. Another store sells a 6-pound bag of the same rice for $13.50. How much less per pound does the cheaper bag cost?

3. A truck travels 350 miles on 25 gallons of fuel. At the same rate of fuel use, how many gallons are needed to travel 476 miles?

4. A group of 187 people must be transported by bus. Each bus seats 45 people. What is the smallest number of buses needed so that everyone gets a seat?

5. In a training company of 480 recruits, 1 out of every 6 recruits is assigned to the motor pool. How many recruits are NOT assigned to the motor pool?

6. A construction crew mixes gravel and sand in a 3 to 5 ratio by weight to produce 400 pounds of mix. How many pounds of sand are in the mix?

7. On a map, 1 inch represents 25 miles. Two supply depots are 3.5 inches apart on the map. What is the actual distance between them?

8. A machine purchased for $8,000 loses 10% of its value each year. What is the machine worth at the end of 2 years?

9. A jacket regularly priced at $240 is marked down 25%. A clerk then takes an additional 10% off the sale price. What is the final price?

10. A tool is on sale for $63 after a 30% discount. What was the price before the discount?

11. A salesperson earns a 4% commission on everything sold. If total sales for the month were $18,500, how much commission was earned?

12. A driver travels 120 miles to a job site at an average speed of 60 mph and returns over the same 120 miles at an average speed of 40 mph. What was the average speed for the entire round trip?

13. A truck leaves a depot traveling at a steady 45 mph. One hour later a car leaves the same depot on the same road traveling at a steady 60 mph. How long after the car leaves will it catch up to the truck?

14. Working alone, one worker can unload a truck in 6 hours. A second worker can unload the same truck alone in 12 hours. Working together at those rates, how long will it take them to unload one truck?

15. Four identical machines running together complete an order in 90 minutes. If only 3 of those machines are available and they run at the same rate, how long will the same order take?

16. A worker is paid $18 per hour for the first 40 hours in a week and time-and-a-half for every hour beyond 40. If the worker puts in 46 hours, what is the gross pay for the week?

17. A person deposits $2,400 in an account that pays 5% simple annual interest. How much interest will the deposit earn in 6 months?

18. A student has an average score of 82 on the first 4 tests of a course. What score is needed on the fifth test to raise the average for all 5 tests to 85?

19. A person starts the month with $720. She spends 1/3 of it on rent, then spends 1/4 of what is left on groceries. How much money does she have left after both expenses?

20. A room measures 18 feet by 12 feet. Carpet costs $21 per square yard. What is the cost to carpet the entire room?