ASVAB Arithmetic Reasoning · AR

ASVAB Arithmetic Reasoning
Sample Questions

Practice original Arithmetic Reasoning word problems covering rates, ratios,
percentages, fractions, money, distance, averages, proportions and
multi-step arithmetic.

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Arithmetic Reasoning (AR) Practice

Arithmetic Reasoning measures your ability to solve basic arithmetic word problems. Read the situation carefully, decide which operation or relationship is needed, and then calculate. Select an answer to see a short solution.

You can also practice with ASVAB sample questions and Mathematics Knowledge sample questions.

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A machine seals 420 packages each minute. If it runs at the same rate for 25 minutes, how many packages will it seal?
Rate & Time

Multiply the rate by the time: 420 × 25 = 10,500 packages.

One out of every 8 students in a school rides a bicycle to school. If there are 640 students, how many do not ride a bicycle?
Fractions

One-eighth of 640 is 80. The number who do not ride is 640 − 80 = 560.

A used car is worth $8,400. If its value decreases by 15% in one year, what is it worth after that year?
Percent Change

Fifteen percent of $8,400 is $1,260. Subtract that from $8,400 to get $7,140.

A pump moves 24 gallons of water in 6 seconds. At the same rate, how many gallons will it move in 9 seconds?
Unit Rate

The rate is 24 ÷ 6 = 4 gallons per second. In 9 seconds it moves 4 × 9 = 36 gallons.

The morning temperature was −7°F and the afternoon temperature was 38°F. What was the difference between the two temperatures?
Integers

The distance from −7 to 38 is 38 − (−7) = 45°F.

At a camp, the ratio of boys to girls is 5:3. If there are 64 campers total, how many more boys than girls are there?
Ratios

There are 8 equal ratio parts, so each part is 64 ÷ 8 = 8. Boys = 40 and girls = 24, a difference of 16.

A jacket costs $48 before a 25% discount. What is the sale price?
Discount

Twenty-five percent of $48 is $12. Subtract the discount: $48 − $12 = $36.

A driver travels 180 miles in 3 hours at a constant average rate. What is the average speed?
Distance

Average speed = distance ÷ time = 180 ÷ 3 = 60 mph.

A tank is 3/5 full and currently contains 24 gallons. What is the tank's total capacity?
Fractions

If 3/5 equals 24 gallons, one-fifth is 8 gallons. Five-fifths is 40 gallons.

A student earns scores of 72, 84, 90, and 78 on four tests. What is the average score?
Average

Add the scores: 72 + 84 + 90 + 78 = 324. Divide by 4 to get 81.

Apples cost $3.20 per pound. How much will 2.5 pounds cost?
Money

Multiply price per pound by pounds purchased: $3.20 × 2.5 = $8.00.

Eighteen workers pack 540 boxes in 6 hours. If all workers pack at the same rate, how many boxes does each worker pack per hour?
Work Rate

The group packs 540 ÷ 6 = 90 boxes per hour. Then 90 ÷ 18 = 5 boxes per worker per hour.

A savings account earns simple interest at 4% per year. How much interest is earned on $1,500 in 2 years?
Simple Interest

Simple interest = principal × rate × time = 1,500 × 0.04 × 2 = $120.

A recipe uses 3 cups of flour for 2 batches of bread. At the same rate, how many cups are needed for 5 batches?
Proportion

The recipe uses 3 ÷ 2 = 1.5 cups per batch. For 5 batches: 1.5 × 5 = 7.5 cups.

A restaurant bill is $37.50. If a customer leaves a 12% tip, how much is the tip?
Percent

Twelve percent of $37.50 is 37.50 × 0.12 = $4.50.

Maya buys 3 notebooks for $2.40 each and one pen for $1.75. What is the total cost?
Multi-Step Money

Three notebooks cost 3 × $2.40 = $7.20. Add $1.75 for the pen to get $8.95.

On a map, 1 inch represents 12 miles. Two towns are 3.5 inches apart on the map. What is the actual distance?
Scale

Multiply the map distance by the scale: 3.5 × 12 = 42 miles.

Forty percent of 250 recruits completed a task in under 10 minutes. How many recruits is that?
Percent

Convert 40% to 0.40 and multiply: 0.40 × 250 = 100.

A theater has 80 seats. Three-fourths of the seats are occupied, and then 10 more people take empty seats. How many seats are now occupied?
Fractions & Addition

Three-fourths of 80 is 60. Add 10 more occupied seats to get 70.

A printer produces 6 posters per hour and needs 8 hours to finish an order. If a faster printer produces 8 posters per hour, how many hours would it need for the same order?
Work Rate

The order contains 6 × 8 = 48 posters. At 8 posters per hour, 48 ÷ 8 = 6 hours.