ASVAB Arithmetic Reasoning practice
Arithmetic Reasoning (AR) tests your ability to solve arithmetic word problems, and it is one of the four subtests that make up the AFQT. The 17 questions below are original, untimed and explained by hand with no calculator.
Last updated · Published by Certloom Learning · Written by Certloom Learning for AptiStep and checked by recomputing every answer. Not real ASVAB questions.
What does ASVAB Arithmetic Reasoning cover?
The official description is “Ability to solve arithmetic word problems” (Official ASVAB: What to Expect (checked 2026-11-12)). In practice that means turning a short story into one or two calculations: unit prices, speed and time, percent change, ratios and averages. The word problem lesson shows the method; the ratios and rates lesson and percent lesson go deeper.
How is Arithmetic Reasoning tested on the CAT-ASVAB and on paper?
On the computer version the official table lists 15 scored questions and up to 15 unscored tryout questions, with a time limit of 55 minutes without tryout questions or 113 minutes with them. On paper it has 30 questions in 36 minutes. Source: Official ASVAB: What to Expect (checked 2026-11-12).
The computer version is adaptive, so the next question depends on your previous answer (Official ASVAB: The CAT-ASVAB). That makes accuracy on early questions matter.
Free Arithmetic Reasoning practice questions
Try each question first, then open the explanation. Say the unit of the answer out loud before you calculate.
A pack of 6 notebooks costs $9. At the same price per notebook, how much do 10 notebooks cost?
- $12
- $15
- $18
- $60
Show answer and explanation
Answer: B. $15
Find the unit price: $9 ÷ 6 = $1.50 per notebook. Then multiply $1.50 × 10 = $15. The units are dollars per notebook × notebooks = dollars.
A $60 jacket is discounted by 15%. What is the sale price before tax?
- $9
- $45
- $51
- $69
Show answer and explanation
Answer: C. $51
Ten percent of $60 is $6, and five percent is $3. The discount is $9. Subtract it from the original price: $60 − $9 = $51. The question asks for the sale price, not the amount saved.
A tank holds 40 gallons when full. It is 30% full. How many gallons are in it?
- 10
- 12
- 28
- 30
Show answer and explanation
Answer: B. 12
Ten percent of 40 is 4. Thirty percent is three times as much: 3 × 4 = 12 gallons.
A cyclist travels 24 miles in 2 hours at a steady speed. How far will the cyclist travel in 3 hours at that speed?
- 16 miles
- 26 miles
- 36 miles
- 72 miles
Show answer and explanation
Answer: C. 36 miles
The speed is 24 ÷ 2 = 12 miles per hour. At that rate, 3 hours covers 12 × 3 = 36 miles.
A mix uses 2 cups of concentrate for every 5 cups of water. How much concentrate is needed for 15 cups of water?
- 3 cups
- 6 cups
- 10 cups
- 12 cups
Show answer and explanation
Answer: B. 6 cups
The water amount grows from 5 to 15 cups, a factor of 3. Multiply the concentrate by the same factor: 2 × 3 = 6 cups.
Five identical boxes weigh 35 pounds in total. What do eight boxes weigh?
Show answer and explanation
Answer: 56 pounds
Find one box: 35 ÷ 5 = 7 pounds. Scale to eight: 7 × 8 = 56 pounds. Keep the weight per box constant.
A van travels 150 miles in 3 hours at a steady speed. How long would 250 miles take at that speed?
Show answer and explanation
Answer: 5 hours
The speed is 150 ÷ 3 = 50 miles per hour. Required time is distance divided by speed: 250 ÷ 50 = 5 hours. The question asks for time, not another distance.
A shelf has 24 books. One quarter are reference books. How many are not reference books?
Show answer and explanation
Answer: 18 books
One quarter of 24 is 6. The requested group is the remaining books, so subtract: 24 − 6 = 18. Stopping after the first calculation answers a different question.
A worker earns $16 per hour for 7 hours and spends $12 on transport. How much remains from that pay?
Show answer and explanation
Answer: $100
First find gross pay for this example: 16 × 7 = 112 dollars. Then subtract the stated transport cost: 112 − 12 = 100. No other deductions are specified.
Blue and white tiles are in a ratio of 3:2. There are 25 tiles. How many are blue?
Show answer and explanation
Answer: 15 tiles
The whole contains 3 + 2 = 5 ratio parts. Each part is 25 ÷ 5 = 5 tiles. Blue uses three parts: 3 × 5 = 15.
Four pounds of rice cost $10. At the same unit price, how much do seven pounds cost?
Show answer and explanation
Answer: $17.50
One pound costs 10 ÷ 4 = $2.50. Seven pounds cost 7 × $2.50 = $17.50. The rate has units of dollars per pound.
A mix has 2 cups of concentrate for every 7 cups of water. How much water goes with 6 cups of concentrate?
Show answer and explanation
Answer: 21 cups
Concentrate scales from 2 to 6, a factor of 3. Apply that factor to water: 7 × 3 = 21 cups. Preserve the order of the ratio.
A printer makes 84 labels in 6 minutes at a steady rate. How many labels does it make in 5 minutes?
Show answer and explanation
Answer: 70 labels
Find the unit rate: 84 ÷ 6 = 14 labels per minute. Multiply by 5 minutes to get 70 labels. Less time should produce fewer than 84 labels.
A $90 bag is 20% off. What is its sale price before tax?
Show answer and explanation
Answer: $72
Ten percent is $9, so 20% is $18. Subtract the discount: $90 − $18 = $72. The amount saved is not the requested sale price.
A weekly cost rises from $50 to $60. What is the percentage increase?
Show answer and explanation
Answer: 20%
The increase is $10. Divide by the original $50: 10/50 = 1/5 = 20%. The new $60 amount is not the base for this increase calculation.
Eighteen of 60 seats are occupied. What percentage is occupied?
Show answer and explanation
Answer: 30%
The occupied share is 18/60 = 3/10. Three tenths is 30 out of 100, or 30%. The 60 seats represent the whole.
A $100 price rises 10%, then the new price falls 10%. Is it back to $100?
Show answer and explanation
Answer: No; it is $99
The increase makes $110. Ten percent of the new $110 is $11, so the reduction gives $99. Equal percentage changes do not cancel when their starting amounts differ.
How do I get faster at Arithmetic Reasoning?
Write what the question asks (“cost of ten notebooks, in dollars”) before using any number, find the unit rate first, and check that the answer has the right size. Percent questions are quickest when you build from 10% and 5%. Timed practice only helps after the method is steady.
Frequently asked questions
Is there a calculator on the ASVAB?
No. See the official statement (source, checked 2026-11-12).
How many Arithmetic Reasoning questions are there?
15 scored questions on the CAT-ASVAB and 30 on paper.