ASVAB Arithmetic Reasoning: practice, strategy and a free drill

Arithmetic Reasoning (AR) is the ASVAB's word-problem subtest: 15 questions in 55 minutes on the computer (CAT) version and 30 in 36 minutes on paper, with no calculator. It is a quarter of your AFQT and sits inside the Army GT score. Most questions are one of seven set-ups: rates, percentages, ratios, work, averages, interest and unit conversion.

15 / 55 min
CAT questions and time: 30 / 36 min
paper questions and time: 25%
of the AFQT: 12 free
timed drill questions

Last checked 20 October 2026 · Question counts and times from the official ASVAB site

Start the free Arithmetic Reasoning drill

12 questions, 14:24 on the clock, every answer explained. No sign-up.

By the LifeScore Editorial Team · Updated 20 October 2026 · How we check facts · How this is scored

Free ASVAB-style drill

Try 12 Arithmetic Reasoning questions against the paper clock

30 questions in 36 minutes is the real paper pace, so 12 questions get 14:24. Original questions, scored on our server, with every answer explained at the end. It is a taster of one subtest, not an AFQT estimate: for that, take the full free practice test.

12
questions
14:24
time limit
Free
every answer explained

How many questions are on ASVAB Arithmetic Reasoning, and how long do you get?

15 questions in 55 minutes on the CAT-ASVAB and 30 questions in 36 minutes on the paper ASVAB, with no calculator on either.

ASVAB Arithmetic Reasoning: the official format, and what our drill copies
CAT-ASVAB (computer)	15 questions in 55 minutes, about 220 seconds eachPublished by the ownerOfficial ASVAB, "The CAT-ASVAB"
Paper ASVAB (P&P)	30 questions in 36 minutes, about 72 seconds eachPublished by the ownerOfficial ASVAB, "What to expect when you take the ASVAB"
Calculator	Not allowed on either versionPublished by the ownerDepartment of Defense, "The use of calculators on the ASVAB" (2026 note)
Weight in the AFQT	A quarter: AFQT = AR + MK + 2 × VEPublished by the ownerOfficial ASVAB, "ASVAB Technical Bulletin No. 1" (AFQT formula)
Guessing	Paper: no penalty, so never leave a blank. CAT: unfinished questions are scored as random guesses, so do not click through at the endPublished by the ownerOfficial ASVAB, "ASVAB scoring"
Our free drill	12 original questions, 14:24 on the clock (the paper pace), every answer explainedLifeScore

What does ASVAB Arithmetic Reasoning test?

The official description is short: arithmetic word problems. In practice that means a few lines of everyday text (a trip, a sale, a recipe, a pay check) and a question whose numbers you have to pull out and put in the right order. The arithmetic itself is rarely harder than long division and fractions; what costs points is the set-up.

The two versions feel very different. On paper you get 30 questions at about 72 seconds each, so speed matters. On the CAT you get 15 questions with about 220 seconds each, but the test adapts: get one right and the next is harder. Neither version allows a calculator, and on the CAT you cannot go back to an answered question.

AR is one of the four AFQT subtests and a quarter of the AFQT formula. It also sits inside the Army GT, CL, EL and FA line scores, most Navy rating sums, the Air Force General, Mechanical and Electronics composites, and the Marine Corps GT.

See which jobs ask for which scores, branch by branch: Army jobs, Navy jobs, Air Force jobs, Marine Corps jobs.

What kinds of word problems are on ASVAB Arithmetic Reasoning?

Nearly every AR question is one of seven set-ups. Name the type in the first few seconds and the equation follows.

The seven AR set-ups and the equation each one needs (our summary)
Type	Clue in the wording	Set-up
Rate, distance, time	miles per hour, how long, how far	distance = rate × time
Percent and discount	percent off, tax, increase, of the original	part = percent × whole; after a 20% cut you pay 80%
Ratio and proportion	for every, in the ratio, at the same rate	split the total into ratio parts, or cross-multiply
Work together	working together, both pumps, two painters	add the rates: 1/a + 1/b = 1/time
Average	mean, average, what must the next score be	needed total = average × count; subtract what you have
Simple interest	interest, per year, loan, savings	interest = principal × rate × years
Units and money	feet, yards, dozens, change from a bill	convert first, then calculate

Write the formula before you write any numbers. It takes three seconds, it stops you reaching for the wrong operation, and it is the habit that fixes most AR errors.

What do ASVAB Arithmetic Reasoning questions look like?

Like these 6, which we wrote in the style of the official description: the first two are worked open, the rest hide the answer until you try. None is a real ASVAB question.

ASVAB-style question 1 · Rate
A delivery van travels 168 miles in 3.5 hours. At the same speed, how far will it travel in 5 hours?
1. A210 miles
2. B240 miles
3. C252 miles
4. D280 miles
Worked answer
B: 240 miles. The speed is 168 ÷ 3.5 = 48 miles per hour, and 48 × 5 = 240 miles.
1. Name the type: rate, distance, time. Write d = r × t.
2. Find the rate: 168 ÷ 3.5. Double both to clear the decimal: 336 ÷ 7 = 48 mph.
3. Distance in 5 hours: 48 × 5 = 240 miles.
The trap: 252, from adding 168 to half of 168. Scaling by eye is fast but 5 hours is not 1.5 times 3.5 hours; find the rate.
ASVAB-style question 2 · Percent
After a 20% discount, a jacket costs $64. What was the price before the discount?
1. A$76.80
2. B$80.00
3. C$82.00
4. D$84.00
Worked answer
B: $80.00. After a 20% discount you pay 80% of the original, so the original is 64 ÷ 0.8 = $80.
1. $64 is what is left after 20% came off, so $64 is 80% of the original.
2. Original = 64 ÷ 0.80 = 80.
3. Check: 20% of $80 is $16, and $80 − $16 = $64.
The trap: $76.80, from adding 20% of $64. The 20% was taken off the original price, not off $64.
ASVAB-style question 3 · Ratio
A concrete mix uses sand and gravel in the ratio 2 : 5. How many cubic feet of gravel are in 42 cubic feet of the mix?
1. A12
2. B16.8
3. C30
4. D35
Show the worked answer
C: 30. There are 2 + 5 = 7 parts, each 42 ÷ 7 = 6 cubic feet, so gravel is 5 × 6 = 30.
1. Add the ratio parts: 2 + 5 = 7.
2. One part: 42 ÷ 7 = 6 cubic feet.
3. Gravel is 5 parts: 5 × 6 = 30.
The trap: 16.8, from treating 2 : 5 as 2 out of 5 (40%) of 42. A ratio of 2 : 5 means 2 out of 7.
ASVAB-style question 4 · Work
One pump can empty a tank in 6 hours. A second pump can empty it in 3 hours. How long will it take with both pumps working together?
1. A2 hours
2. B3 hours
3. C4.5 hours
4. D9 hours
Show the worked answer
A: 2 hours. Together they empty 1/6 + 1/3 = 1/2 of the tank an hour, so it takes 2 hours.
1. Turn each time into a rate: 1/6 and 1/3 of the tank per hour.
2. Add them: 1/6 + 2/6 = 3/6 = 1/2 of the tank per hour.
3. Half a tank an hour means 2 hours for the whole tank.
The trap: 4.5 hours, the average of 6 and 3. Two pumps together must be faster than the faster pump alone, so anything over 3 hours is wrong.
ASVAB-style question 5 · Average
A recruit scored 82, 90, 77 and 85 on four fitness tests. What must she score on the fifth test to average 85 across all five?
1. A85
2. B88
3. C91
4. D93
Show the worked answer
C: 91. An average of 85 over five tests needs 425 points; she has 334, so she needs 91.
1. Total needed: 85 × 5 = 425.
2. Total so far: 82 + 90 + 77 + 85 = 334.
3. Fifth score: 425 − 334 = 91.
The trap: 85, the target average itself. Her first four average 83.5, so she needs more than 85 to pull the average up.
ASVAB-style question 6 · Interest
Sam puts $2,400 in an account that pays 3.5% simple interest a year. How much interest does he earn in 2 years?
1. A$84.00
2. B$168.00
3. C$170.94
4. D$240.00
Show the worked answer
B: $168.00. Simple interest is principal × rate × time: 2,400 × 0.035 × 2 = $168.
1. Write I = P × r × t.
2. One year: 2,400 × 0.035 = 84.
3. Two years: 84 × 2 = 168.
The trap: $170.94, which is compound interest. The question says simple, so the interest does not earn interest.

4 more Arithmetic Reasoning drills, and full mocks

The free drill is one set. The ASVAB Pass Pack has 16 subtest drills across the four AFQT subjects, 6 full ASVAB-style mocks and a score predictor.

The ASVAB Pass Pack gives you 6 full mocks on the real clock, 16 drills of 12 questions for the sections that cost you points, and a predictor that turns your mocks into the odds of reaching your target. One payment, no subscription, and your free score stays free.

Prep courses for these tests usually cost $19 to $129. The ASVAB Pass Pack is US$39 (£29), once.

See the ASVAB Pass Pack How our questions are built and checked

6
timed mocks: 16
topic drills: 1
score predictor

How do you get a better ASVAB Arithmetic Reasoning score?

The question is usually in the final sentence. Read it first so you know what number you are hunting for before you read the story. The rest of our method is below.

Our method, in order of how much it usually helps

Read the last line first
The question is usually in the final sentence. Read it first so you know what number you are hunting for before you read the story.
Name the set-up in five seconds
Rate, percent, ratio, work, average, interest or units. Once you know the type you know the formula; the table above is the list.
Estimate before you calculate
Round the numbers and get a rough answer first. On paper it lets you rule out two options at once; on the CAT it catches the slip before you lock the answer in.
Check the answer against the story
Two pumps faster than one, a discounted price lower than the original, an average between the lowest and highest score. A ten-second sense check saves more points than any formula.
Keep the paper pace: about 72 seconds
On paper, 30 questions in 36 minutes is a minute and a bit each. If a question passes two minutes, guess, mark it and move on: there is no penalty for a wrong answer on paper.
On the CAT, never click through at the end
The CAT penalises unfinished questions as if you had guessed at random, so a rushed run of guesses can cost you. Use the time you have; you have far more per question than on paper.

What are the most common ASVAB Arithmetic Reasoning mistakes?

Percent of the wrong number: discounts and increases are always a percent of the original. When the question gives you the after-price, divide, do not add.

The traps we see most often, and the fix

Percent of the wrong number
Discounts and increases are always a percent of the original. When the question gives you the after-price, divide, do not add.
Ratio parts versus totals
A 2 : 5 ratio has 7 parts. Add the parts before you divide the total.
Averaging rates
Average speed for a round trip and time for two workers are never the simple average. Add rates; add distances and divide by total time.
Units that change mid-problem
Minutes and hours, inches and feet, cents and dollars. Convert everything to one unit before you start.
Answering a different question
The problem asks for the gravel, not the sand; the interest, not the new balance. Underline the last few words of the question.

How should you study for ASVAB Arithmetic Reasoning in a week?

Start with the free drill to find your weak spots, spend five days on them, then retake the drill. Twenty to forty minutes a day is enough to see a change.

A 7-day Arithmetic Reasoning plan (ours)
Day	What to do
Day 1	Take the free drill below cold. Write down which set-ups you missed.
Day 2	Rates and percent: 15 problems each, formula written first every time.
Day 3	Ratio, work and averages: 10 problems each. Say the trap out loud before you answer.
Day 4	Interest and unit conversions, then 20 mixed problems with no calculator.
Day 5	A timed set at the paper pace (72 seconds a question). Review every miss: set-up or arithmetic?
Day 6	Mental arithmetic: fractions to decimals, percentages of round numbers, long division. Ten minutes, three times.
Day 7	Retake the drill. If your score has not moved, repeat days 2 to 4 on your weakest set-ups.

Then put it together: the how to pass the ASVAB guide plans all four AFQT subjects, the free ASVAB-style practice test gives an estimated AFQT, and what is a good ASVAB score shows what each branch asks for. The other subtest guides: Word Knowledge, Paragraph Comprehension, Mathematics Knowledge.

Frequently asked questions

How many questions are on ASVAB Arithmetic Reasoning?

15 on the CAT-ASVAB, with 55 minutes, and 30 on the paper ASVAB, with 36 minutes, per the official ASVAB site.

Can you use a calculator on ASVAB Arithmetic Reasoning?

No. Calculators are not allowed on either version. You get scratch paper, so practise long division, fractions and percentages by hand.

What math is on Arithmetic Reasoning?

Arithmetic in word problems: rates, percentages, ratios, averages, simple interest, work problems and unit conversions. Algebra and geometry belong to Mathematics Knowledge.

How do I get better at ASVAB word problems fast?

Learn the seven set-ups on this page, write the formula before the numbers, and check every answer against the story. Then drill a few problems a day: set-up speed is what improves.

Is Arithmetic Reasoning the hardest ASVAB subtest?

Many people find it so because it combines reading with math under time pressure. It is also very trainable, because the same few set-ups come up again and again.

How much does Arithmetic Reasoning count towards the AFQT?

A quarter. The AFQT formula is AR + MK + 2 × VE, where VE comes from Word Knowledge and Paragraph Comprehension.

Make Arithmetic Reasoning your strongest subtest

16 subtest drills, 6 full ASVAB-style mocks and a predictor for the score your job needs.