Arithmetic Reasoning practice: ASVAB word problems
Ten word problems in two sets of five, the kind of arithmetic the AR subtest asks for: pay, speed, discounts, averages and rates. No calculator, as on test day.
Correct answers
0 / 5
0 of 5 answered: the explanations appear below as you go.
| Subtests covered | AR |
Practice items written by Radif Partners for this site, not real ASVAB questions. A share of correct answers does not convert into a standard score or an AFQT percentile.
Prepared by Radif Partners · Method · official sources read on October 22, 2026 · published formulas and tables
Arithmetic Reasoning (AR) is the ASVAB subtest of word problems: a short situation, a question, four answers, and no calculator. The computer version gives 15 questions in 55 minutes, about 220 seconds each, the most generous time of any subtest; the paper version gives 30 questions in 36 minutes, about 72 seconds each. AR counts once in the AFQT sum AR + MK + 2 × VE, it is half of the Army GT line score, and it enters 3 of the four Air Force areas and 3 of the four Marine Corps line scores, more than any other subtest. A candidate with AR 43, MK 52 and VE 51 reads AFQT 45; five more points on AR alone give 50. The ten practice problems on this page are written by Radif Partners, not taken from the real test, and a share of right answers does not convert into a standard score.
What Arithmetic Reasoning measures
AR checks whether you can pick the right operation from a description. The ten questions on this page cover the usual families: wages over a week, average speed of a convoy, a sale price after a discount, a recipe scaled up, a fraction of a group, simple interest, the score needed to reach an average, a tank filling while it leaks, a percent increase, and two pumps working together. None needs more than four operations and fractions, but each one hides the key number in a sentence. The real subtest uses the same kind of short situations, as the Official ASVAB sample questions show.
The second set of five sits below. Take the first set in the tool above, read every explanation, then try these without looking back.
Time per question and how to use it
The Official ASVAB fact sheet gives 15 AR questions in 55 minutes on the computer test, or about 220 seconds each. On paper the same subtest has 30 questions in 36 minutes, about 72 seconds each, so a paper candidate must work about 3 times faster. In practice, aim to finish a five question set in under ten minutes, then bring it down. Write every intermediate result on your scratch paper: most AR errors come from a lost digit, not from a wrong idea. The test length page has a pace calculator for every subtest.
Traps worth knowing
- The base of a percent change. A price that goes from 40 to 50 rose by 10, and 10 is 25% of the old price, not 20% of the new one. Always divide by the starting value.
- Averaging rates. One pump fills a pool in 6 hours, another in 3. Together they do not take 4.5 hours, nor 9: add what each does in one hour, 1/6 + 1/3 = 1/2, so the pool fills in 2 hours.
- The complement. When 3/8 of 48 recruits failed a run, the question may ask how many passed. Compute the 18 who failed, then answer 30.
- Net rates. A tank filling at 8 gallons a minute while 3 leak out gains 5 a minute, not 8 or 11.
- Units. Minutes and hours, cents and dollars, feet and yards: convert before you compute, never after.
A quick check catches most of these: estimate the answer before computing it. If the sale price comes out above the regular price, or two pumps together are slower than the faster one alone, the setup is wrong.
Where the AR score goes
AR enters the AFQT once, in the sum AR + MK + 2 × VE read in the 1997 conversion table. Take a candidate with AR 43, MK 52 and VE 51: the AFQT is 45. With AR at 48, all else equal, it becomes 50. The same five points move the Army GT score, built only from AR and VE, from 94 to 99; the Army GT page explains why that score matters for many specialties. In the Air Force, AR is part of 3 areas (M = AR + MC + AS + 2VE; G = AR + VE; E = GS + AR + MK + EI), and in the Marine Corps it is part of 3 line scores (MM = AR + MC + EI + AS; GT = AR + MC + VE; EL = GS + AR + MK + EI). No other subtest appears in so many composites, which is why AR deserves practice even after the AFQT minimum is met.
A study approach that works
Learn the handful of setups first: rate × time = distance, part = percent × whole, new average × count = total, and work rates added per hour. Then drill them in mixed sets, so that you practice recognizing which setup a story calls for, which is the real skill tested. Review the arithmetic you do by hand: long division, fractions to decimals, and percent of a number. Mathematics Knowledge tests the algebra behind these steps, so the Math Knowledge page is the natural next stop; the study plan page shows how many points on AR would reach your AFQT target, and the practice test mixes AR with the other subtests.