Arithmetic Reasoning (AR)

25% of the AFQT · blueprint AFQT = AR + MK + 2×VE (WK+PC), per officialasvab.com (2026)

Short answer

Arithmetic Reasoning is one of the four AFQT subtests and counts once in the formula. It is word problems, not raw computation — ratios and proportions, percentages and percent change, rates (speed, work, unit price), unit conversion, simple interest, averages and multi-step problems where you must decide which operation the story is asking for. On paper it is 30 questions in 36 minutes.

Why it matters

AR is where careful readers who are "bad at math" lose points on translation, not arithmetic. Every AR question hides one or two operations inside a sentence.

Key concepts

Translate first: "of" = multiply, "per" = divide, "is" = equals, "less than" reverses order.
Ratios/proportions: set up a/b = c/d and cross-multiply; keep units aligned.
Percent: part = percent × whole; percent change = (new − old) ÷ old.
Rates: distance = rate × time; combined work = 1/a + 1/b per unit time.
Averages: total = average × count; to find a missing value, work from the total.
Units: 12 in/ft, 3 ft/yd, 16 oz/lb, 60 min/h; convert before computing.

Common mistakes

Answering the intermediate number (e.g., the discount) instead of the final quantity (the sale price).
Mixing minutes and hours in a rate problem.

Worked example

A crew paves 3/4 mile in 6 hours. At that rate, how far in 10 hours? Rate = 0.75 ÷ 6 = 0.125 mi/h; × 10 = 1.25 miles.

Original practice questions

Arithmetic Reasoning (AR)Difficulty 2/5

A crew paves 3/4 of a mile of road in 6 hours. At the same rate, how many miles will it pave in 10 hours?

A1.25
B1.5
C0.9
D2.0

Show answer and rationale

Correct: A. Rate = 0.75 mi ÷ 6 h = 0.125 mi/h. Over 10 h: 0.125 × 10 = 1.25 miles.

B — 1.5 would need a rate of 0.15 mi/h.
C — 0.9 mixes up the ratio.
D — 2.0 assumes 0.2 mi/h.

Arithmetic Reasoning (AR)Difficulty 2/5

A jacket priced at $80 is marked 25% off. Sales tax of 5% is then added to the sale price. What is the final cost?

A$60.00
B$63.00
C$64.00
D$66.00

Show answer and rationale

Correct: B. 25% off $80 = $60 sale price. 5% tax on $60 = $3. Final: $63.00. Watch for the intermediate answer ($60) among the choices.

A — $60 is the sale price before tax.
C — $64 applies tax to $80 then subtracts $20.
D — $66 adds 10% instead of 5%.

Arithmetic Reasoning (AR)Difficulty 3/5

The ratio of trucks to cars in a lot is 2:5. If there are 84 vehicles in total, how many are trucks?

Show answer and rationale

Correct: C. 2 + 5 = 7 parts; 84 ÷ 7 = 12 per part; trucks = 2 × 12 = 24.

B — 12 is one part, not two.
D — 30 would be 2.5 parts.
A — 60 is the number of cars.

All 5 Arithmetic Reasoning (AR) questions →

Tools for this topic

ASVAB / AFQT score explorer — Enter the AFQT percentile from your official score report to see your category (I–V) and what the percentile means against the national reference group; optionally add your AR, MK, PC and WK standard scores to see how the four AFQT subtests compare.

2 flashcards for Arithmetic Reasoning (AR)

Practice this topic

Blueprint-mapped questions with full rationales for every choice.

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Primary references

Understanding ASVAB Scores — AFQT computation, percentiles, categories, standard scores — Official ASVAB (U.S. Department of Defense) · government · retrieved 2026-09-21, verified 2026-09-21
What to Expect — CAT-ASVAB and paper-and-pencil subtests, counts and time limits — Official ASVAB (U.S. Department of Defense) · government · retrieved 2026-09-21, verified 2026-09-21

Last reviewed: 2026-09-21Next review by: 2026-12-20Draft — pending editorial reviewHow we verify facts