Free tool · OAR Math Skills
OAR math practice test
15 Math Skills questions from the OAR Prep question bank, from rates and ratios to probability. Work them on scratch paper, then check the worked answer.
15 Math Skills questions · about 20 minutes · scratch paper, no calculator. Pick an answer to see whether you’re right and why.
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Answer: A. 70 minutes
3.5 hours = 210 minutes. She has practiced 45 + 45 + 25 + 25 = 140 minutes, leaving 210 − 140 = 70 minutes.
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Answer: C. 7
Add 7 to both sides: 4x = 28. Divide by 4: x = 7.
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Answer: C. 50
Sum = 250; divide by the 5 values: 250 ÷ 5 = 50.
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Answer: C. 24
n + (n + 1) = 47 → 2n + 1 = 47 → n = 23, so the larger integer is 24.
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Answer: C. 31.4 inches
Circumference = π × diameter = 3.14 × 10 = 31.4 inches.
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Answer: A. 76
Order them: 68, 72, 76, 84, 90. The middle value is 76.
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Answer: D. 5 hours
Outbound groundspeed is 250 + 50 = 300 mph, so 600 ÷ 300 = 2 hours. Return groundspeed is 250 − 50 = 200 mph, so 600 ÷ 200 = 3 hours. Total = 5 hours.
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Answer: B. 6 hours 40 minutes
Net rate = 1/5 − 1/20 = 3/20 tank per hour, so time = 20/3 hours = 6 hours 40 minutes.
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Answer: A. 15 liters
The acid stays at 5 L (50% of 10 L). For a 20% solution, 5 ÷ total = 0.20, so the total is 25 L: add 25 − 10 = 15 L of water.
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Answer: C. $360
Simple interest = P × r × t = 2,000 × 0.06 × 3 = $360.
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Answer: B. 2/15
P(both red) = 4/10 × 3/9 = 12/90 = 2/15.
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Answer: A. $3
Write 3p + 2n = 12 and 2p + 4n = 16. Halve the second: p + 2n = 8. Subtract it from the first: 2p = 4, so p = $2, and then 2n = 6, so n = $3.
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Answer: D. 32
With the same base, add the exponents when multiplying and subtract them when dividing: 3 + 4 − 2 = 5, so the answer is 2⁵ = 32.
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Answer: A. 25
The ratio 1:9 gives 10 parts in total, so officers = 250 ÷ 10 = 25.
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Answer: D. 1/2
Burned = 1/3 of 3/4 = 1/4 of the tank. Remaining = 3/4 − 1/4 = 1/2.
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What the OAR Math Skills Test covers
The Math Skills Test is one of the three OAR subtests. It covers arithmetic, fractions, percentages, ratios, algebra, geometry and word problems, all without a calculator. Most questions are short word problems, so reading the question carefully matters as much as the arithmetic.
Problem types in this test
- Rates and work: distance = rate × time, average speed over a round trip, two pumps working together.
- Ratios and percents: splitting a total in a ratio, successive discounts, mixtures and dilutions.
- Algebra: one-variable equations and a pair of equations in two unknowns.
- Geometry and data: circumference, angles, mean and median, probability without replacement.
Formulas you need are on the OAR formula sheet. To speed up the arithmetic itself, use theno-calculator math drill.
FAQ
- What math is on the OAR?
- The Math Skills Test covers arithmetic, fractions, percentages, ratios and proportions, basic algebra, geometry (area, perimeter, angles, circles) and data such as averages and probability, usually framed as word problems.
- Can you use a calculator on the OAR math section?
- No. Calculators are not allowed on any part of the OAR, so practice doing arithmetic, fractions and percentages by hand. The no-calculator math drill on this site is built for that.
- How do I get faster at OAR word problems?
- Learn the handful of setups that repeat (rate × time = distance, combined work rates, mixtures, percent change, ratios), write the equation before you calculate, and drill mental arithmetic so the calculation step is quick.
Sources
Original practice questions from the OAR Prep question bank — not actual OAR or ASTB-E test items. The U.S. Navy does not endorse this test.