Navy OAR study guide
Learn the methods, try an example for each skill and prepare for a full sitting without a calculator.
Worked examples
These teaching examples introduce the methods. They are separate from the 288-question practice bank, which includes longer passages and more demanding problems.
Math Skills
Arithmetic, ratios & rates
Write the quantities and units first. Turn percentages into multipliers and work problems into rates. Combine the underlying quantities before finding an average.
Common mistake: Averaging speeds without accounting for time, or reversing a percentage by adding the same percentage.
Practice this skillPump A fills a tank in 6 hours and pump B in 3 hours. At their constant rates, how long do both pumps together take to fill the empty tank?
Algebra, exponents & logarithms
Simplify before calculating. State any domain restrictions, isolate the unknown and substitute the result back into the original expression. Rewrite logarithms as powers.
Common mistake: Losing a negative sign, reversing an inequality incorrectly or admitting a value that makes a denominator zero.
Practice this skillIf log₂(x − 1) = 3, what is x?
Geometry & measurement
Sketch the figure and label known values. Distinguish linear, square and cubic units. With similar figures, square the length scale for area and cube it for volume.
Common mistake: Using the diameter as a radius or applying a length scale directly to an area.
Practice this skillTwo similar triangles have corresponding side lengths in the ratio 2:5. The smaller triangle has area 12 cm². What is the area of the larger triangle?
Probability & data
Define the sample space. For successive draws, check whether an object is replaced. Distinguish ordered choices from unordered groups, and use a complement when it is shorter.
Common mistake: Treating dependent events as independent or counting the same group more than once.
Practice this skillA bag contains 3 red and 2 blue counters. Two counters are drawn without replacement. What is the probability that both are red?
Reading Comprehension
Finding the supported statement
Read for the central claim, then check each option against a specific sentence. A good paraphrase preserves the subject, time period and scope even when its wording changes.
Common mistake: Choosing a plausible statement that requires an extra fact the passage never supplies.
Practice this skillTo be eligible for same-day review, a report must arrive before noon with a complete supporting file. Eligible reports are reviewed in order of urgency. If the daily review capacity is reached, remaining reports move to the next working day.
Which statement is supported by the passage?
Drawing inferences
Distinguish what is stated from what must follow. Join the relevant claims and test whether the proposed conclusion could be false while the passage remains true.
Common mistake: Turning an association into a cause or confusing a possible explanation with the only explanation.
Practice this skillEvery station using the replacement sensor has completed validation. Some coastal stations use that sensor. Other stations continue to use the older sensor while their validation results are reviewed.
Which conclusion follows?
Qualifiers & precise language
Track words such as only, some, ordinarily and unless. Compare the exact population and time window in the option with those in the passage.
Common mistake: Strengthening some into all, or dropping an exception from an otherwise accurate paraphrase.
Practice this skillAll overnight inspections require advance approval. Daytime remote inspections also require advance approval when they involve access to a restricted area. The regional team carries out several such daytime inspections each month.
Which statement is supported?
Procedures & conditions
Separate requirements from permissions. Write the sequence of conditions, identify exceptions, and apply only the conditions the scenario actually satisfies.
Common mistake: Assuming that a necessary condition is sufficient for approval or that an exception removes every other requirement.
Practice this skillTeams ordinarily submit travel notice at least two days before departure. Emergency authorization waives this notice requirement. Every team, including a team with emergency authorization, must complete an equipment check before departure.
A team has emergency authorization but has not completed the equipment check. What follows?
Mechanical Comprehension
Forces, motion & energy
Draw the forces and choose a direction. Check whether the situation involves equilibrium, acceleration or energy transfer. Use the force component in the direction of motion.
Common mistake: Treating motion as proof of an unbalanced force or assuming equal force means equal acceleration.
Practice this skillTwo carts of mass 2 kg and 4 kg each experience the same constant net force. How does the 2 kg cart’s acceleration compare with the 4 kg cart’s?
Gears, pulleys & levers
Trace each connection. Count rope segments supporting a moving load, compare perpendicular lever arms, and remember that a force advantage costs distance in an ideal machine.
Common mistake: Counting every visible pulley as a force multiplier or ignoring the direction change at a gear mesh.
Practice this skillThe ideal lever is balanced. What downward force F is needed on the right?
Fluids, pressure & heat
Identify the fluid depth, area or displaced volume that matters. Separate pressure from force and temperature from transferred heat. State the idealization before calculating.
Common mistake: Assuming equal pressure means equal force on pistons with different areas.
Practice this skillConnected hydraulic pistons have areas 2 cm² and 10 cm². Ignoring height differences and friction, a 20 N input force on the small piston produces what force at the large piston?
Electricity & circuits
Identify which components share a branch or the same two nodes. In series the current is common; in parallel the voltage is common. Check the effect of opening or closing a path.
Common mistake: Treating a drawn crossing as a connection without a junction, or assuming current is used up by a resistor.
Practice this skillTwo identical resistors are connected in parallel across an ideal battery. If one resistor’s branch is opened, what happens to the current through the remaining resistor?
Practice formula reference
Use these relationships to understand the worked solutions. This is our study reference, not a copy of the official formula sheet. The same reference is available during math and mechanical practice.
Math Skills formulas
- Percent change
- (new − original) ÷ original × 100%
- Rate
- distance = speed × time; work completed = rate × time
- Average
- mean = sum ÷ count
- Powers and logarithms
- aᵐ × aⁿ = aᵐ⁺ⁿ; logₐ(b) = c means aᶜ = b
For real logarithms: a > 0, a ≠ 1, b > 0.
- Triangles and circles
- area of triangle = bh/2; a² + b² = c²; circle area = πr²; circumference = 2πr
The Pythagorean relation applies to a right triangle, with c the hypotenuse.
- Volumes
- rectangular prism = lwh; cylinder = πr²h; cone = πr²h/3
- Probability
- P(A and B) = P(A) × P(B given A); P(not A) = 1 − P(A)
Mechanical Comprehension formulas
- Force and weight
- F_net = ma; weight = mg
F_net is the total force in newtons, m is mass in kilograms, a is acceleration in m/s², and g is gravitational acceleration.
- Work and energy
- W = Fd; kinetic energy = mv²/2; gravitational potential energy = mgh
For W = Fd, the force is constant and acts along the displacement.
- Torque
- torque = force × perpendicular distance from pivot
- Fluids
- pressure = force ÷ area; fluid pressure increase = ρgh; buoyant force = displaced fluid weight
ρ is density (kg/m³), g is gravitational acceleration (m/s²), and h is depth (m). With SI units, pressure is in pascals.
- Ideal machines
- input work = output work
Assumes no friction or other energy loss.
- Electricity
- V = IR; P = VI; series R = R₁ + R₂; parallel 1/R = 1/R₁ + 1/R₂
V is voltage in volts, I is current in amperes, R is resistance in ohms, and P is electrical power in watts.
Official test and practice format
| Feature | Navy OAR | Our full practice |
|---|---|---|
| Subjects | Math Skills, Reading Comprehension, Mechanical Comprehension | The same three subjects, using original content |
| Length | Adaptive; question counts vary | Up to 20 questions per subject, 60 total |
| Time | Navy guidance estimates 1–2 hours overall | Practice clocks: math 30 min, reading 30 min, mechanical 15 min |
| Selection | Proprietary adaptive testing | Three editorial difficulty levels; starts at intermediate in each subject |
| Navigation | No skipping, revisiting or changing earlier answers | Answer and continue; no skip or back button |
| Aids | No calculator; relevant formulas and scratch paper supplied | No calculator; original formula reference available |
| Feedback | OAR result after testing | Accuracy, section results and original explanations at the end |
Our full question counts, section clocks, between-section breaks and difficulty adjustment are preparation settings. They do not reproduce the Navy’s precise administration or stopping rule. Short drills have eight questions, no clock and feedback after each answer. Read official candidate guidance.
A practical study plan
- Check your application requirements. Confirm whether you need OAR alone or the full ASTB-E. Match preparation to the exact officer program and testing instructions.
- Try the short drills. Work through all three subjects and note weak topics. Use scratch paper. In reading, justify the right choice from the passage and identify the precise flaw in each distractor.
- Repair the gaps. Review methods, then replay weak skills on less familiar questions. Explain mechanical relationships before reaching for a formula. Practice math without a calculator.
- Take a full sitting. Work forward through the three timed sections. No answer feedback appears during the sitting. A section ends when its practice clock expires or its 20 questions are answered.
- Compare like with like. Look at section coverage, time, question difficulty and previous exposure as well as accuracy. Recheck weak topics on new material before relying on a remembered high score.
Understand your practice results
Practice results show the questions you reached, answers, explanations, section coverage and time. Unanswered and unreached questions remain visible in the summary. Timing out after a small number of accurate answers does not meet a full-practice goal.
Difficulty adapts, so a higher accuracy alone does not prove a stronger performance. Compare the number of challenging questions, your accuracy on them and whether the items were new to you. Our demanding goals are editorial study targets, not validated OAR cutoffs or a prediction of selection.
The Navy uses its own scoring model and program requirements. We do not convert a practice percentage into an official OAR score or simulate an applicant percentile. A recruiter can confirm the current requirements for your intended officer program.
Before test day
- Confirm the appointment, required identification, assessment components and local instructions with the testing office.
- Use the Navy’s linked sample questions to familiarize yourself with the content. They are examples, not a complete inventory of what can be tested.
- Practice without a calculator and get comfortable writing short, organized calculations on scratch paper.
- Work briskly while preserving accuracy. A harder question can reflect adaptive selection; it does not itself mean you are doing badly.
- Discuss any needed accessibility arrangements in advance. Follow the testing office’s instructions about permitted materials and breaks.
Independent original preparation. Not affiliated with or endorsed by the U.S. Navy or Department of Defense. Practice targets are not official selection standards.