AFOQT Arithmetic Reasoning Practice Test (25 Questions, 29 Minutes)

You will not fail this on the arithmetic

Twenty-nine minutes for twenty-five word problems is about seventy seconds each — the second most generous allowance on the battery. The numbers are chosen to work out cleanly, because the subtest is not testing whether you can perform long division under pressure. It is testing whether you can turn a paragraph into the correct equation.

That distinction should shape how you practise. Grinding through arithmetic drills improves the thing you were already good at. Reading a problem, writing down what is actually being asked, and only then calculating is the habit that moves the score.

The distractors are numbers you legitimately produced

This is the defining feature of the subtest and the reason careless candidates lose points they had earned. The wrong answers are not random. They are the intermediate values you compute on the way to the answer.

• Asked how many aircraft are available when three-eighths are in maintenance, the option showing the number in maintenance is waiting for you.
• Asked what remains after two deductions, the option showing the amount spent is waiting.
• Asked for a total including tax, the option showing the pre-tax subtotal is waiting.
• Asked for one part of a ratio, the option showing the value of a single share is waiting.

The fix is mechanical and it works: underline the quantity the question asks for before you calculate anything, and check your answer against that underline before you mark it. Two seconds, and it recovers more points on this subtest than any amount of mental-arithmetic practice.

The patterns worth drilling

Rate, time and distance

Distance equals rate times time, rearranged as needed. The trap is average speed: it is total distance over total time, never the average of two speeds. A journey of 150 miles at 50 mph and 210 at 70 takes three hours each way, so 360 miles over six hours is 60 mph — the shortcut happens to agree there only because the legs took equal time, and it usually does not.

Work rate

Add rates, not times. A crew doing a job in six hours works at one sixth per hour; one doing it in three works at one third. Together that is one half per hour, so two hours. Averaging six and three to get four and a half is the classic error and it appears as an option.

Percentages, and percent of a remainder

A second percentage applies to what is left, not to the original. Forty percent of an $80,000 budget on fuel leaves $48,000; twenty-five percent of that is $12,000, not $20,000. This is the single most common multi-step trap on the subtest.

Ratios

Convert to parts, find one part, then scale. A 2:9 ratio across 528 people is eleven parts, so one part is 48 — two of them is 96. That turns almost every ratio question into one division and one multiplication.

Averages

Work in totals. To average 80 across five tests you need 400 points; four tests at 78 gives 312; so the fifth must be 88. Thinking in totals rather than averages makes these near-instant.

Estimate before you commit

With clean numbers and five spread-out options, a rough estimate usually eliminates three choices before you calculate anything. If a twenty percent discount is involved, the answer sits near four-fifths of the original — anything above the original is gone without arithmetic. If a percentage increase is asked and the numbers rose by about a quarter, options near ten percent and near fifty percent are gone.

This matters more than it sounds, because estimating first also catches setup errors. An answer that comes out wildly away from your estimate usually means you solved a different problem, and that is exactly the failure this subtest is built around.

Pacing

Seventy seconds is comfortable for a two-step problem and tight for a four-step one. If you are ninety seconds into a question and have not written an equation, mark it and move — there is no bonus for finishing the hard one while the clock runs out on three easy ones you would have got right.

Because the allowance is generous relative to the other subtests, this is a good place to bank time by not second-guessing yourself. Once you have set the problem up correctly and checked the answer against what was asked, move on.

And never leave a blank. There is no penalty for a wrong answer, so an unanswered item is pure loss.

Where it fits

Arithmetic Reasoning is the applied half of the quantitative material, alongside Math Knowledge, which tests whether you remember the rules rather than whether you can apply them. They fail differently and need different practice, which is why we treat them separately rather than as “the maths”. The quantitative pathway page covers how to split time between them.

Write the equation down

Not the working — the equation. One line, before any arithmetic, stating what you are solving for. It takes four seconds out of a seventy-second allowance and it is the highest-return habit available on this subtest, because it forces the translation step to happen explicitly instead of in your head where it goes wrong silently.

It also gives you something to check against. When your answer does not appear among the options, the equation tells you immediately whether you set the problem up wrongly or simply slipped in the arithmetic — and those need different fixes under time pressure.