DAA Numerical Reasoning: worked examples and quick tips

The Numerical Reasoning section of the Defence Aptitude Assessment (DAA) tests fast, applied maths under real time pressure. There is no calculator (paper and pencil are allowed), and the clock is tight. That combination catches a lot of people out — not because the maths is hard, but because it has to be quick and accurate at the same time. This guide explains what the section covers, walks through two fully worked examples, and shares practical tips to help you keep your head on the day.

Read this first. The Royal Navy's free official DAA familiarisation questions show the real format: the real test has two numerical parts — fractions, decimals and equations (12 questions in 4 minutes), and interpreting graphs and tables (15 questions in 11 minutes, across 4 scenarios). No calculator is allowed, but paper and pencil are. Our practice covers the arithmetic topics below, but it does not yet include graph-and-table questions, so use the official questions for that part. Try the official questions before you rely on this guide.

What Numerical Reasoning actually tests

This section is not about advanced mathematics. It is about the everyday number skills you would use in a practical role: reading a figure, doing something with it, and picking the right answer before the clock beats you. Because you have no calculator and a tight clock, the section is really testing confident arithmetic and clear thinking under pressure. Speed matters, but so does accuracy — a rushed slip costs you just as much as not finishing.

The topics our practice covers

The real test's first part covers fractions, decimals and equations, and its second part is graphs and tables (see the note above). Our questions drill the arithmetic behind both, drawn from a fairly predictable set of topics:

• Percentages — finding a percentage of a quantity, percentage increase or decrease, and working backwards from a percentage.
• Fractions — simplifying, comparing and applying fractions to real quantities.
• Ratios and proportion — splitting amounts in a given ratio and scaling quantities up or down.
• Averages — usually the mean of a small set of numbers.
• Speed, distance and time — rearranging the relationship between the three.
• Unit conversions — between units of length, weight, time and money, including metric and imperial.
• Number sequences — spotting the pattern and finding the next or missing term.

Worked example 1: a percentage question

A common style is a straightforward percentage of a quantity. Take this example:

A unit has 240 personnel. 35% are deployed overseas. How many is that?

1. Start with 10%, which is easy: 10% of 240 = 24.
2. So 30% = 24 × 3 = 72.
3. Now 5% is half of 10%, so 5% = 12.
4. Add them together: 30% + 5% = 72 + 12 = 84.

You can check it directly if you prefer: 0.35 × 240 = 84. Breaking the percentage into 10% and 5% chunks is often faster to do in your head than multiplying by a decimal, and it is easier to keep track of without writing much down.

Worked example 2: a speed, distance and time question

These questions rely on one relationship: speed = distance ÷ time. Rearrange it depending on what you are asked for. Take this example:

A vehicle travels 90 km in 1 hour and 30 minutes. What is its average speed in km/h?

1. Convert the time to hours: 1 hour 30 minutes = 1.5 hours.
2. Apply the formula: speed = distance ÷ time = 90 ÷ 1.5.
3. 90 ÷ 1.5 = 60 km/h.

If a question then asks for the answer in miles per hour, use the rough conversion that 1 mile is about 1.6 km. So 60 km/h ÷ 1.6 ≈ 37.5 mph. Knowing that conversion cold saves you a lot of time.

Tips to score well

The section is very trainable, and a handful of habits make a real difference:

• Sharpen your mental arithmetic. Drill times tables up to 12, and practise percentages, fractions and ratios by hand until they are instant. This is the single biggest lever you have.
• Learn to estimate and eliminate. You often do not need the exact answer to rule out most of the options. A quick estimate can leave just one sensible choice, which is faster and safer than a full calculation.
• Memorise the common conversions. Roughly 1 mile ≈ 1.6 km, 1 kg ≈ 2.2 lb, 1 hour = 60 minutes. Having these ready removes a step from many questions.
• Do not get stuck. If a question is not coming, make your best estimate, mark it in your mind and move on. One hard question is not worth three easy ones you never reach.
• Work in easy chunks. Break percentages into 10% and 5% blocks, and round awkward numbers to something friendlier before adjusting.

Put it into practice

Reading about the section only takes you so far — the gains come from doing timed questions until the arithmetic feels automatic. Work through our numerical reasoning practice under realistic time pressure, review anything you get wrong, and build a steady rhythm before the day. For the wider picture, see how to prepare for the DAA and our overview of the DAA explained. This is independent practice and is not affiliated with, endorsed by or connected to the RAF, the Royal Navy or the Ministry of Defence.