Numerical Reasoning and Quantitative Aptitude
What the domain tests
This domain tests arithmetic fluency and quantitative reasoning in practical contexts: percentages, ratios, averages, rates, unit conversion, data interpretation and multi-step word problems. Fire-service settings may involve pump output, tank capacity, hose lengths, crew allocation, response distances and inspection statistics. The challenge is usually not advanced mathematics but selecting the right operation and keeping units consistent.
Core rules to apply
- Rate equation: quantity = rate × time. Rearrange to time = quantity ÷ rate. For a pump, time = volume ÷ flow rate.
- Ratio: express parts of a whole as a ratio, find the total number of parts, then multiply by the value per part.
- Percentage change: change ÷ original × 100%. Percentage points are not the same as percent change.
- Weighted average: multiply each group value by its size, add, then divide by total size. Do not average averages.
- Unit conversion: 1 m³ = 1,000 L; 1 hour = 60 minutes; 1 km = 1,000 m. Convert before calculating.
- Inverse proportion: if flow rate rises while volume is fixed, time falls in the same ratio.
Worked example
A tank holds 7,200 L. A pump delivers 1,200 L/min, but only 80% of the delivery reaches the tank because of losses. How long will filling take? Reasoning: effective flow = 1,200 × 0.80 = 960 L/min. Time = 7,200 ÷ 960 = 7.5 minutes. If the question asked for minutes and seconds, 0.5 minute = 30 seconds, so the answer is 7 minutes 30 seconds. A common error is to divide 7,200 by 1,200 and ignore the efficiency loss, giving 6 minutes.
Traps that cost marks
Read whether a percentage is of the original or the new value. Do not mix litres per minute with cubic metres per hour. Check whether a rate is per appliance or for the whole crew. In data interpretation, confirm whether the chart shows totals, averages or percentages. Round only at the end unless the question specifies otherwise. If an answer asks for a whole number of appliances or crews, round up because a partial unit cannot be deployed.
Exam technique
Write the formula before substituting numbers. Carry units through each line. Estimate the answer first so you can reject impossible options. For multi-step problems, label intermediate results so you do not reuse a wrong figure.