Numerical Reasoning - FRNSW Cognitive Test
Numerical reasoning in the FRNSW cognitive test checks practical arithmetic and data interpretation: pump rates, tank capacity, response distances, percentages, ratios, averages and unit conversions. Questions are usually short, but the distractors are built from common calculation shortcuts, so the mark goes to the candidate who sets out the quantities and units before computing.
Core rules
- Convert units before calculating. A flow may be given in L/min while a tank is in litres and a duration in minutes; a speed may be km/h while a distance is in metres.
- Rate problems: time = volume ÷ flow rate; distance = speed × time. Carry units through and check they cancel.
- Percentage reserve: reserve = percentage × total; usable = total − reserve. Do not apply the percentage to the amount already used.
- Ratios: distinguish part-to-part from part-to-whole. If the ratio of foam concentrate to water is 1:20, concentrate is 1 part in 21 of the mix.
- Averages: total = average × number of items. A weighted average is not the simple average of group averages.
- Estimate first to eliminate impossible options, then compute exactly.
Worked example
A tanker carries 4,500 L. Crew must retain a 20% reserve. The branch flows 180 L/min. How long can the branch run before the reserve is reached? Reasoning: reserve = 0.20 × 4,500 = 900 L. Usable water = 4,500 − 900 = 3,600 L. Time = 3,600 ÷ 180 = 20 min. If setting up the branch takes 3 min, the working duration is 20 − 3 = 17 min. The common wrong answer is 4,500 ÷ 180 = 25 min, which ignores the reserve. Another error is taking 20% of 3,600 after subtracting, giving 720 L and 19.2 min.
Traps that cost marks
- Mixing litres with L/min, or minutes with hours, without converting.
- Calculating a percentage of the wrong base - total versus remaining.
- Averaging two averages as if group sizes were equal.
- Rounding early and carrying the error into the final option.
- Treating a percentage increase and a percentage decrease as symmetrical: a 20% rise followed by a 20% fall does not return to the original value.