Mathematics and Numerical Reasoning
What this domain tests
Numerical reasoning measures speed and accuracy with arithmetic, percentages, ratios, averages, rates, basic algebra, geometry, and data interpretation. The aim is not advanced mathematics but clean setup under time pressure.
Core rules
- Convert everything to the same unit before calculating.
- For averages, use total = average x number; for weighted averages, weight each group.
- Average speed = total distance divided by total time, not the average of the speeds.
- In ratios, find the multiplier by dividing a known total by the sum of ratio parts.
- Estimate first to eliminate impossible options.
Worked example
A patrol travels 18 km at 6 km/h and then 12 km at 4 km/h. What is the average speed for the whole journey? Time = 18/6 + 12/4 = 3 + 3 = 6 hours. Total distance = 30 km. Average speed = 30/6 = 5 km/h. The simple average of 6 and 4 also gives 5 here, but that is coincidence; the valid method is total distance over total time.
Traps
Averaging two speeds directly; mixing minutes and hours; treating a percentage increase and a percentage decrease as cancelling; reading 'percentage points' as 'percent'; and rounding too early. In data interpretation, check whether the chart shows totals or rates, and whether the question asks for a value or a change.
Practice discipline
Work in short timed sets, write the setup line before calculating, and keep a one-line error log by category: setup, arithmetic, unit, misread. Fix the category, not just the question.