Numerical Reasoning
Shared numerical reasoning
This guide practises percentages, ratios, averages, rates, unit conversions and number series as shared recruitment-aptitude foundations. Set up quantities and assumptions carefully before computing, and verify that the result answers the question actually asked. The scenarios provide their own quantities and do not establish current recruitment, staffing or operational rules.
Core rules to have automatic
- Order of operations: work brackets first, then powers and roots, then × and ÷ left to right, then + and −.
- Percentage change: use multipliers. +20% = ×1.20; −15% = ×0.85. Successive changes multiply, so +20% then −20% gives ×0.96, a net 4% fall, not zero.
- Ratio and proportion: scale both parts by the same factor. To split a total in ratio a:b, the total represents a+b parts.
- Averages: total = average × count. When a new value is added, the new total is the old total plus the new value.
- Rates: combine rates by adding or subtracting the work done per unit time; never average the times directly.
- Series: test first differences, then second differences, then ratios; check for alternating or two interleaved sequences.
Worked example
A 240-litre tank is filled by pipe A in 6 hours and emptied by pipe B in 8 hours. With both open, how long does the tank take to fill?
A fills 240 ÷ 6 = 40 litres per hour. B empties 240 ÷ 8 = 30 litres per hour. Net rate = 40 − 30 = 10 litres per hour. Time = 240 ÷ 10 = 24 hours. The trap is to average 6 and 8 and answer 7 hours; rates combine additively, but times do not.
Traps that cost marks
- Adding percentage changes instead of multiplying them.
- Using the original value as the denominator when the question asks for change relative to the new value.
- Mixing units (minutes with hours, grams with kilograms) before calculating.
- Solving a series with the first pattern found without checking it against every term.
- Rounding early; keep full precision until the final line.