Numerical Reasoning and Mathematics
The core toolkit
Most papers draw on a narrow set of tools used quickly: fractions, decimals and percentages; ratio and proportion; averages and weighted averages; rates (speed, distance, time; work and pipes); simple and compound interest; profit and loss; number series; LCM and HCF; basic probability and counting; perimeter, area and volume; and simple data interpretation from tables or charts.
Concepts worth drilling
- Percentage change is always measured against a base. "A rises 20% then falls 20%" is not back to start: 1.2 x 0.8 = 0.96, a net 4% fall.
- Successive changes multiply, never add. Two changes of +20% and +10% give a multiplier of 1.32, i.e. +32%.
- Average speed is total distance over total time, not the mean of the two speeds.
- Series usually alternate operations or move through differences; check second differences before committing.
Traps that appear
- Answering in the wrong unit (minutes for hours, grams for kilograms).
- Using the old value as the base after a change.
- Percent of versus percentage points.
- Distractor options that match an intermediate step - always check what the question actually asks for.
- Rounding too early in multi-step work.
Worked example
A price of 500 is discounted 20%, then a further 10% at the till. What is the total discount? Do not add the rates. Multipliers: 0.80 x 0.90 = 0.72, so 28% is removed, not 30%. Final price 500 x 0.72 = 360, a saving of 140. Rule of thumb: turn every percentage change into a multiplier and chain them; only convert back to a percentage at the end.