Numerical Reasoning
Numerical Reasoning tests arithmetic fluency, ratio and proportion, percentages, rates, and data interpretation. Most items are short but combine two steps, so the mark depends on setting up the calculation correctly before pressing equals.
Core rules
- Follow order of operations: brackets, indices, multiplication and division, then addition and subtraction.
- A ratio compares parts; scale all parts by the same factor. If A:B = 3:5 and A is 12, the multiplier is 4, so B is 20.
- Percentage change = change divided by original value, times 100. Percentage points compare two percentages directly; percent compares a change to a base.
- For rates, keep units consistent. Speed = distance divided by time; density = mass divided by volume.
- In tables and graphs, read the axis labels, units, and whether bars start at zero.
Worked example
A team of 12 reservists has food for 18 days. After 6 days, 4 reservists leave. How long does the remaining food last? Total food = 12 x 18 = 216 person-days. In 6 days the team consumes 12 x 6 = 72 person-days, leaving 144. With 8 people remaining, 144 divided by 8 = 18 days. The food lasts 18 more days.
Traps
- Adding percentages instead of multiplying successive changes.
- Mixing percentage points with percent.
- Using the new value as the denominator for a percentage decrease.
- Rounding early and carrying the error into later steps.
- Ignoring units such as minutes versus hours or grams versus kilograms.