Numerical Reasoning Formulas & Shortcuts
Most numerical reasoning questions reduce to a handful of formulas. Knowing them cold frees your attention for reading the data correctly. Here are the ones worth memorising, with the shortcuts that save the most time.
The core formulas
- Percentage change = (new − old) ÷ old × 100. Positive for an increase, negative for a decrease.
- Percentage of a value = value × (percent ÷ 100).
- Ratio sharing: add the ratio parts, divide the total by that sum to get one part, then multiply.
- Currency conversion = amount × rate; to reverse, divide by the rate.
- Average (mean) = sum ÷ count.
- Reverse percentage: if a value already includes a % increase, divide by (1 + percent/100) to get the original.
Time-saving shortcuts
- ×1.1 adds 10%; ×0.9 removes 10%; ×0.25 gives a quarter.
- To grow a number by 20%, add a fifth of it.
- Learn the common conversions: 1/4 = 25%, 1/5 = 20%, 1/8 = 12.5%, 3/4 = 75%.
Worked example
A price rises 25% to £150. What was the original? Divide by 1.25: 150 ÷ 1.25 = £120. Reverse percentage is the most-missed formula — practise it until it's automatic.
Tips
- Write the formula down before you plug in numbers.
- Keep percentages as decimals when you chain several steps.
- Watch for “percentage points” versus “percent” — they are not the same.
- Drill reverse-percentage questions specifically; they trip up most candidates.
Frequently asked questions
Do I need to memorise formulas for a numerical reasoning test?
A small core set, yes — it saves the time you'd otherwise lose deriving them mid-test.
Are formulas provided during the test?
Usually not, so learn the core set in advance.
What maths level do numerical reasoning tests require?
Around GCSE or high-school level: percentages, ratios and basic arithmetic.
Which formula causes the most mistakes?
Reverse percentage — working back from a value that already includes an increase. It's worth extra practice.
Related guides
Independent practice platform. Not affiliated with any test publisher or employer.