Numerical Reasoning Formulas & Shortcuts
These formulas can be used for the original examples below. Choose the formula that matches the quantities and units in the question, then check its assumptions. This list does not establish the content, permitted aids or difficulty of your own assessment. Free numerical worked examples are readable on the introduction page; the JTP timed numerical run requires sign-in.
The core formulas
- Percentage change = (new − old) ÷ old × 100. Positive for an increase, negative for a decrease. The original value must be nonzero.
- 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 multiplied by the stated rate, when that rate is quoted as target currency per unit of the original currency. Reverse the same conversion by dividing by that nonzero rate.
- Average (arithmetic mean) = sum divided by count, for a nonempty set of values.
- Reverse percentage: if a value already includes a % increase, divide by (1 + percent/100) to get the original.
Arithmetic shortcuts to check
- ×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
Tips
- Write down what each quantity represents before substituting numbers.
- Keep percentages as decimals when multiplying successive factors.
- Distinguish a percentage-point change from a relative percentage change.
- For a reverse-percentage question, reconstruct the increase from the proposed original value to check your answer.
Frequently asked questions
Do I need to memorise formulas for a numerical reasoning test?
Work through a formula until you can explain its inputs and result. Check your actual assessment instructions for any requirements or permitted reference material.
Are formulas provided during the test?
This guide does not establish whether your assessment supplies formulas. Read your invitation and provider instructions.
What maths level do numerical reasoning tests require?
The examples here use percentages, ratios and basic arithmetic. They do not establish the mathematics level required by a particular employer assessment.
Which formula causes the most mistakes?
No candidate mistake-rate comparison is established here. The reverse-percentage example illustrates why the final value must be divided by the increase factor.
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