Numerical Reasoning
What is tested
Numerical reasoning measures accurate arithmetic under time pressure plus the judgement to choose the right operation: percentages, ratios and proportion, averages, rates (speed, work, flow), sequences, currency and unit conversion, and reading figures from a described table or chart.
Concepts to master
- Percentages: a 20% increase multiplies by 1.20; a 20% decrease multiplies by 0.80. To reverse a percentage change, divide rather than subtract.
- Ratios: convert to parts of a whole. A 3:5 split of €400 is 8 parts, so each part is €50.
- Averages: total ÷ count. For average speed over two legs, use total distance ÷ total time, never the average of the two speeds.
- Work rates: add rates, not times. If one person does a job in 6 days (1/6 per day) and another in 12 (1/12), together they do 3/12 = 1/4 per day, so 4 days.
- Sequences: check differences, then ratios, then alternating rules.
Traps
- A percentage increase then decrease is not neutral: 100 → 120 → 96 is a 4% net loss.
- Unit mismatch - minutes against hours, grams against kilograms, cents against euro.
- Wrong base in reverse-percentage questions (a price that includes VAT is 120% of the pre-VAT price).
- Answering with more precision than the options allow; estimate first and eliminate.
- Misreading which row or column of a table the question refers to.
Worked example
A jacket costs €80. Its price rises 20%, then falls 20% in a sale. Final price: 80 × 1.20 = €96; 96 × 0.80 = €76.80 - a €3.20 net loss, not the original €80. The common wrong answer, €80, comes from subtracting the same 20% from the increased price.
Rule of thumb: write the units beside every number, sketch the steps, and sanity-check the size of your answer before selecting.