Numerical Reasoning: Percentages, Ratios and Data Interpretation
Core toolkit
Numerical reasoning here is mostly arithmetic under time pressure: percentages and percentage points, ratios and proportions, weighted averages, index numbers based on 100, growth rates and unit conversion. Be fluent at reading tables whose footnotes change the meaning of a column (thousands vs millions, euro vs thousand euro), and estimate before computing.
Traps
- Percentage vs percentage point: a rate moving from 4% to 5% rises by one percentage point but by 25%.
- A changing base: a fall of 20% needs a rise of 25% to return to the original value.
- Averaging averages without weights.
- Mismatched units or periods (annual vs quarterly rates).
- Rounding early and compounding the error.
- "How many more" vs "how many times as many".
Rule of thumb
Always write the base next to a percentage: change = (new − old) ÷ old. Estimate the answer to one significant figure first; if the precise result differs by an order of magnitude, you have misread a unit.
Worked example. A budget line rises from €120m to €138m while the total budget rises from €600m to €720m. The line grows 15%, the total 20%, so the line's share falls from 20.0% to 19.2% - a drop of about 0.8 percentage points, not the 5 percentage points a careless subtraction (20 − 15) would suggest.