Numerical Reasoning: Choosing the Right Operation and Base
Numerical reasoning in EPSO AST/SC presents data in tables, charts or short word problems and asks for one correct value among five options. The arithmetic is school-level; the difficulty is choosing the right operation, tracking units and bases, and avoiding answers that are intermediate steps. Items are designed so that a careless reader finds a plausible wrong option.
Core operations
- Percentages: increase = base x (1 + r); decrease = base x (1 - r); percentage change = (new - old) / old x 100.
- Percentage points versus percent: a rate rising from 4% to 6% rises 2 percentage points, or 50%.
- Ratios and shares: part divided by whole. If a share is '30% of the remainder', multiply by 0.70 first.
- Averages: total divided by count; a weighted average weights each group by its size.
- Unit conversion: thousands versus millions, kilograms versus tonnes, minutes versus hours.
Worked example
A unit's travel budget is 240,000 euros. Flights take 45% and accommodation 30% of the budget. The unit must cut total spending by 12% and applies the cut proportionally. What is the new subsistence (remaining) budget? Flights: 240,000 x 0.45 = 108,000. Accommodation: 240,000 x 0.30 = 72,000. Subsistence: 240,000 - 180,000 = 60,000. A proportional 12% cut leaves 60,000 x 0.88 = 52,800 euros. The option 60,000 ignores the cut; 67,200 wrongly applies the cut only to the other lines.
Traps that cost marks
- Applying a percentage to the wrong base after an earlier change.
- Adding percentages that refer to different totals.
- Reading a chart whose vertical axis does not start at zero.
- Rounding at every step instead of at the end.
- Answering the intermediate value the question did not ask for.
- Mixing units within a table, such as thousands of euros in one column and euros in another.
Where an on-screen calculator is available, use it for arithmetic, not for setting up the problem. Write the operation and units before calculating.