Numerical and Verbal Reasoning
This domain tests speed and precision on business data, plus the discipline of reading statements for exactly what they claim. Most lost marks come from base-rate and quantifier errors, not hard maths.
Numerical rules
- Percentages versus percentage points: 5% to 7% is +2 points but +40% relative.
- Reverse percentages: a 20% fall needs a 25% rise to recover (1 ÷ 0.8 = 1.25).
- Never average averages - weight by base size.
- Compound growth: (1 + r)^n; CAGR = (end ÷ start)^(1/n) − 1; doubling time ≈ 70 ÷ growth rate in %.
- Index numbers and currency conversions: fix the base and the exchange rate before comparing.
Verbal rules
- An inference must follow from the passage; a recommendation, cause or prediction usually does not.
- Track quantifiers (all, most, some, none) and scope - a claim about one region cannot be generalised.
- Watch for the classic substitutions: correlation stated as cause, plan stated as outcome, opinion stated as fact.
Worked example
Region A has 200 customers averaging £50; Region B has 800 averaging £30. The naive average of £40 is wrong. Weighted average = (200 × 50 + 800 × 30) ÷ 1,000 = £34. Separately, revenue grew from £100m to £161m in five years: CAGR = (161 ÷ 100)^(1/5) − 1 ≈ 10%, since 1.1^5 ≈ 1.61. Reasoning: both answers depend on choosing the right base before dividing.
Traps
- Averaging percentages across unequal groups.
- Adding percentage changes instead of compounding them.
- Accepting a plausible inference that the passage never states.