Quantitative Reasoning and Numerical Ability
What to master
Numerical ability questions reward fluency with percentages, ratios, proportions, averages, rates (speed/distance/time), simple and compound interest, and basic data interpretation (tables, bar charts, pie charts). You should also be comfortable with number properties - divisibility rules, factors and multiples, LCM/HCF, squares and cubes - and with quick estimation.
Typical traps
- Percentage change applied to the wrong base. A 20% rise then a 20% fall does not return to the original value; the fall is taken on the larger figure. Net change = (1.2)(0.8) − 1 = −4%.
- Ratio mixing. In a 2:3 mixture, adding 5 litres of water changes the total, not just one part. Always track the total.
- Average confusion. "Average speed" over equal distances is the harmonic mean, not the arithmetic mean of the two speeds.
- Unit slips. Minutes vs hours, paise vs naira, thousands vs millions.
- Interest compounding periods. 10% per annum compounded half-yearly means 5% per half-year, two periods per year.
Rule of thumb
For any percentage word problem, write the base explicitly: percentage of what? Then set up a single equation rather than chaining step-by-step calculations, which accumulates error.
Worked example
A trader buys an item for ₦4,000, marks it up 25%, then gives a 10% discount. Selling price = 4,000 × 1.25 × 0.90 = ₦4,500. Profit = ₦500, i.e. 12.5% on cost. Note the markup and discount do not cancel - the discount is on the marked price, not the cost.