Numerical Ability: Arithmetic Rules and Speed Traps
Numerical Ability tests arithmetic speed and accuracy: number system, simplification, percentage, ratio and proportion, average, profit and loss, simple and compound interest, time-speed-distance, time and work, mensuration, and data interpretation. Calculation shortcuts and careful unit handling decide the score.
Rules to keep ready
- BODMAS: brackets, orders, division and multiplication, addition and subtraction.
- Fraction-percentage equivalents: 1/8 = 12.5%, 1/6 = 16.67%, 1/3 = 33.33%, 1/16 = 6.25%.
- Percentage change is always calculated on the original or base value.
- Profit and loss percentages are on cost price unless stated otherwise; discount is on marked price.
- 1 km/h = 5/18 m/s; average speed = total distance divided by total time, not the mean of the speeds.
- SI = PRT/100; CI = P(1 + R/100)^T - P.
Worked example
A shopkeeper marks an article 40% above cost and allows a 25% discount. Find the profit percentage. Take CP = 100. Then MP = 140. SP = 140 x 0.75 = 105. Profit = 5 on a cost of 100, so profit = 5%.
Traps
- Adding successive discounts directly; 10% plus 10% is not 20%.
- Taking discount on cost price or profit on selling price.
- Forgetting to convert minutes to hours in speed questions.
- Using the SI formula for CI, or compounding for part-years without adjusting.
- Cancelling terms in simplification before applying BODMAS order.