Numerical Ability: Arithmetic Shortcuts and Data Interpretation
What the section tests
Numerical Ability, also called Quantitative Aptitude, tests simplification and approximation, number series, quadratic equations, percentage, ratio, average, profit and loss, simple and compound interest, time-work, speed-distance, mensuration, probability and data interpretation. The LIC HFL paper favours speed with accuracy, so fraction and percentage equivalents matter as much as formal formulas.
Core rules to apply
- Percentage change = (change / original) x 100; always divide by the original base, not the new value.
- Compound interest: A = P(1 + r/100)^n for annual compounding; CI = A - P. For two years, the effective rate is r + r + r^2/100.
- Simple interest: SI = P x R x T / 100.
- Work: if A finishes in x days and B in y days, together they finish in xy/(x + y) days.
- Data interpretation: read units and totals first; calculate only the required value instead of solving every row.
Worked example
Find the compound interest on Rs 20,000 at 10% per annum for 2 years, compounded annually. Reasoning: A = 20,000 x (1.10)^2 = 20,000 x 1.21 = Rs 24,200. CI = 24,200 - 20,000 = Rs 4,200. A shortcut is the effective two-year rate: 10 + 10 + (10 x 10)/100 = 21%, so CI = 21% of 20,000 = Rs 4,200.
Traps that cost marks
Do not use the new value as the base in percentage-change questions. Do not confuse CI with SI: for two years at 10%, SI is Rs 4,000, not Rs 4,200. Convert minutes to hours in speed questions. In data interpretation, check whether the question asks for a ratio, a difference or a percentage.
Key points
- Percentage change is always divided by the original base.
- Two-year CI effective rate is r + r + r^2/100.
- SI uses P x R x T / 100; CI uses compounding.
- Combined work time is xy/(x + y).
- In DI, identify units and the exact quantity asked before calculating.