Quantitative Aptitude / Numerical Ability
Quantitative Aptitude / Numerical Ability
The numerical section rewards speed on standard templates: simplification and approximation, number series (missing and wrong term), quadratic equations, percentage, ratio, average, profit and loss, simple and compound interest, time-speed-distance, time and work, pipes and cisterns, mixtures and alligation, partnership, ages, elementary probability and mensuration, plus data interpretation on tables, bars, pie charts and caselets.
Core rules
- Percentage change is always measured on the original base. A 20% rise followed by a 20% fall leaves a net 4% fall, because 1.2 × 0.8 = 0.96.
- Successive discounts: use a + b − ab/100 rather than adding the percentages.
- Two-year CI − SI difference = P(r/100)².
- Alligation gives the ratio in which two priced quantities must be mixed to reach a mean price.
- DI: read the unit line first (in lakh, in thousand, in %) - most errors are unit errors, not calculation errors.
Worked example
₹20,000 is invested at 10% per annum compounded annually. Find the difference between CI and SI for two years. Reasoning: SI = 20,000 × 10 × 2/100 = ₹4,000. CI = 20,000 × (1.1² − 1) = 20,000 × 0.21 = ₹4,200. Difference = ₹200. Shortcut: P(r/100)² = 20,000 × 0.01 = ₹200. The difference exists because year-two interest is earned on first-year interest.
Traps
- Applying a discount percentage to the marked price in one step when two successive discounts are given.
- In time and work, averaging individual times instead of adding rates (1/a + 1/b).
- In DI, comparing absolute values when the question asks for a percentage share.
- Over-rounding in approximation questions and then not matching any option.