Quantitative Aptitude: Arithmetic and Data Interpretation
What the quantitative section tests
Numerical Ability in Prelims has 40 questions for 50 marks in the shared 45-minute window; Mains Quantitative Aptitude has 40 questions for 50 marks. The paper mixes simplification and approximation, number series, quadratic equations, arithmetic word problems and data interpretation (DI). Accuracy on DI and arithmetic decides the score because these carry multi-question sets.
Core rules and formulas
- Successive percentage change: net = a + b + ab/100, with signs. Two successive discounts of 20% and 10% give 28% off.
- Profit and loss: always compare selling price with cost price. Marked price is not profit.
- Simple interest = PRT/100; compound interest = P[(1 + R/100)^T - 1].
- Time and work: add rates, not days. If A alone takes 12 days and B alone 18, combined rate = 1/12 + 1/18 = 5/36, so time = 36/5 = 7.2 days.
- Speed: average speed for equal distances is 2xy/(x+y), not (x+y)/2.
- Alligation: ratio of quantities = (mean - cheaper)/(dearer - mean).
Worked example
A shopkeeper marks an article 25% above cost and allows a 12% discount. Find profit percent. Let CP = 100. MP = 125. SP = 125 × 0.88 = 110. Profit = 10 on CP 100, so 10%. The discount is calculated on MP, not CP.
Traps that cost marks
Applying a second percentage to the original base; averaging speeds arithmetically; mixing SI and CI; ignoring units in speed and mensuration; reading the wrong year or unit in a DI table; and over-calculating when options are far apart.