Mathematics and Quantitative Reasoning
The maths portion rewards method over memory. Recurring topics are percentages, ratio and proportion, averages, profit and loss, simple and compound interest, work and time, speed-distance-time, basic algebra, area and perimeter, and number series.
Formulas to have automatic
- Profit% = (SP - CP)/CP x 100; discount% is calculated on the marked price, not the cost price.
- SI = PRT/100; CI = P(1 + R/100)^T - P.
- Work: combined rate = 1/a + 1/b, so time together = ab/(a + b).
- Distance = speed x time; average speed = total distance / total time.
Worked example
A Preventive Officer's salary of Rs 60,000 is raised by 10% and later cut by 10%. What is the final figure? 60,000 x 1.10 = 66,000; then 66,000 x 0.90 = 59,400. The net change is not zero, because the cut applies to a larger base. Shortcut: net% = a + b + ab/100 = 10 + (-10) + (10 x -10)/100 = -1%, so the officer ends 1% below the starting salary.
Traps
Taking average speed as (u + v)/2 when equal distances are covered at different speeds; the correct result is the harmonic mean 2uv/(u + v). Applying a discount to the cost price instead of the marked price. Forgetting to convert units - minutes to hours, paisa to rupees, centimetres to metres. Reading 'increased by 10%' as 'became 10'. In series questions, checking only first differences and missing an alternating pattern.