Mathematical Reasoning and Aptitude
Mathematical Reasoning and Aptitude
Ten to fifteen questions of Paper I are numerical: number series, ratio and proportion, percentage, profit and loss, average and mixture, simple and compound interest, time–work, time–speed–distance, mensuration, permutations and basic probability.
Fast rules
- Successive percentage changes: use the multiplying factors, 1.10 × 0.90 = 0.99, so a 10% rise followed by a 10% fall is a 1% net fall - never 0%.
- Average speed for equal distances is the harmonic mean, 2xy/(x+y), not (x+y)/2.
- Compound interest: A = P(1 + r/100)^n; CI − SI over two years equals P(r/100)².
- Ratio–HCF–LCM link for two numbers: a × b = HCF × LCM.
- Time–work: convert to one-day rates; combined rate is the sum of individual rates.
Worked example
Two numbers are in the ratio 3 : 4 and their LCM is 240. Find their HCF and the numbers.
Let the numbers be 3x and 4x. Their HCF is x and their LCM is 12x. So 12x = 240, giving x = 20. The numbers are 60 and 80, and the HCF is 20. Check: 60 × 80 = 4800 and HCF × LCM = 20 × 240 = 4800, so the identity holds.
Traps that cost marks
- Reading "5% more than" as "5 percentage points higher" - these differ.
- Using the arithmetic mean for average speed on equal distances.
- Taking simple interest when the stem says "compounded annually".
- Forgetting to convert units (km/h to m/s: multiply by 5/18).
- In permutations, ignoring whether order matters - arrangement of letters favours permutation, selection of a committee favours combination.