Aptitude Test
The three fronts
Aptitude in Paper 2B is really three skills tested together. Quantitative aptitude: ratio and proportion, percentage, profit and loss, simple and compound interest, averages, mixtures and alligation, time–work, time–speed–distance, and data interpretation from tables, bar and pie charts. Logical reasoning: number and letter series, analogies, coding–decoding, blood relations, direction sense, syllogism, ranking and seating arrangements. Visual reasoning: mirror and water images, paper folding and cutting, embedded figures, figure counting, and pattern completion - the last group carries disproportionate weight for a planning aspirant, so practise sketching rather than only reading.
Traps that repeat every year
Percentage change is not additive: two successive changes of a% and b% give a net change of a + b + ab/100. "By what percent is A more than B" is not the same as "B is less than A" - the base changes. In direction sense, record the facing direction after each turn, not just the net displacement. In syllogism, statements about "possibility" must be judged on whether a valid arrangement exists, not on what is usually true. In clocks, use the angle |30H − 5.5M|; in calendars, count odd days.
Worked example
A trader marks goods 40% above cost and allows a 25% discount. Net change = 40 + (−25) + (40)(−25)/100 = 15 − 10 = 5, i.e. a 5% profit. Rule of thumb: convert every statement to a multiplier on a single base - here 1.4 × 0.75 = 1.05.