Elementary Mathematics and General Reasoning
Arithmetic: fast, reliable methods
Percentage: successive changes of a% and b% equal a + b + ab/100, with signs. Profit and loss are calculated on cost price unless stated; discount is on marked price. SI = PRT/100; CI = P[(1 + R/100)^T − 1]. In time and work, take the LCM of days as total work; efficiency is inversely proportional to time. For equal distances, average speed = 2xy/(x + y).
Reasoning: pattern types
Number and letter series, coding-decoding, blood relations, direction sense, syllogism, seating arrangement, analogy, odd one out, clock and calendar. In syllogism, draw minimal Venn diagrams; a conclusion is valid only if true in every possible diagram. In direction questions, fix north and trace each turn carefully.
Worked example
Two successive discounts of 20% and 10% on ₹1,000. After 20%: ₹800; after 10%: ₹720. Total discount = ₹280, i.e. 28%. Formula: 20 + 10 − (20 × 10)/100 = 28%.
Traps
Adding successive percentages directly; applying profit percentage on selling price; ignoring equal distances in average speed; treating a possible syllogism conclusion as definite; off-by-one errors in calendar and clock problems.