Mathematics and Reasoning
Mathematics and Reasoning rewards method: most questions are one-step percentage, ratio, average, interest or series problems, plus standard reasoning patterns.
Arithmetic rules
- Profit percentage is calculated on cost price unless stated; loss likewise.
- SI = PRT/100; CI = P(1 + r)^n - P; for two years, CI exceeds SI by P(r/100)^2.
- Time and work: convert days into rates, then add rates for workers together.
- Successive percentage changes multiply factors: +20% then -20% gives 0.96, a 4% fall.
Reasoning patterns
- Number series: check differences first, then ratios, then squares and cubes.
- Coding: compare letter positions; direction sense: draw the path and fix north.
- Blood relations: draw a family tree and mark gender.
- Syllogism: test the conclusion against every possible diagram; it is valid only if true in all of them.
Worked example
An article bought for Rs 800 is sold for Rs 920. Profit = 120, so percentage = 120/800 x 100 = 15%. If instead the selling price Rs 920 and 15% profit are given and cost price is asked, divide: 920/1.15 = Rs 800. Never compute profit percentage on selling price.
Traps
Applying profit percentage to SP; adding successive percentages directly; ignoring the new direction after a turn; treating a 'some' statement as 'all' in syllogisms.