General Aptitude - Quantitative Aptitude and Numerical Ability
High-yield blocks
Percentages, profit and loss, simple and compound interest; ratio, proportion and alligation; time and work with pipes and cisterns; time–speed–distance including trains and boats; averages and ages; number system, HCF/LCM and divisibility; mensuration and data interpretation (tables, bar and pie charts). The paper favours one- or two-step arithmetic over long multi-stage puzzles, so shortcut fluency matters more than exhaustive theory.
Shortcuts that are safe
- Successive percentage changes of a% then b% net to a + b + ab/100.
- Difference between CI and SI for 2 years = P(r/100)².
- Alligation: ratio of quantities = (mean − cheaper) : (dearer − mean).
- If A is x% more than B, then B is 100x/(100 + x)% less than A - the percentages are not symmetric.
- Divisibility: by 3 or 9 via digit sum, by 11 via alternating digit sum, by 8 via the last three digits.
Worked example
A finishes a job in 12 days, B in 18 days; together with C they finish in 6 days. How long for C alone? Take total work = 36 units (LCM of 12, 18 and 6). A does 36/12 = 3 units/day, B does 2 units/day, and all three do 36/6 = 6 units/day. So C does 6 − 5 = 1 unit/day and needs 36/1 = 36 days alone. The unit method avoids fraction slips in the middle.
Traps that cost marks
- Averaging two speeds arithmetically; average speed is total distance divided by total time.
- Adding successive discounts instead of compounding them (20% then 10% is 28%, not 30%).
- Confusing 'percent' with 'percentage points' - 20% to 25% is 5 percentage points but a 25% rise.
- Reading a pie-chart slice as a raw count rather than a proportion of the whole.
- Forgetting that work rates add while times do not.