Paper I - Mathematical Reasoning and Aptitude
Mathematical Reasoning and Aptitude tests quantitative fluency under time: number series, percentages, ratio and proportion, averages, profit and loss, simple and compound interest, time-work, speed-distance, and basic algebra and geometry.
Rules to apply
- Percentage change = (new minus old) divided by old, times 100; successive changes multiply, they do not add.
- Average speed for equal distances = total distance divided by total time, not the mean of the speeds.
- Ratio a:b means a divided by b; to divide N in ratio a:b, the shares are Na/(a+b) and Nb/(a+b).
- Profit percentage and loss percentage are conventionally on cost price unless stated otherwise.
- Work rates add: if A finishes in a days and B in b days, together they do 1/a + 1/b per day.
Worked example
A train covers 120 km at 60 km/h and returns at 40 km/h. Time = 2 h + 3 h = 5 h; total distance = 240 km; average speed = 240/5 = 48 km/h. The trap answer 50 km/h is the arithmetic mean of 60 and 40, which is wrong because the times differ.
Traps that cost marks
Adding successive percentage discounts (10% plus 10% is 19% off, not 20%); using selling price as the profit base; mixing minutes and hours; rounding too early.