Engineering aptitude, reasoning, and quantitative ability
Engineering aptitude, reasoning, and quantitative ability tests numerical fluency and logical structure rather than advanced mathematics. Typical areas are arithmetic (percentage, ratio, average, time-speed-distance, interest), algebra, geometry and mensuration, data interpretation, series, coding-decoding, blood relations, direction sense, syllogism, and non-verbal reasoning.
Core rules and concepts
- Percentage change: successive changes multiply, not add. A 20% increase followed by a 20% decrease gives 0.96 of the original, a 4% net decrease.
- Average speed for equal distances is the harmonic mean: 2xy/(x + y), not (x + y)/2.
- Time and work: if A does a job in a days and B in b days, together they take ab/(a + b) days.
- Ratio and proportion: set up a common unit; keep the same base for comparison.
- Series: check differences, ratios, squares, cubes, and alternating patterns.
- Syllogism: valid conclusions must follow from all premises; a possible conclusion is not a definite one.
Worked example
A train covers 120 km at 60 km/h and returns at 40 km/h. Average speed is not 50 km/h. Total distance = 240 km; total time = 120/60 + 120/40 = 2 + 3 = 5 h; average speed = 240/5 = 48 km/h. The harmonic mean 2(60)(40)/(100) = 48 confirms it.
Traps
Adding percentage changes directly; using the arithmetic mean for average speed over equal distances; ignoring units (km/h versus m/s); and treating 'some A are B' as 'all A are B'. In data interpretation, read the axis scale and the year labels before calculating.