Quantitative Aptitude and Logical Reasoning
What this domain tests
This section tests percentages, ratio, averages, profit and loss, interest, time-speed-distance, mensuration, data interpretation, series, coding, blood relations, syllogism, and seating. Excise-themed mixtures and dilution are common.
Core rules
- Percentage change = (change ÷ original) × 100. Successive changes multiply: a 40% rise then a 25% fall gives 1.40 × 0.75 = 1.05, a 5% net rise.
- In dilution, track the pure component, which does not change when water is added.
- Average speed for equal distances is the harmonic mean, not the arithmetic average.
- Syllogism: a conclusion follows only if it is true in every possible diagram. 'Some A are B' does not imply 'some B are A' unless the premise is read as convertible; standard categorical logic treats 'some' as symmetric, but 'all' is not.
Worked example
60 litres of a spirit solution is 80% alcohol. How much water must be added to make it 40% alcohol? Pure alcohol = 60 × 0.80 = 48 L. At 40%, total solution = 48 ÷ 0.40 = 120 L. Water to add = 120 − 60 = 60 L. The trap is taking 40% of the original 60 L instead of fixing the alcohol quantity.
Traps that cost marks
- Confusing percentage points with percent.
- Adding successive discounts instead of multiplying.
- Using arithmetic average for average speed.
- Treating a possible conclusion as a definite one in syllogism.
Exam focus
Write the unchanged quantity first; it usually unlocks ratio and mixture problems.