Mathematics and Reasoning
What the domain tests
Mathematics and Reasoning tests arithmetic speed and logical pattern recognition. Expect percentage, ratio, average, profit and loss, simple interest, time-work, speed-distance, number series, coding-decoding, blood relations, direction sense, syllogism and non-verbal series.
Core rules and concepts
- Percentage: always identify the base. Profit percent is calculated on cost price unless the question says otherwise.
- Ratio: convert to a common unit before comparing; use the unitary method for proportional parts.
- Average: sum of observations divided by number of observations.
- Series: check differences, squares, cubes, primes and alternating patterns.
- Direction: draw a quick compass; turn left or right from the facing direction, not from north.
- Syllogism: test only the given statements; do not use real-world knowledge.
Worked example
An article costs ₹400 and sells for ₹500. Find profit percent. Profit = 500 − 400 = ₹100. Profit percent = (100/400) × 100 = 25%. A common error is dividing by selling price, which gives 20% and is wrong because profit percent is on cost price.
Traps that cost marks
- Calculating profit percent on SP instead of CP.
- Averaging speeds directly when times are unequal.
- Ignoring BODMAS in simplification.
- In blood relations, forgetting that a maternal uncle is the mother's brother.
- In series, stopping at the first pattern without checking the next term.
Practice method
Solve 20 mixed arithmetic and 20 reasoning questions in a timed set, then review every wrong answer for the rule missed.