Arithmetic and Reasoning
What this domain tests
Arithmetic tests number sense and speed: percentage, ratio and proportion, average, profit and loss, simple and compound interest, time and work, speed and distance, and basic mensuration. Reasoning tests pattern recognition: series, analogy, coding–decoding, blood relations, directions, syllogism, seating arrangement, and clock or calendar problems. The aim is accuracy under a short per-question time.
Core rules and concepts
- Successive percentage changes multiply; never add them.
- For time and work, use rates: A's one-day work = 1/a; combine rates, then invert for total time.
- In direction questions, draw axes and track left and right turns from the facing direction.
- In syllogism, test conclusions against a Venn diagram; some A are B does not mean all B are A.
- In blood relations, draw a family tree and mark gender symbols explicitly.
Worked example
Question: A number is increased by 20% and then decreased by 20%. What is the net change? Reasoning: Let the number be 100. A 20% increase gives 120. The next 20% decrease is calculated on 120, not on 100: 120 × 0.80 = 96. The net change is 100 − 96 = 4, i.e. a 4% decrease. The two percentages do not cancel because the second is taken on a larger base. Answer: 4% decrease.
Traps that cost marks
Do not apply a percentage to the original value when the question says on the new value. Average speed is total distance divided by total time, not the average of two speeds. In syllogism, do not convert some into all. In seating puzzles, fix one person first and test each clue; avoid redrawing from scratch.