Mathematics and Mental Ability / Reasoning
Mathematics and Mental Ability/Reasoning tests arithmetic, number series, ratio, percentage, average, time-work, time-speed-distance, coding-decoding, direction sense, blood relations, syllogism and simple logical puzzles. Speed comes from pattern recognition, not long calculation.
Core rules
- Percentage change = (change/original) × 100; successive percentage changes do not simply add.
- Average = sum/count; if a new item raises the average, compare total increase with the number of items.
- Time and work: work rate = 1/time; combine rates by adding.
- Series: check differences, ratios, squares, cubes and alternating patterns.
- Direction sense: draw a rough diagram and track left/right turns from the facing direction.
- Syllogism: use Venn diagrams; do not assume real-world truth beyond the statements.
Worked example
Find the next term: 3, 8, 15, 24, ?. Reasoning: differences are 5, 7, 9; the next difference should be 11; 24 + 11 = 35. Check: terms are n² − 1 for n = 2, 3, 4, 5, so next is 6² − 1 = 35.
Traps
In percentage problems, a 20% increase followed by a 20% decrease is not zero; it is a 4% decrease. In direction questions, turning left after facing south means facing east, not west. In syllogism, some A are B does not prove some B are A unless the statement allows conversion.