Arithmetical & Numerical Ability
Arithmetical and Numerical Ability tests number sense and quick computation: simplification, percentage, ratio and proportion, average, profit and loss, simple and compound interest, time-speed-distance, time and work, and basic mensuration.
Core rules
- Percentage change = (change ÷ original) × 100. Successive changes multiply, not add: a 20% increase followed by a 20% decrease leaves 0.96 of the original, a net 4% decrease.
- A ratio a:b gives parts, not actual values; convert quantities to a common unit before comparing.
- Average = sum ÷ count. For equal distances at speeds x and y, average speed = 2xy/(x+y), not (x+y)/2.
- Time and work: convert days to one-day work (1/n); combined rate is the sum of individual rates.
- SI = PRT/100; CI = P(1+R/100)^T − P. For two years, CI − SI = P(R/100)².
Worked example
A can finish a task in 12 days and B in 18 days. Working together, how long will they take? Reasoning: A's one-day work is 1/12 and B's is 1/18. Combined work = 1/12 + 1/18 = 3/36 + 2/36 = 5/36. Time is the reciprocal, 36/5 = 7.2 days, that is 7 days 4.8 hours. Answer: 7.2 days.
Traps
- Applying a discount and then a tax to the wrong base; identify the original price first.
- Using the arithmetic mean for average speed over equal distances.
- Mixing simple and compound interest formulas, or using months without converting to years.
- Forgetting unit conversions such as cm to m or minutes to hours before computing.