Arithmetic and Numerical Ability
What this domain tests
Number system, HCF and LCM, ratio and proportion, percentage, average, profit and loss, simple and compound interest, time and work, time–speed–distance, basic mensuration and data interpretation. Speed matters, so standard results should be recalled rather than derived.
Standard results
- Successive discounts of a% and b% equal a + b − ab/100 per cent.
- For two years, compound interest minus simple interest equals P(r/100)².
- If A alone takes x days and B alone y days, together they take xy/(x + y) days.
- Weighted average, not the simple mean of means, applies when group sizes differ.
Worked example
A finishes a job in 12 days and B in 18 days. Working together, how long? Take the LCM of 12 and 18 as 36 units of work. A does 3 units a day, B does 2, so together 5 units a day. Time = 36/5 = 7.2 days, i.e. 7 days and 4.8 hours (4 hours 48 minutes).
Traps that cost marks
- A rise of 20% followed by a fall of 20% leaves 96, not 100.
- Discount is calculated on marked price; profit percentage is calculated on cost price.
- Compound interest is not double the simple interest for two years; use the formula.
- Percentage points and per cent are different: 5% to 7% is a 2 percentage-point rise but a 40% increase.
- In time–speed problems with two legs, average speed is total distance over total time, never the mean of the two speeds.