Mathematics: Percentages, Ratios, Averages and Basic Algebra
The Mathematics portion tests fast, accurate arithmetic rather than advanced maths: percentages, ratio and proportion, averages, profit and loss, simple interest, unit conversion and one-variable algebra.
Core rules
- BODMAS: brackets, orders, then division and multiplication left to right, then addition and subtraction.
- Percentage change = (change / original) x 100. A raise or discount is always calculated on the original amount.
- A ratio a : b splits a total into (a + b) parts; one part = total / (a + b).
- Average = sum / count, therefore sum = average x count.
- Profit % and loss % are on the cost price unless the question says otherwise.
- In an equation, do the same operation to both sides and collect the variable on one side.
Worked example
A clerk earns Rs 48,000. His pay is raised by 15% and later cut by 15%. Is he back at Rs 48,000?
- Raise: 48,000 x 1.15 = Rs 55,200.
- The cut is taken on the new pay: 55,200 x 0.85 = Rs 46,920. He is Rs 1,080 worse off, because the 15% cut applied to the larger amount.
Second check: Rs 4,500 is shared in the ratio 4 : 5. Total parts = 9, one part = 500, so the shares are Rs 2,000 and Rs 2,500.
Traps that cost marks
- Applying a percentage to the wrong base, such as taking profit % on the selling price.
- Mixing units: 2 hours 30 minutes must become 2.5 hours before dividing.
- Averaging two averages as though the groups were equal in size.
- Dropping a minus sign when moving a term across the equals sign.