Percentages appear again and again in UCAT Quantitative Reasoning. If you can handle them confidently, you remove a major source of hesitation.
The simplest type is finding a percentage of an amount.
To find 20% of 150, you can calculate 0.20 × 150.
But mental methods can sometimes be quicker. Ten per cent of 150 is 15, so twenty per cent is 30.
Percentage increase and decrease questions are also common.
If a price rises by 15%, the new price is 115% of the original. You can multiply by 1.15.
If it falls by 15%, the new price is 85% of the original. Multiply by 0.85.
Reverse percentages are a common trap because students apply the percentage in the wrong direction.
If an item costs £80 after a 20% discount, £80 represents 80% of the original price. To find the original, divide by 0.80.
Another important idea is percentage change:
change ÷ original × 100
Students often divide by the final value by mistake. The denominator should be the original amount.
The fastest method depends on the numbers. Sometimes mental maths is best. Sometimes the calculator is quicker.
Do not force one method every time.
Practise until you can recognise whether the question is asking for:
- a percentage of an amount
- a percentage increase
- a percentage decrease
- a reverse percentage
- a percentage change
Once you can identify the type immediately, the calculation becomes much faster.
