Percentages and Proportions in Context

Percentage and proportion questions in the UCAT DM subtest are less about raw calculation and more about understanding what the numbers mean in context. The test designers build in common traps — percentage of a percentage, confusion between percentage change and percentage point change, and base rate errors. This lesson equips you to avoid every one of them.

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Percentage Basics: A Quick Review

$\text{Percentage} = \frac{\text{Part}}{\text{Whole}} \times 100$Percentage=WholePart​×100

Calculation	Formula
Finding a percentage of a number	(percentage / 100) × number
Finding what percentage A is of B	(A / B) × 100
Percentage increase	((new − old) / old) × 100
Percentage decrease	((old − new) / old) × 100

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Trap 1: Percentage Change vs Percentage Point Change

This is the single most common percentage trap in the UCAT.

"The pass rate increased from 60% to 75%."

Measure	Calculation	Answer
Percentage point change	75% − 60%	15 percentage points
Percentage change	(75 − 60) / 60 × 100	25%