Percentages & Proportions in Data — Practice

Practice bank for UCAT Decision Making questions involving percentage calculations, proportions, and ratio reasoning.

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Quick-Reference: Percentage Formulas

Basic Percentage

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

Percentage Change

$\text{Percentage change} = \frac{\text{New value} - \text{Old value}}{\text{Old value}} \times 100$Percentage change=Old valueNew value−Old value​×100

• Positive result = increase
• Negative result = decrease

Reverse Percentage (Finding the Original)

If a value increased by 20%, the new value = 1.20 × original.

$\text{Original} = \frac{\text{New value}}{1 + \text{percentage increase as decimal}}$Original=1+percentage increase as decimalNew value​

Successive Percentage Changes

Two successive changes of +a% and +b% are NOT the same as +(a+b)%.

$\text{Overall multiplier} = (1 + a/100) \times (1 + b/100)$Overall multiplier=(1+a/100)×(1+b/100)

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Quick-Reference: Proportions and Ratios

Ratio to Fraction

A ratio of 3:2 means 3 parts and 2 parts = 5 parts total.

• First quantity = 3/5 of the total
• Second quantity = 2/5 of the total

Scaling Ratios

To compare ratios, convert to a common base or to fractions/decimals.

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Common Pitfalls