Percentages & Proportions in Data — Practice

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

---

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)

---

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.

---

Common Pitfalls

• Calculating percentage change using the wrong base (new vs old)
• Adding successive percentage changes instead of multiplying multipliers
• Confusing "percentage points" with "percent" (a change from 10% to 15% is 5 percentage points, but a 50% increase)

---

Strategy

• Read carefully: "percentage of what?" — identify the denominator
• Use multipliers for successive changes
• Target: 30–45 seconds (these should be quick)

---

Practice

Complete the 10 assessment questions.