Percentages and Percentage Change

Percentage questions are the most frequently tested topic in the UCAT Quantitative Reasoning subtest. This lesson covers every type of percentage calculation you might encounter, with worked examples using the kind of data presentations you will see on test day.

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Finding a Percentage of a Number

The most basic percentage calculation: finding X% of Y.

Formula: X% of Y = (X / 100) × Y

Mental shortcut: Use the 10%, 5%, 1% building-block method from Lesson 2.

Worked Example

Data: A hospital has 1,400 staff members. 35% are nurses.

Question: How many nurses work at the hospital?

Solution:

• 10% of 1,400 = 140
• 30% = 3 × 140 = 420
• 5% = 140 ÷ 2 = 70
• 35% = 420 + 70 = 490 nurses

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Expressing One Number as a Percentage of Another

Formula: (Part / Whole) × 100

Worked Example

Data:

Department	Staff
Cardiology	84
Neurology	56
Oncology	70
Paediatrics	42
Total	252

Question: What percentage of total staff work in Neurology?