You are viewing a free preview of this lesson.
Subscribe to unlock all 10 lessons in this course and every other course on LearningBro.
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.
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 |
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% |
These are very different numbers. A "15 percentage-point increase" and a "25% increase" describe the same change but in different ways.
UCAT Tip: Read the question carefully. "Increased by what percentage?" asks for the percentage change (25%). "By how many percentage points did it increase?" asks for the absolute difference (15).
"80% of students passed the exam. Of those who passed, 30% achieved a distinction. What percentage of all students achieved a distinction?"
Calculation: 80% × 30% = 0.80 × 0.30 = 0.24 = 24%
The trap: some candidates answer 30%, forgetting that the 30% applies only to the subset who passed, not to all students.
In a hospital, 40% of staff are nurses. Of the nurses, 25% are male. What percentage of all hospital staff are male nurses?
0.40×0.25=0.10=10%
Key Rule: When "X% of Y%" is described, multiply the two percentages (as decimals) to get the overall percentage.
"A hospital's budget increased by 20% in Year 1 and then decreased by 20% in Year 2. Is the budget back to its original level?"
No. Let the original budget be £100.
The budget is now £96, which is 4% less than the original. A 20% increase followed by a 20% decrease does NOT return to the starting value.
General Rule: Successive percentage changes do not cancel out. A% increase followed by A% decrease always results in a net loss (specifically, a loss of A²/100 percent of the original).
| Increase | Then Decrease | Net Effect |
|---|---|---|
| +10% | −10% | −1% |
| +20% | −20% | −4% |
| +50% | −50% | −25% |
Subscribe to continue reading
Get full access to this lesson and all 10 lessons in this course.