UCAT Decision Making 3 — Questions and Answers
Question 1: A spinner has 8 equal sections numbered 1–8. What is the probability of spinning an odd number greater than 3?
- 1/4 (Correct answer)
- 3/8
- 1/2
- 1/8
Correct answer: 1/4
Odd numbers greater than 3: 5, 7 — two outcomes. Probability = 2/8 = 1/4.
Question 2: 'Some athletes are vegetarian. All vegetarians avoid red meat.' Which conclusion is valid?
- Some athletes avoid red meat (Correct answer)
- All athletes avoid red meat
- No athletes eat red meat
- All vegetarians are athletes
Correct answer: Some athletes avoid red meat
The overlap between athletes and vegetarians means some athletes (those who are vegetarian) also avoid red meat. 'All' and 'No' are too strong given 'some'.
Question 3: A table shows sales data. Year 1: £120k, Year 2: £150k, Year 3: £180k. What is the percentage increase from Year 1 to Year 3?
- 50% (Correct answer)
- 60%
- 30%
- 45%
Correct answer: 50%
Increase = £180k − £120k = £60k. Percentage = (60/120) × 100 = 50%.
Question 4: Two dice are rolled. What is the probability both show a 6?
- 1/36 (Correct answer)
- 1/6
- 1/12
- 2/36
Correct answer: 1/36
P(6 on die 1) × P(6 on die 2) = 1/6 × 1/6 = 1/36. Independent events multiply.
Question 5: A logical argument: 'All managers approve budgets. James does not approve budgets.' What follows?
- James is not a manager (Correct answer)
- James is a bad manager
- James manages a small team
- All budget approvers are managers
Correct answer: James is not a manager
Modus tollens: if all managers approve budgets (M→B), and James does not approve budgets (¬B), then James is not a manager (¬M).
Question 6: A hospital has 3 wards. Ward A has 40 patients, Ward B has 35, Ward C has 25. A random patient is selected. What is the probability they are from Ward B?
- 35/100 (Correct answer)
- 35/75
- 7/20
- 1/3
Correct answer: 35/100
Total patients = 100. P(Ward B) = 35/100 = 7/20. Both 35/100 and 7/20 are equivalent; 35/100 is the direct calculation.
UCAT Decision Making 3
A spinner has 8 equal sections numbered 1–8.
What is the probability of spinning an odd number greater than 3?