UCAT Decision Making 4 — Questions and Answers
Question 1: A Venn diagram shows: Group X only = 8, Group Y only = 12, Both = 5, Neither = 3. How many people are in the survey?
- 28 (Correct answer)
- 25
- 23
- 30
Correct answer: 28
Total = 8 + 12 + 5 + 3 = 28.
Question 2: 'Either the project finishes on time or we lose the contract. The project finished on time.' What follows?
- The contract is not necessarily saved — other conditions may apply (Correct answer)
- We definitely keep the contract
- We lost the contract
- The project will be profitable
Correct answer: The contract is not necessarily saved — other conditions may apply
The 'either…or' is stated as a sufficient condition for one outcome, but we are not told it is the only condition for keeping the contract. We cannot conclude with certainty.
Question 3: If P → Q and Q → R, and P is true, what is true?
- R is true (Correct answer)
- R may be true
- Q is false
- P implies not-R
Correct answer: R is true
Hypothetical syllogism: P → Q, Q → R, P is true → Q is true → R is true. This is a transitive chain.
Question 4: A car depreciates by 20% per year. It costs £25,000 new. What is it worth after 2 years?
- £16,000 (Correct answer)
- £15,000
- £17,500
- £18,000
Correct answer: £16,000
After year 1: £25,000 × 0.8 = £20,000. After year 2: £20,000 × 0.8 = £16,000. Compound depreciation, not simple.
Question 5: A scheduling puzzle: A must happen before B. C must happen before A. D must happen after B. What is a valid order?
- C, A, B, D (Correct answer)
- A, C, B, D
- B, A, C, D
- D, B, A, C
Correct answer: C, A, B, D
Constraints: C < A < B < D. Only C, A, B, D satisfies all three ordering rules.
Question 6: In a group of 100 patients, 60 were given a treatment. Of those, 45 improved. Of the 40 untreated, 20 improved. What is the relative risk of improvement with treatment?
- 1.5 (Correct answer)
- 0.75
- 2.25
- 1.125
Correct answer: 1.5
Risk with treatment = 45/60 = 0.75. Risk without = 20/40 = 0.5. Relative risk = 0.75/0.5 = 1.5.
UCAT Decision Making 4
A Venn diagram shows: Group X only = 8, Group Y only = 12, Both = 5, Neither = 3.
How many people are in the survey?