UCAT Decision Making Practice — Questions and Answers
Question 1: All qualified paramedics on the ambulance rota have completed advanced trauma training. Zara has completed advanced trauma training. Which conclusion follows logically?
- Zara is a qualified paramedic on the rota
- Zara might or might not be a qualified paramedic on the rota (Correct answer)
- Zara is definitely not a paramedic
- Zara completed the training before joining the rota
Correct answer: Zara might or might not be a qualified paramedic on the rota
The premise only says paramedics have the training, not that everyone with the training is a paramedic (affirming the consequent), so we cannot conclude Zara is one - only that it's possible.
This is a classic syllogism trap: 'All paramedics have trauma training' establishes training as a necessary condition for being a paramedic, not a sufficient one. Having the training (Zara's situation) does not logically guarantee paramedic status, since other roles (e.g. nurses, first responders) could also require that same training. The only logically valid conclusion is that her paramedic status remains undetermined.
Question 2: A hospital reports that 70% of patients who receive Treatment X recover within a week, and 90% of patients who receive Treatment Y recover within a week. A patient recovered within a week. Which is the strongest valid conclusion?
- The patient definitely received Treatment Y
- The patient more likely received Treatment Y than Treatment X, if treatments were assigned equally often
- The patient definitely received Treatment X
- No conclusion can be drawn about which treatment was used (Correct answer)
Correct answer: No conclusion can be drawn about which treatment was used
Without knowing how many patients received each treatment overall (the base rates), we cannot determine the probability of which treatment a recovered patient received - this requires Bayesian reasoning with base rates, which are not given.
This tests recognition of missing information for a Bayesian inference. Recovery rates alone (70% vs 90%) describe P(recovery | treatment), not P(treatment | recovery). To find which treatment a recovered patient more likely received, we would also need the proportion of patients given each treatment (the base rates / priors). Since those are not provided, no valid probabilistic conclusion can be drawn, even though option B sounds plausible - it requires an unstated assumption of equal assignment which is not given as fact.
Question 3: A hiring manager states: 'Every strong candidate we've shortlisted this year has at least two years of clinical experience.' Ben has three years of clinical experience but was not shortlisted. What is the most logical explanation consistent with the manager's statement?
- The manager's statement is false
- Having two years of experience alone does not guarantee being shortlisted as strong (Correct answer)
- Ben must have lied about his experience
- All candidates with experience are shortlisted
Correct answer: Having two years of experience alone does not guarantee being shortlisted as strong
The statement only says shortlisted candidates have experience (necessary condition), not that all experienced people are shortlisted (which would be a false converse). Ben not being shortlisted is fully consistent with this.
This is another necessary-vs-sufficient condition item. 'Every strong candidate has X' means X is required for the shortlist, but plenty of other factors (interview performance, reference checks, fit) could still exclude someone who has X. There is no contradiction between the manager's statement and Ben's exclusion, so no logical fault or lie needs to be assumed.
Question 4: In a bag there are 4 red, 3 blue, and 3 green tokens. One token is drawn at random and not replaced, then a second token is drawn. What is the probability that both tokens are red?
- 4/10 x 4/10 = 16/100
- 4/10 x 3/9 = 12/90 (Correct answer)
- 3/10 x 3/9 = 9/90
- 4/10 x 3/10 = 12/100
Correct answer: 4/10 x 3/9 = 12/90
P(first red) = 4/10. After removing one red token without replacement, P(second red) = 3/9. Multiply: 4/10 x 3/9 = 12/90 = 2/15.
This is a sequential dependent-probability question, common in UCAT Decision Making. The first draw has probability 4/10 of being red (4 red out of 10 total). Since the token is not replaced, only 9 tokens remain, of which 3 are red (one red was removed), giving 3/9 for the second draw. Multiplying dependent probabilities: 4/10 x 3/9 = 12/90, which simplifies to 2/15.
Question 5: Statement: 'Either the ward is understaffed, or the discharge process is delayed - possibly both.' It is confirmed the discharge process is NOT delayed. What must be true?
- The ward is understaffed (Correct answer)
- The ward is not understaffed
- Nothing can be determined
- Both conditions are false
Correct answer: The ward is understaffed
This is an inclusive 'or' (possibly both), so if one disjunct (delayed discharge) is false, the other disjunct (understaffed ward) must be true for the original statement to hold.
Logical disjunction (A OR B, inclusive) is false only when both A and B are false. We are told B (delayed discharge) is false. For the compound statement to remain true, A (understaffed ward) must be true. This is a standard disjunctive syllogism, a common Decision Making format testing formal logic under real-world phrasing.
Question 6: A clinic wants to reduce missed appointments. Option A: send SMS reminders (historically reduces no-shows by 25%, costs low). Option B: charge a small deposit (historically reduces no-shows by 40%, costs administrative overhead and may deter low-income patients). Which conclusion is best supported by weighing these trade-offs alone?
- Option A is always better because it is cheaper
- Option B is strictly superior in every situation
- Option B reduces no-shows more but carries an equity trade-off that must be weighed against the goal (Correct answer)
- Neither option has any effect on no-shows
Correct answer: Option B reduces no-shows more but carries an equity trade-off that must be weighed against the goal
Weighing conflicting factors (effectiveness vs. equity/cost) rather than picking an absolute winner reflects correct UCAT-style balanced judgement - neither option is 'always' or 'strictly' better once side effects are considered.
Decision Making often tests balanced evaluative reasoning rather than pure logic. Both extreme options (A 'always' better, B 'strictly superior') ignore stated trade-offs. The correct answer recognises Option B's superior raw effectiveness (40% vs 25%) while acknowledging its explicitly stated downside (equity concerns, overhead), which is the most defensible, non-absolute conclusion given the information.
UCAT Decision Making Practice
All qualified paramedics on the ambulance rota have completed advanced trauma training.
Zara has completed advanced trauma training.
Which conclusion follows logically?