Decision Making

In a logic puzzle, all Glorbits are Wumps. Some Wumps are Flargs. Which of the following must be true?

• AAll Flargs are Glorbits
• BNo Glorbits are Flargs
• CAll Glorbits are Flargs
• DSome Glorbits may be Flargs✓

Answer: Since all Glorbits are Wumps and some Wumps are Flargs, it is possible (but not certain) that some Glorbits are Flargs. We cannot say all or none are Flargs.

Five colleagues — Alice, Ben, Cara, Dan, and Eve — are seated in a row. Alice is not at either end. Ben is immediately to the left of Cara. Dan is at the right end. Eve is not next to Alice. Which position is Alice in?

• APosition 2
• BPosition 3✓
• CCannot be determined
• DPosition 4

Answer: Dan is at position 5. Alice is not at the ends, so positions 2-4. Eve is not next to Alice. Working through constraints, Alice must be in position 3.

A committee must choose between three health policies. Policy A saves 400 lives with certainty. Policy B has a 75% chance of saving 600 lives and a 25% chance of saving nobody. Policy C has a 50% chance of saving 900 lives and a 50% chance of saving nobody. Which policy has the highest expected value?

• APolicy A
• BPolicy B
• CPolicy C
• DPolicies B and C are equal✓

Answer: Expected value: Policy A saves 400 with certainty. Policy B: 0.75 x 600 = 450. Policy C: 0.5 x 900 = 450. Both B and C beat A, but they are identical at 450, so neither is better than the other — the correct response is that they are equal.

Maria can complete a report in 4 hours. James can complete the same report in 6 hours. If they work together, how long will it take them to complete the report?

• A2 hours
• B2 hours 30 minutes
• C2 hours 24 minutes✓
• D3 hours

Answer: Combined rate: 1/4 + 1/6 = 3/12 + 2/12 = 5/12 per hour. Time = 12/5 = 2.4 hours = 2 hours 24 minutes.

A patient is prescribed medication A and medication B. Medication A must be taken at least 2 hours before medication B. Medication B must be taken with food. The patient eats at 8am and 6pm. If medication A is taken at 7am, what is the earliest medication B can be taken?

• AAny time after 9am with food
• B8am with breakfast
• C9am
• D6pm with dinner✓

Answer: Medication A at 7am means B cannot be taken until 9am at the earliest. B must also be taken with food, and the meals are at 8am and 6pm. The 8am meal is too early to satisfy the two-hour gap, so the first meal that works is dinner at 6pm.

If it is false that 'all swans are white', which of the following must be true?

• ANo swans are white
• BAt least one swan is not white✓
• CBlack swans exist in all countries
• DMost swans are not white

Answer: If 'all swans are white' is false, then at least one swan must not be white — the logical negation of a universal affirmative is a particular negative.

A diagnostic algorithm categorises patients as high, medium, or low risk. High-risk patients are seen within 24 hours, medium within 72 hours, and low within 2 weeks. A patient classified as medium risk deteriorates significantly before their appointment. What is the most likely systemic issue?

• AThe doctor did not review the patient sooner
• BMedium-risk patients should always be seen within 24 hours
• CThe patient should have attended A&E
• DThe risk classification may not capture dynamic changes in patient condition✓

Answer: The scenario suggests the static classification system failed to account for a patient's worsening condition — a systemic issue with the algorithm's inability to capture dynamic deterioration.

In a Venn diagram, set A contains multiples of 3 up to 30, and set B contains multiples of 4 up to 30. How many numbers are in the intersection?

• A2✓
• B3
• C4
• D5

Answer: Multiples of 12 (LCM of 3 and 4) up to 30: 12, 24. That gives 2 numbers in the intersection.

A survey of 200 patients shows 120 are satisfied with their care, 50 are neutral, and 30 are dissatisfied. What is the ratio of satisfied to dissatisfied patients?

• A5:1
• B4:1✓
• C6:1
• D3:1

Answer: Satisfied:Dissatisfied = 120:30 = 4:1.

Three friends split a restaurant bill. Alice pays £24, Ben pays £18, and Cara pays £12. They want to equalise payments. How much should Cara pay Alice?

• A£6✓
• B£8
• C£2
• D£4

Answer: The bill is 24 + 18 + 12 = 54 pounds, so an equal share is 18 pounds each. Alice paid 24, which is 6 over her share; Cara paid 12, which is 6 under. Ben paid exactly 18 and so neither owes nor is owed. Cara therefore pays Alice 6 pounds.

A nurse must administer medication to 8 patients in a specific order. The first patient must receive medication before the third. The fourth must be before the second. The sixth must be last. How many constraints are given?

• A2
• B3✓
• C4
• D5

Answer: Three constraints are given: patient 1 before patient 3; patient 4 before patient 2; patient 6 is last.

A researcher wants to determine whether a new surgical technique reduces complications. Which study design would provide the strongest evidence?

• ACross-sectional survey
• BExpert opinion
• CCase report
• DRandomised controlled trial✓

Answer: Randomised controlled trials are the gold standard for establishing causation and evaluating the effectiveness of interventions, providing the strongest evidence level.

A bag contains 5 red balls, 3 blue balls, and 2 green balls. One ball is drawn at random. What is the probability it is not red?

• A0.3
• B0.4
• C0.5✓
• D0.6

Answer: Non-red balls: 3 + 2 = 5. Total: 10. P(not red) = 5/10 = 0.5.

'Every patient who presents with chest pain and elevated troponin is having a myocardial infarction.' A patient has elevated troponin due to myocarditis. Which type of reasoning error does the original statement represent?

• ACircular reasoning
• BHasty generalisation✓
• CFalse dichotomy
• DPost hoc reasoning

Answer: The statement incorrectly generalises that all chest pain + elevated troponin cases are MIs, ignoring other causes like myocarditis. This is a hasty generalisation.

A sequence of shapes follows a specific rule: Circle, Triangle, Square, Circle, Triangle, Square... What is the 17th shape in the sequence?

• APentagon
• BSquare
• CCircle
• DTriangle✓

Answer: The pattern Circle, Triangle, Square repeats every 3 shapes. 17 ÷ 3 = 5 remainder 2, so the 17th shape is the 2nd in the cycle: Triangle.

All members of the surgical team are doctors. Some doctors are researchers. Which of the following must be true?

• ASome members of the surgical team are researchers
• BSome members of the surgical team may be researchers✓
• CNo members of the surgical team are researchers
• DAll researchers are members of the surgical team

Answer: From 'all surgical team are doctors' and 'some doctors are researchers' we cannot conclude any are or are not researchers; only that some may be. that statement must be true.

A bag contains 4 red, 3 blue and 5 green counters. If one counter is drawn at random, what is the probability it is NOT green?

• A1/2
• B5/12
• C7/12✓
• D3/12

Answer: There are 12 counters; 5 are green, so 7 are not green. P(not green) = 7/12.

Four friends - Anya, Ben, Cara and Dev - sit in a row. Anya is not at either end. Ben sits immediately to the left of Cara. Dev sits at the far right. Which arrangement (left to right) is possible?

• ABen, Anya, Cara, Dev
• BAnya, Ben, Cara, Dev
• CCara, Ben, Anya, Dev
• DBen, Cara, Anya, Dev✓

Answer: Dev is far right, so C is out. Anya cannot be at an end, ruling out B. Ben must be immediately left of Cara, which holds in D (Ben, Cara) but not A (Anya between them). D satisfies all constraints.

If the statement 'No patients in Ward A have been discharged' is true, which of the following must also be true?

• AWard A has no patients
• BAll patients in the hospital are in Ward A
• CSome patients in Ward A have been discharged
• DEvery patient in Ward A is still admitted✓

Answer: If no Ward A patient has been discharged, then every Ward A patient remains admitted. B must be true; A directly contradicts the premise.

A clinic offers a test that is 90% accurate. If a condition affects 1 in 100 people, which statement best reflects sound reasoning about a single positive result?

• ABecause the condition is rare, many positives may be false positives✓
• BA positive result means the person almost certainly has the condition
• CThe person definitely does not have the condition
• DThe test is useless

Answer: With a rare condition, even an accurate test yields many false positives relative to true positives, so a single positive is far from certain. B reflects correct probabilistic reasoning.

Consider the relationship: all cardiologists are physicians; no physicians are surgeons. Which conclusion follows?

• ASome cardiologists are surgeons
• BSome surgeons are cardiologists
• CNo cardiologists are surgeons✓
• DAll surgeons are physicians

Answer: Cardiologists are a subset of physicians, and no physicians are surgeons, so no cardiologists can be surgeons. B follows.

A rota requires that whenever Dr Patel works, Dr Quinn does not, and whenever Dr Quinn works, Dr Rao works. If Dr Rao is NOT working today, what can be concluded?

• ADr Quinn is working
• BDr Quinn is not working✓
• CDr Patel is not working
• DBoth Patel and Quinn are working

Answer: If Quinn worked, Rao would work. Rao is not working, so Quinn is not working. B follows. Nothing forces a conclusion about Patel.

Which of the following best describes 'deductive reasoning'?

• AUpdating beliefs based on new evidence
• BReaching a specific conclusion that must be true if the premises are true✓
• CMaking an educated guess about what is likely to happen, based on past experience
• DDrawing broad general conclusions from a small number of specific observed examples

Answer: Deductive reasoning moves from general premises to a specific, logically necessary conclusion. If the premises are true and the argument is valid, the conclusion must be true.

A doctor wants to test whether a new drug lowers blood pressure more than the existing standard drug. She randomly assigns 100 patients to each group. What type of study is this?

• ACohort study
• BRandomised controlled trial✓
• CCase-control study
• DCross-sectional study

Answer: Random assignment to two treatment groups to compare outcomes is the defining feature of a randomised controlled trial.

A medication costs 12 pounds for 20 tablets and is sold only in whole packs. A patient needs 3 tablets per day for 30 days. What is the minimum cost to cover the full course?

• A60 pounds✓
• B36 pounds
• C54 pounds
• D48 pounds

Answer: The course needs 90 tablets. Packs of 20 mean 5 packs (100 tablets) are required, costing 5 x 12 = 60 pounds.

'Correlation does not imply causation.' A study finds a strong positive correlation between ice cream sales and drowning rates. Which of the following best explains this finding?

• AThe study is methodologically flawed
• BDrowning incidents cause an increase in ice cream consumption
• CA confounding variable (hot weather) drives both✓
• DEating ice cream directly causes people to drown while swimming

Answer: Hot weather causes both increased ice cream sales and more swimming (leading to more drownings). This is a classic example of a confounding variable creating a spurious correlation.

'The Hawthorne effect refers to individuals modifying their behaviour when they know they are being observed.' A clinical audit shows improved hand hygiene rates during the audit period compared to routine monitoring. What might explain this finding?

• AHand hygiene actually improved permanently because of an education programme on the ward
• BStaff may have changed their behaviour because they knew they were being observed✓
• CHand hygiene rates are naturally higher during the winter months than at any other time
• DThe audit methodology was seriously flawed and produced results that cannot be relied upon

Answer: The Hawthorne effect explains the audit finding — staff awareness of observation during the audit period may have temporarily improved compliance.