Decision Making Flashcards

A logic puzzle: If A is true, B is false. If B is false, C is true. A is true. What is C?

Answer: True

A is true → B is false → C is true. The chain of conditionals resolves fully.

A map shows 3 routes from X to Y. Route 1: 60 km at 60 km/h. Route 2: 80 km at 80 km/h. Route 3: 90 km at 60 km/h. Which is fastest?

Answer: Routes 1 and 2 are equally fast

Time = distance/speed. Route 1: 60/60 = 1h. Route 2: 80/80 = 1h. Route 3: 90/60 = 1.5h. Routes 1 and 2 both take 1 hour.

A company's profit increased by 25% in Year 1 and decreased by 20% in Year 2 from the Year 1 figure. Compared to the start, profit is:

Answer: The same as the original

If start = 100: after +25% → 125. After −20% of 125 → 125 × 0.8 = 100. Back to original.

Four statements about a number N: (1) N is even. (2) N is divisible by 5. (3) N > 20. (4) N < 30. Which number satisfies all four?

Answer: 30 is excluded; the answer is that no number in range works — wait: N=25 is odd. N=20: 20 is even, divisible by 5, but not > 20. So no number satisfies all four.

Even numbers divisible by 5 between 20 and 30 (exclusive): candidates are 10, 20, 30. 20 is not >20; 30 is not <30. There is no such number — this tests recognising when no solution exists.

In a population, disease prevalence is 1%. A test has 95% sensitivity and 90% specificity. What is the approximate positive predictive value?

Answer: About 9%

Using 10,000 people: 100 diseased, 9,900 not. True positives = 95. False positives = 990. PPV = 95/(95+990) ≈ 8.8% ≈ 9%. Low prevalence causes low PPV even with a good test.

A decision matrix: Option A gives £500 if condition X occurs (P=0.6) and £100 if not. Option B gives £400 regardless. What is the expected value of A?

Answer: £340

E(A) = 0.6×500 + 0.4×100 = 300 + 40 = £340. Option B gives £400 with certainty, making B higher in expected value.