UCAT Decision Making 2 — Questions and Answers
Question 1: A statement says: 'If it rains, the match is cancelled. The match was not cancelled.' What can be concluded?
- It did not rain (Correct answer)
- It rained
- The match was rescheduled
- Rain is unlikely tomorrow
Correct answer: It did not rain
This is modus tollens: if P → Q, and ¬Q, then ¬P. The match not being cancelled means it did not rain.
Question 2: A pie chart shows: Category A = 30%, B = 45%, C = 25%. If total value = £2,000, what is the value of B minus A?
- £300 (Correct answer)
- £150
- £600
- £450
Correct answer: £300
B = 45% × £2,000 = £900. A = 30% × £2,000 = £600. B − A = £900 − £600 = £300.
Question 3: In a class, 12 students study French, 15 study Spanish, and 5 study both. How many study at least one language?
- 22 (Correct answer)
- 32
- 17
- 27
Correct answer: 22
At least one = 12 + 15 − 5 = 22. Inclusion-exclusion removes the double count.
Question 4: A logical puzzle: P is taller than Q. R is shorter than P. S is taller than R but shorter than Q. Who is second tallest?
- Q
- P (Correct answer)
- R
- S
Correct answer: P
Order from tallest: P > Q > S > R. P is tallest, Q is second tallest.
Question 5: A factory produces 400 units per day. After a 15% efficiency improvement, how many units does it produce?
- 460 (Correct answer)
- 480
- 420
- 440
Correct answer: 460
400 × 1.15 = 460 units per day.
Question 6: Which statement follows logically? 'No birds are reptiles. All parrots are birds. Snakes are reptiles.'
- No parrot is a reptile (Correct answer)
- Some parrots are reptiles
- All reptiles are parrots
- Snakes are birds
Correct answer: No parrot is a reptile
Since all parrots are birds and no birds are reptiles, no parrot can be a reptile. Follows by transitivity of set exclusion.
UCAT Decision Making 2
A statement says: 'If it rains, the match is cancelled.
The match was not cancelled.' What can be concluded?