UCAT Decision Making 1 — Questions and Answers
Question 1: A bag contains 3 red, 4 blue, and 5 green balls. If one ball is drawn at random, what is the probability it is NOT green?
- 7/12 (Correct answer)
- 5/12
- 1/3
- 1/2
Correct answer: 7/12
Total balls = 12. Non-green = 3 + 4 = 7. Probability = 7/12.
Question 2: A company has 5 managers and needs to select a team of 2. How many different teams are possible?
- 10 (Correct answer)
- 20
- 15
- 25
Correct answer: 10
Combinations: C(5,2) = 5!/(2!×3!) = 10. Order does not matter for team selection.
Question 3: In a survey, 60% of people own a car, 40% own a bike, and 25% own both. What percentage own neither?
- 25% (Correct answer)
- 35%
- 15%
- 20%
Correct answer: 25%
By inclusion-exclusion: car or bike = 60 + 40 − 25 = 75%. Neither = 100 − 75 = 25%.
Question 4: All doctors are professionals. Some professionals work long hours. Which conclusion must be true?
- Some doctors may work long hours (Correct answer)
- All doctors work long hours
- No doctors work long hours
- All professionals are doctors
Correct answer: Some doctors may work long hours
Since some professionals work long hours and all doctors are professionals, it is possible (but not certain) that some doctors work long hours. The word 'must' makes only the weakest provable claim valid.
Question 5: A train travels at 80 km/h for the first half of a journey and 120 km/h for the second half (equal distances). What is the average speed?
- 96 km/h (Correct answer)
- 100 km/h
- 104 km/h
- 90 km/h
Correct answer: 96 km/h
Harmonic mean for equal distances: 2×(80×120)/(80+120) = 2×9600/200 = 96 km/h. The arithmetic mean (100) is wrong when speeds cover equal distances.
Question 6: Four friends — A, B, C, D — sit in a row. A must not sit next to D. How many valid arrangements are there?
- 12 (Correct answer)
- 24
- 16
- 18
Correct answer: 12
Total arrangements = 4! = 24. Arrangements where A sits next to D: treat AD as a block → 3! × 2 = 12. Valid = 24 − 12 = 12.
UCAT Decision Making 1
A bag contains 3 red, 4 blue, and 5 green balls.
If one ball is drawn at random, what is the probability it is NOT green?