UCAT Decision Making

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?

Accepted Answer

7/12

Answer

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?

Accepted Answer

10

Answer

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?

Accepted Answer

25%

Answer

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?

Accepted Answer

Some doctors may work long hours

Answer

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?

Accepted Answer

96 km/h

Answer

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.

UCAT Practice Test

UCAT Practice Test

UCAT Decision Making