UCAT/ UKCAT Question Analysis - Decision Making Question 40
A study looks at the commuting distances of all working inhabitants of towns A and B. The pie charts below show the number of inhabitants in each town and how far they need to travel to get to work.
Based on the data provided, which of the following must be true?
A. More people in Town A than in Town B live less than 2- miles away from their workplace.
B. If the two towns were located 30 miles apart then some people would be counted in both pie charts.
C. Town B inhabitants who commute less than 30 miles commute on average 17 miles.
D. The average commuting distance for Town A inhabitants is equal to or greater than 19 miles.
Answer and Explanation
D. The average commuting distance for Town A inhabitants is equal to or greater than 19 miles.
The calculation of the minimum possible commutin distance for Town A inhabitants is :
15%*0 + 20%*10 + 25%*20 + 40%*30 (i.e. you need to assume everyone lives at the lower end of their band)
= 2 + 5 + 12
= 19
Look at the other options:
A. More people in Town A than in Town B live less than 20 miles away from their workplace. Town A: (15% + 20%)* 1600 = 560. This compares to Town B: (10% + 20%)* 2000 = 600.
B. If the two towns were located 30 miles apart then some people would be counted in both pie charts. In reality this would make no difference as the pie charts record people according to where they live. So someone living in Town A and working in Town B would be recorded only in the Town A chart.
C. Town B inhabitants who commute less than 30 miles commute on average 17 miles. Without knowing individual commuting distances for all inhabitants, or at least an average for each band, we are unable to calculate any average at all.