3. A survey of 30 people finds that 16 are teachers, 12 own motorcycles, and 8 are neither. How many own motorcycles?
Answer: B
14 people own motorcycles.
In the survey of 30 people, after accounting for those who are neither teachers nor motorcycle owners, we can determine that 14 individuals own motorcycles based on the provided data.
A) 12
This option is incorrect because the survey indicates that 12 people own motorcycles; however, this does not account for the overlap with teachers or the total population being surveyed. The correct calculation shows that more than 12 must own motorcycles when considering the exclusions.
B) 14
This option is correct as it appropriately considers the total number of people surveyed and the exclusions. Since 8 people are neither teachers nor motorcycle owners, this leaves 22 individuals who are either teachers, motorcycle owners, or both. The calculations confirm that 14 must be motorcycle owners when the overlap is considered.
C) 16
This option is incorrect because it suggests that all 16 teachers own motorcycles, which contradicts the survey’s findings. The data indicates that the total number of motorcycle owners must be lower than the number of teachers due to the presence of individuals who are neither.
D) 18
This option is also incorrect since it exceeds the total number of motorcycle owners based on the calculations derived from the survey. With only 30 people and 8 being neither, it is impossible to have 18 motorcycle owners without exceeding the total.
Conclusion
The correct answer is 14, as it accurately reflects the number of motorcycle owners after considering those who are neither teachers nor motorcycle owners. All other options either misinterpret the data or exceed logical limits set by the total number of survey participants.