1. Survey: 34 took calculus, 19 statistics, 3 both, 11 neither. Total surveyed?
Answer: C
The total number of individuals surveyed is 61.
To find the total number of individuals surveyed, we add those who took calculus, those who took statistics, and those who took neither while ensuring not to double count those who took both subjects. This calculation yields a total of 61 participants.
A) 39
This option is incorrect because it does not account for the total number of students surveyed. The calculation of 34 (calculus) + 19 (statistics) - 3 (both) + 11 (neither) exceeds 39, indicating a miscalculation.
B) 42
Option B is also incorrect. While it attempts to sum the participants, it fails to include the necessary adjustment for those who took both subjects and does not account for all individuals surveyed based on the provided data.
C) 61
This is the correct answer. The total is calculated as follows: 34 (calculus) + 19 (statistics) - 3 (both) + 11 (neither) = 61. This correctly represents the total number of unique individuals surveyed.
D) 67
This option is incorrect as it suggests a total that exceeds the actual number of participants. It does not accurately reflect the data provided, particularly failing to adjust for the overlap of students taking both calculus and statistics.
Conclusion
The correct answer is 61, which accurately reflects the total number of individuals surveyed after considering all groups and avoiding double counting. Options A, B, and D fail to provide a correct total, highlighting the importance of careful calculations in surveys to ensure accurate representation of the data.