Survey: 34 took calculus, 19 statistics, 3 both, 11 neither. Total surveyed?

Rationale

There were 61 individuals surveyed in total.

To find the total number of individuals surveyed, we can use the principle of inclusion-exclusion. We add the number of students taking calculus and statistics, subtract those counted twice (those taking both), and then account for those who took neither.

A (39) YOUR ANSWER

This option does not account for the students who took both calculus and statistics correctly. If we only add 34 (calculus) and 19 (statistics), we mistakenly count the 3 students taking both classes twice, thus leading to an incorrect total of 34 + 19 - 3 = 50. This is still not the total surveyed.

B (42) YOUR ANSWER

While this option also assumes a miscalculation, it reflects an incomplete consideration of the students taking neither. By taking 34 + 19 and subtracting 3, we would get 50. Adding the 11 students taking neither results in 50 + 11 = 61, not 42.

C (61) CORRECT

This is the correct calculation: starting with 34 students in calculus and 19 in statistics, we subtract the 3 students counted in both categories, which gives us 34 + 19 - 3 = 50. Adding the 11 students who took neither gives us a total of 50 + 11 = 61 surveyed individuals.

D (67) YOUR ANSWER

This option inaccurately sums the groups without accounting for the overlap and the students who took neither. Adding the totals directly (34 + 19 + 11) gives 64, but still neglects the overlap of 3 students taking both courses, leading to a miscalculation.

Conclusion

Using the principle of inclusion-exclusion, we determined that 61 individuals were surveyed in total. By accounting for those who took both courses and those who took neither, we arrived at the correct total, validating our calculations against the incorrect options, which either miscounted overlaps or neglected the students who did not participate in either class.

Survey: 34 took calculus, 19 statistics, 3 both, 11 neither. Total surveyed?

There were 61 individuals surveyed in total.

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