A useful formula for two overlapping sets:
Total = Group 1 + Group 2 - Both + Neither
johng2016 wrote:
In a marketing survey, 60 people were asked to rank three flavors of ice cream, chocolate, vanilla, and strawberry, in order of their preference. All 60 people responded, and no two flavors were ranked equally by any of the people surveyed. If 3/5 of the people ranked vanilla last, 1/10 of them ranked vanilla before chocolate, and 1/3 of them ranked vanilla before strawberry, how many people ranked vanilla first?
A. 2
B. 6
C. 14
D. 16
E. 24
The formula above can be applied to this problem as follows:
Total = (number who ranked V before C) + (number who ranked V before S) - (number who ranked V before BOTH C AND S) + (number who ranked V before NEITHER C NOR S)According to the prompt:
Total = 60
Number who ranked V before C = (1/10)(60) = 6
Number who ranked V before S = (1/3)(60) = 20
Number who ranked V before neither S nor C = number who ranked V last = (3/5)(60) = 36
Plugging these values into the blue equation above, we get:
60 = 6 + 20 - (number who ranked V before both S and C) + 36
60 = 62 - (number who ranked V before both S and C)
Number who ranked V before both S and C = 62-60 = 2
Thus, the number who ranked vanilla first = 2