Question

A yogurt stand gave out 200 free samples of frozen yogurt, one free sample per person. The three sample choices were vanilla, chocolate, or chocolate & vanilla twist. 162 people tasted the vanilla and 115 people tasted the chocolate, some of those people tasted both because they chose the chocolate and vanilla twist. How many people chose chocolate and vanilla twist?

Answer 1

77

Explanation:

(V ∪ C) = V + C - (V ∩ C)
This is the same as: (V or C) = V + C - (V and C)

(V ∪ C) represents the number of people that chose chocolate or vanilla (or possibly both)

(V ∩ C) represents the number of people that chose chocolate and vanilla twist.

(V ∪ C) = V + C - (V ∩ C) ⇔ 200 = 162 + 115 - (V ∩ C)
(V ∩ C) = 162 + 115 - 200 = 77