everybody plays Soccer or Hockey --> Neither = 0



Exactly one sport = Only Soccer + Only Hockey = 50 + 70 = 120

IMO Option D

Pls Hit kudos if you like the solution

I'd normally just draw a Venn diagram for similar questions, put 'x' in the middle, and fill it in, since that will work for any similar problem. But we can solve without a diagram: if we add the 80 soccer players and the 100 hockey players, to get 180, we're double-counting everyone who plays both sports. Since there are only 150 people, subtracting, we must be double-counting 30 of them, so 30 play both sports. The rest only play one sport, so 120 play only one sport.
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Given:
1. In a group of 150, everybody plays Soccer or Hockey.
2. 80 play Socker and 100 play Hockey

Asked: How many members in the group play exactly one of the two sports?



Total = Soccer + Hockey - Both + Neither
150 = 80 + 100 - Both + 0
Both = 30

Number of members in the group play exactly one of the two sports = Soccer + Hockey - 2*Both = 50 + 70 = 80 + 100 - 2*30 = 120

IMO D
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