Problem Solving

There are 150 students at Seward High School. 66 students play baseball, 45 play basketball, and 42 play soccer. 27 students play exactly two sports, and three students play all three of the sports. How many of the 150 students play none of the three sports?
A) 0
B) 27
C) 30
D) 99
E) 78

Do we get B as the OA?

it's C.

Let the number of students who play both baseball and soccer be a.
basketball and baseball be b.
basketball and soccer be c.
a+b+c= 27

We can express the number of students who play as:

66+(45-3)-b-c+(42-3)-a-c+c= 66+42+39-b-c-a=147-(a+b+c)
whic equals 147-27=120

so 120 students play, therefore 150-120=30 students play none of the games.

Yes. Agree. Answer is C. 30 players.

answer is C.