Problem Solving

[sanjay]

Hello everyone, if you could help me out understanding the concept in solving this particular question.

Q: There are 150 students in a high school. 66 students play Baseball, 45 play Basketball and 42 play soccer. 27 students play exactly two sports and 3 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. 78
e. 99

Thanks

[Ben Ku]

Please cite the source (author) of this problem. We cannot reply unless a source is cited (and, if no source is cited, we will have to delete the post!). Thanks.

[sanjay]

Sorry about that, it just missed my mind to do that. This is an online test from 800score.com, test# 3, Q.no 35. I hope this will do.

[kanikagoyal]

the answer is C=30

If Ba= Students who only play baseball
Bk= only basketball & So= only soccer
and (x+y+z)=27 for students who play exactly 2 sports each. x= student playing Ba and Bk, y= student playing Bk and So,z= student playing So and Ba,

then, Ba+x+y+3=66
Bk+y+z+3=45
So+x+z+3=42

Adding all 3, Ba+Bk+So+2(x+y+z)=144
Ba+Bk+So+2(27)=144
Ba+Bk+So=90

No student playing any sport =150 -( Ba+Bk+So + x+y+z+3)= 150-90-27-3=30

Cheers
Kanika

[sanjay]

Thanks Kanika,

Even I figured it out by myself. It was just a small language problem, which at first I overlooked and made a wrong equation.

[Ben Ku]

I'm glad the problem was resolved. Please post if there are additional questions.