GeeksforGeeks » Multiple Choice Questions
A GATE 2010 CS question
(5 posts)-
25 persons are in a room. 15 of them play hockey, 17 of them play football and 10 of them play both hockey and football. Then the number of persons playing neither hockey nor football is:
(A) 2
(B) 17
(C) 13
(D) 3 -
Answer is 3. Ten both. 5 hockey, 7 football so none is three
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How is it pL z Expalin it Clearly..........
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darkprince
Member
Posted 6 months ago #
Becoz ....
Hockey = 15
Football = 17
Both = 10
ONly Hockey = Total Hockey - both = 15-10=5
ONly Football = Total Football- both = 17-10=7So Total students = ONly hockey + only Football + Both + None play either of them
25=5+7+10+X
=>X=3So the answer is 3 Students
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we can use rules of set
let n(x) is notation for number of peoples who plays X game
n(X +Y) who plays both games
N total peoples
not(X + Y) = not plays any of 2
N= n(hokey)+n(football)-n(hockey + football) + not(hockey + football)
25=15 + 17 -10 +not(hockey + football)
25=22 +not(hockey + football)
25-22 =not(hockey + football)
therefor not(hockey + football) =3
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