Algebra-2 (Sets) (GATE-2010)

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
Solution follows here:

Solution:

Number of persons playing both Hockey & football = 10, which is common to both the streams.

Number of persons playing Hockey = 15

Hence Number of persons playing only Hockey = 15-10 = 5

Number of persons playing Football = 15

Number of persons playing only Football = 17-10 = 7

From the diagram, it is evident that the persons playing neither hockey nor football

Can be depicted out side both the circles.   

Hence number of persons playing neither hockey nor football

= 25-5-10-7 = 25-22 = 3

Answer (D)