Question

In a class of 60 students, 23 play Hockey 15 Play Basket-ball and 20 play cricket. 7 play Hockey and Basket-ball, 5 play cricket and Basket-ball, 4 play Hockey and Cricket and 15 students do not play any of these games. Then (a) 4 play Hockey, Basket-ball and Cricket (b) 20 play Hockey but not Cricket (c) 1 plays Hockey and Cricket but not Basket-ball (d) All above are correct

Answer 1

Answer: (c) 1 plays Hockey and Cricket but not Basket-ball

a+e+f+g=23

b+d+f+g=15

c+d+e+g=20

f+g=7;d+g=5

e+g=4

a+b+c+d+e+f+g=60−15=45

By substitutions, a+e=16,b+d=8,b+f=10,c+e=15,c+d=16

Also, b+c+d=22,a+c+e=30,a+b+f=25

From these, we get b=6,a=15,c=14e=1,d=2,f=4 and g=3

Clearly (a) is not correct

for (b) a + f= 19 ⇒ (b) is incorrect for (c) e = 1 ⇒ (c) is correct.