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 Basketball
• D. All of the above are correct

Answer 1

The correct option is C 1 plays Hockey and Cricket but not Basketball

$a+e+f+g=23$
$b+d+f+g=15$
$c+d+e+g=20$
$f+g=7;d+g=5$
$e+g=4$
$a+b+c+d+e+f+g=60-15=45$
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 $\Rightarrow$ (b) is incorrect for (c) e = 1 $\Rightarrow$ (c) is correct.