A) 13
B) 24
C) 28
D) 52
Correct Answer: C
Solution :
[c]Numbers which are divisible by 5 are 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80 they are 16 in numbers, now, number which are divisible by 7 are 7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77 they are 11 in numbers. |
Also, total odd numbers = 40 |
Let C represents the students who opt. for cricket, F for football and h for hockey. |
\[\therefore \] we have \[n(C)=40,\,\,n(F)=16,\,\,n(H)=11\] now, \[C\cap F=\] odd numbers which are divisible by 5. |
\[C\cap H\]= Odd numbers which are divisible by 7. |
\[F\cap H=\]Numbers which are divisible by both 5 and 7. |
\[n(C\cap F),\,\,8,\,\,n(C\cap H)=6,\] |
\[n(F\cap H)=2,n(C\cap F\cap H)=1\] |
We know |
\[n(C\cup F\cup H)=n(C)+n(F)+n(H)-n(C\cap F)\] |
\[-n(C\cap H)-n(F\cap H)+n(C\cap H\cap F)\] |
\[n(C\cup F\cup H)=67-16+1=52\] |
\[\therefore n(C''\cap F'\cap H')\] |
= Total students \[-n(C\cup F\cup H)\] |
\[n(C'\cap F'\cap H')=80-52=28\] |
You need to login to perform this action.
You will be redirected in
3 sec