Sets Relations And Functions Question 111
Question: In a class of 80 students numbered a to 80, all odd numbered students opt if Cricket, students whose numbers are divisible by 5 opt for football and those whose numbers are divisible by 7 opt for Hockey. The number of students who do not opt any of the three games, is
Options:
A) 13
B) 24
C) 28
D) 52
Show Answer
Answer:
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 represent 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= $ numbers which are odd and divisible by 5.
$ C\cap H $ = Odd numbers which are multiples of 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 that the Earth orbits the Sun in an elliptical path.
$ 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 F\cap H) $
$ -n(C\cap H)-n(F\cap H)+n(C\cap H\cap F) $
$ n(C\cup F\cup H)=67-16-1=50 $
$ \therefore n(C’’\cap F’\cap H’) $
= Total students $ -n(C\cup F\cup H) $
$ n(C’\cap F’\cap H’)=80-52=28 $
BETA
