Question

In a class of $140$ students numbered $1$ to $140$, all even numbered students opted mathematics course, those whose number is divisible by $3$ opted Physics course and those whose number is divisible by $5$ opted Chemistry course. Then the number of students who did not opt for any of the three courses is :

• A. 102
• B. 42
• C. 1
• D. 38

Answer 1

Answer: (D)

Let $n(A)$ = number of students opted Mathematics = $70$,
$n(B)$ = number of students opted Physics = $46$,
$n(C)$ = number of students opted Chemistry = 28,
$n(A\cap B)=23,$
$n(B\cap C)=9,$
$n(A\cap C)=14,$
$n(A\cap B\cap C)=4,$
Now $n(A\cup B\cup C)$
$=n(A)+n(B)+n(C)-n(A\cap B)-n(B\cap C)$
$-n(A\cap C)+n(A\cap B\cap C)$
$=70+46+28-23-9-14+4=102$
So number of students not opted for any course
= Total - $n(A\cup B\cup C)$
$=140-102=38$