Question

There are $100$ students in a class. In an examination, $50$ of them failed in Mathematics, $45$ failed in Physics, $40$ failed in Biology and $32$ failed in exactly two of the three subjects. Only one student passed in all the subjects. Then the number of students failing in all the three subjects.

• A. is 12
• B. is 4
• C. is 2
• D. cannot be determined from the given information

Answer 1

Answer: (C)

is 2

Answer 2

According to question,
$a + b + c + d + e + f + g + h=100$ ...(i)
$h=1$ ...(ii)
$a + b + d +e=50$ ...(iii)

Venn diagram shows failed students
$b + c + d +f=45$ ...(iv)
$d + e + f +g=40$ ...(v)
$b + e +f=32$ ...(vi)
On solving, the above equations, we get $d=2$