CAT 2018 Slot 1 QA Question 11: Each of 74 students in a class studies at least one of the three subjects H, E and P. Ten students study all three subjects, while twenty study H and E, but not P. Every student who studies P also stu

Question

Each of 74 students in a class studies at least one of the three subjects H, E and P. Ten students study all three subjects, while twenty study H and E, but not P. Every student who studies P also stu

Accepted Answer

Let only H = a, only E = b, H and P only = x, and E and P only = y.
No student studies only P, because every P-student also studies H or E or both.
Total: $a + b + 20 + x + y + 10 = 74$
$a + b + x + y = 44$
The number studying H equals the number studying E.
$a + 20 + x + 10 = b + 20 + y + 10$
$a +