CAT 2018 Slot 1 — QA Question 31
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 studies H or E or both. If the number of students studying H equals that studying E, then the number of students studying H is
Answer & solution
Answer: 52
Every student who studies P also studies. It means there is not one who studies only P.
Let ‘a’ and ‘c’ denote the number of students studying only H and only E respectively while ‘b’ denote the number of students studying H and P (but not E) and ‘d’ denote the number of students studying E and P (but not H).
Total number of students = a + b + c + d + 30 = 74
⇒ a + b + c + d = 44 ...(1)
Number of students studying H = Number of students studying E
∴ a + b = c + d ...(2)
From (1) and (2) we get,
a + b = c + d = 22
∴ The number of students studying in H = 22 + 30 = 52
Hence, 52.