Question

In a secondary examination, 75% of the students have passed in History and 65% in Mathematics, while 50% passed in both History and Mathematics. If 35 candidates failed in both the subjects, what is the total number of candidates sit for that exam?

(a) 658

(b) 398

(c) 764

(d) 350

The question was asked during an interview for a job.

Question is from Addition Theorem on Probability in division Discrete Probability of Discrete Mathematics

Answer 1

The correct choice is (d) 350

Easiest explanation: 50% passed in both the subjects, (75-50)% or 25% passed only in History and (65-50)% or 15% passed only in Mathematics, (50 + 25 + 15)% or 90% passed in both the subjects and 10% failed in both subjects. From the question, 10% of total candidates = 35. So, total candidates = 350.