Question

In the final semester, an engineering college offers three elective courses and one mandatory course. A student has to register for exactly three courses: two electives and the mandatory course. The registration in three of the four courses is: 45, 55 and 70. What will be the number of students in the elective with the lowest registration?

Accepted Answer

E. Let mandatory course be $M$ and electives be $E_1, E_2, E_3$. Case 1: 70 is mandatory course registration. Total students $N = 70$. Sum of electives = $2N = 140$. Given elective registrations 45, 55, $x$. $45 + 55 + x = 140 \implies x = 40$. Elective counts are 40, 45, 55. Lowest = 40. Case 2: 70 is an elective. Total registrations given = 45, 55, 70 for electives. Total students $N = \frac{45 + 55 + 70}{2} = 85$. Lowest elective = 45. Hence, lowest elective registration is either 40 or 45.

Set Theory - Course Registrations

Explanation

Practise this under exam conditions