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?

The number of candidates registered for 3 of the 4 courses is 45, 55, and 70.
There are 2 cases.
70 can be the total number of students registered in an elective or the mandatory course. 
Case (i):
70 students have registered in an elective. 
Each student will choose 2 electives.
=> Total number of electives chosen = 2* total number of students.
45+55+70 = 2*number of students.
Number of students = 170/2 = 85.
In this case, the number of students in the elective with the lowest registration=45
Case (ii):
70 students have registered in the mandatory class.
=> 45+55+x = 2*70
=> x =40.

In this case, the number of students in the elective with the lowest registration is 40
As we can see, the number of students in the elective with the lowest registration can be 40 or 45. 

Therefore, option E is the right answer.