Question

How many elective courses among E1 to E6 had to decrease in their enrollments after the change process?

• A. 4
• B. 1
• C. 2
• D. 3

Answer 1

The correct option is C 2

STEP I:
Given that after change, E2 is 30 more than before. E2 before was at least 46. E2 (after was 76). So, E2 before must have been 76-30 =46. That indicates that the two empty cells can be filled as 0 each across the row E2. Hence, the table will be as follows (after this condition).

STEP II:
Given that before change E1 = E4 + 6. Now, E1 (before) = 31. Further, E4 (before) must be more than 23 (3 + 2 + 14 + 4 + data in two empty cells). That indicates, the two empty cells across E4 must be 1 and 1. So, after this step, the cells can be filled up as follows.

STEP III:
Given that after change, E1 = E4 -3. It is to be noted that E1 (afterwards) can be at least 16 and at most 18. E4 (column) cannot be 20, as in that case, the total number of zeroes will cross 4. E4 must be 21. So, that E1 (afterwards) will be 18. This indicates, there must be 3 zeroes in E4 and one entry as “1” in the column E4. All other entries will be “1”.

The electives which had a decrease in the enrollments after the change process are E1, E4. So, a total of 2 electives.