There were seven elective courses - E1 to E7 - running in a specific term in a college. Each of the 300 students enrolled had chosen just one elective from among these seven. However, before the start of the term, E7 was withdrawn as the instructor concerned had left the college. The students who had opted for E7 were allowed to join any of the remaining electives. Also, the students who had chosen other electives were given one chance to change their choice. The table below captures the movement of the students from one elective to another during this process. Movement from one elective to the same elective simply means no movement. Some numbers in the table got accidentally erased; however, it is known that these were either 0 or 1.

Further, the following are known:

- Before the change process there were 6 more students in E1 than in E4, but after the reshuffle, the number of students in E4 was 3 more than that in E1.
- The number of students in E2 increased by 30 after the change process.
- Before the change process, E4 had 2 more students than E6, while E2 had 10 more students than E3.

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

- 4
- 1
- 2
- 3

**2. After the change process, which of the following is the correct sequence of number of students in the six electives El to E6?**

- 19, 76, 79, 21, 45, 60
- 19, 76, 78, 22, 45, 60
- 18, 76, 79, 23, 43, 61
- 18, 76, 79, 21, 45, 61

**3. After the change process, which course among El to E6 had the largest change in its enrollment as a percentage of its original enrollment?**

- E1
- E2
- E3
- E6

**4. Later, the college imposed a condition that if after the change of electives, the enrollment in any elective (other than E7) dropped to less than 20 students, all the students who had left that course will be required to re-enroll for that elective.**

**Which of the following is a correct sequence of electives in decreasing order of their final enrollments?**

- E2, E3, E6, E5, El, E4
- E3, E2, E6, E5, E4, El
- E2, E5, E3, El, E4, E6
- E2, E3, E5, E6, El, E3

### Answers

- C
- D
- D
- A

Given that after change, E2 is 30 more than before. E2 before was at least 46 as 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.

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.

Given that after change, E1 = E4 - 3. 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.

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

2. After the change process, correct sequence of number of persons in electives E1 to E6 is: 18, 76, 79, 21, 45 and 61.

3. The maximum change occurs in E6. From 23 to 61. A change of 38 and a % change of approx 165%.

4. Total number of persons in E1 (after the shift) is less than 20. All the 31 persons (earlier in E1) stayed back in E1. This implies no one shifted to E2, E3, E4, E5 and E6. The number of persons in decreasing order: E2, E3, E6, E5, E1, E4.