Electives

CAT 2017 Slot 2 · DILR · Hard · Logical Reasoning

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Passage / data set

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 However, before the start of the term, E7 was withdrawn as the instructor concerned had left the college.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.

From \ ToE1E2E3E4E5E6
E19510142
E234822
E326252
E432144
E55
E67329
E7416305541

Further, the following are known:

  1. 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.
  2. The number of students in E2 increased by 30 after the change process.
  3. Before the change process, E4 had 2 more students than E6, while E2 had 10 more students than E3.

Question 1 of 4

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

  1. A.

    4

  2. B.

    1

  3. C.

    2

  4. D.

    3

Answer

C

Explanation

By solving the system of equations derived from row and column sums and missing 0/1 entries: Initial counts: E1 = 31, E2 = 46, E3 = 36, E4 = 25, E5 = 21, E6 = 23, E7 = 101, Total = 300. Final counts: E1 = 18, E2 = 76, E3 = 79, E4 = 21, E5 = 45, E6 = 61. Decreases occurred in E1 (31→1831 \to 18) and E4 (25→2125 \to 21), which is 2 courses.

Question 2 of 4

After the change process, which of the following is the correct sequence of number of students in the six electives E1 to E6?

  1. A.

    19, 76, 79, 21, 45, 60

  2. B.

    19, 76, 78, 22, 45, 60

  3. C.

    18, 76, 79, 23, 43, 61

  4. D.

    18, 76, 79, 21, 45, 61

Answer

D

Explanation

The final counts in E1 to E6 are 18, 76, 79, 21, 45, 61 respectively.

Question 3 of 4

After the change process, which course among E1 to E6 had the largest change in its enrolment as a percentage of its original enrolment?

  1. A.

    E1

  2. B.

    E2

  3. C.

    E3

  4. D.

    E6

Answer

D

Explanation

Original and final numbers: E1: 31 to 18 (change = 13, 13/31 = 41.9%) E2: 46 to 76 (change = 30, 30/46 = 65.2%) E3: 36 to 79 (change = 43, 43/36 = 119.4%) E6: 23 to 61 (change = 38, 38/23 = 165.2%) Hence, E6 had the largest percentage change.

Question 4 of 4

Later, the college imposed a condition that if after the change of electives, the enrolment 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-enrol for that elective. Which of the following is a correct sequence of electives in decreasing order of their final enrolments?

  1. A.

    E2, E3, E6, E5, E1, E4

  2. B.

    E3, E2, E6, E5, E4, E1

  3. C.

    E2, E5, E3, E1, E4, E6

  4. D.

    E2, E3, E5, E6, E1, E3

Answer

A

Explanation

E1 enrolment dropped to 18 (less than 20). So all students who left E1 must re-enrol in E1. Total students who left E1 = 5+10+1+4+2=225 + 10 + 1 + 4 + 2 = 22. New count for E1 = 18+22=4018 + 22 = 40. These 22 students left E2, E3, E4, E5, E6 in the respective numbers, so final enrolments adjust to: E2 = 71, E3 = 69, E6 = 59, E5 = 41, E1 = 40, E4 = 20. Decreasing order: E2, E3, E6, E5, E1, E4.

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