CAT 2025 Lesson : Selections - Cases 1 & 2

1) A king has unflinching loyalty from eight of his ministers M1 to M8, but he has to select only four to make a cabinet committee. He decides to choose these four such that each selected person shares a liking with at least one of the other three selected. The selected persons must also hate at least one of the likings of any of the other three persons selected.

M1 likes fishing and smoking, but hates gambling.
M2 likes smoking and drinking, but hates fishing.
M3 likes gambling, but hates smoking.
M4 likes mountaineering, but hates drinking.
M5 likes drinking, but hates smoking and mountaineering.
M6 likes fishing, but hates smoking and mountaineering.
M7 likes gambling and mountaineering, but hates fishing.
M8 likes smoking and gambling, but hates mountaineering.
[CAT 2001]

1) Who are the four people selected by the king?

(1) M1, M2, M5 and M6
(2) M3, M4, M5 and M6
(3) M4, M5, M6 and M8
(4) M1, M2, M4 and M7

Solution

The given minister's likes and dislikes can be plotted in a table to interpret easily.


As stated in the question, each selected person shares a like with at least one of the other three selected. The selected persons must also hate at least one of the likes of any of the other three persons selected.

Going by the options,

Option 1: M1 shares likes with M2, M5 shares dislikes with M6. However, M1 hates gambling which is not liked by M2, M5, M6. Therefore, option 1 is rejected

Option 2: M3, M4, M5, M6 have no common like among them. Thus, option 2 is rejected.

Option 3: M4 has no common likes with M5, M6 or M8. Thus, option 3 is rejected.

Option 4 satisfies the given conditions. Hence, option 4 is the answer.

Answer: (4) M1, M2, M4 and M7

Instructions for questions 2 and 3: Answer the questions based on the following information.

Director of an institute wants to distribute teaching assignments of HRM, Psychology, Development Studies, Trade policy and Finance to five of six newly appointed faculty members. Prof. Fotedar does not want any assignment if Prof. Das gets one of the five. Prof. Chaudhury desires either HRM or Finance or no assignment. Prof. Banik opines that if Prof. Das gets either Psychology or Trade Policy then she must get the other one. Prof. Eswar insists on an assignment if Prof. Acharya gets one.
[IIFT 2008]

2) Which of the following is valid faculty-assignment combination if all the faculty preference are considered?

(1) Prof. Acharya - HRM, Prof. Banik - Psychology, Prof. Chaudhury - Development studies, Prof. Das - Trade Policy, Prof. Eswar - Finance
(2) Prof. Chaudhury - HRM, Prof. Das - Psychology, Prof. Acharya - Development studies, Prof. Banik - Trade Policy, Prof. Eswar - Finance
(3) Prof. Acharya - HRM, Prof. Banik - Psychology, Prof. Eswar - Development studies, Prof. Das - Trade Policy, Prof. Fotedar - Finance
(4) Prof. Banik - HRM, Prof. Fotedar - Psychology, Prof. Eswar - Development studies, Prof. Chaudhury - Trade Policy, Prof. Acharya - Finance

3) If Prof. Acharya gets HRM and Prof. Chaudhury gets Finance, then which of the following is not a correct faculty-assignment combination assuming all faculty preferences are considered?

(1) Prof. Das - Development Studies, Prof. Banik - Trade Policy
(2) Prof. Fotedar - Development Studies, Prof. Banik - Trade Policy
(3) Prof. Banik - Development Studies, Prof. Eswar - Trade Policy
(4) Prof. Banik - Development Studies, Prof. Das - Trade Policy

Solution

2)
Let us refer to the 6 newly appointed faculty members Acharya, Banik, Chaudhury, Das, Easwar and Fotedar as A, B, C, D, E and F respectively.

Notes:

{Conditions given}
1. If D = 1 (D has been given an assignment) then F = 0.
2. C = HRM/Finance/No assignment.
3. If D = Psychology/Trade Policy, then B = 1.
4. If A = 1, then E = 1.

Let us consider the options.

Option 1: C must be assigned HRM or Finance or no assignment. Development Studies cannot be assigned to C. Hence, option 1 is rejected. (Condition 2)
Option 2: Does not violate any condition.
Option 3: Both D and F cannot be given assignments together. (Condition 1)
Option 4: C cannot be assigned Trade Policy.

Hence, option 2 is the answer.

3)
Let us refer to the 6 newly appointed faculty members Acharya, Banik, Chaudhury, Das, Easwar and Fotedar as A, B, C, D, E and F respectively.

Notes: {Conditions given}
1. If D = 1(D has been given an assignment) then F = 0.
2. C = HRM/Finance/No assignment.
3. If D = Psychology/Trade Policy, then B = 1.
4. If A = 1, then E = 1.
Let us consider the options.

Options 1, 2 and 3 do not violate any condition.
In option 4, D is assigned Trade Policy, B has to be assigned Psychology but instead B has been assigned Development studies.

Hence, option 4 is the answer.

Answer:
2) (2) Prof. Chaudhury - HRM, Prof. Das - Psychology, Prof. Acharya - Development studies, Prof. Banik - Trade Policy, Prof. Eswar - Finance
3) (4) Prof. Banik - Development Studies, Prof. Das - Trade Policy