Test: Team Formation - 2 - CAT MCQ

Lets consider the different cases here
Case (i): Teams with 2 members:
A cannot be a member of any such team as otherwise at least one of B and C must be selected ( From condition (ii) and if B is selected then D also and if C is selected then E also hence in this case number of teams would be more than Possible teams are:
(B, D), (C, E), (D, E ) and (E, F)
Case (ii): Teams with 3 members: Possible teams with 3 members are (A, C, E), (A, B, D), (C, E, D)
Case (iii): Teams with 4 members: Possible teams with 4 members are (A, B, D, F), (A, C, E, D)
Team with 5 or 6 members is not possible.
From the case (ii) we can say that F can not be a part of the team.

Lets consider the different cases here
Case (i) Teams with 2 members :
A cannot be a member of any such team as otherwise at least one of B and C must be selected ( From condition (ii) and if B is selected then D also and if C is selected then E also hence in this case number of teams would be more than Possible teams are:
(B, D), (C, E), (D, E ) AND (E, F)
Case (ii) Teams with 3 members : Possible teams with 3 members are (A, C, E), (A, B, D), (C, E, D)
Case (iii) Teams with 4 members : Possible teams with 4 members are (A, B, D, F), (A, C, E, D)
Team with 5 or 6 members is not possible.
From the available 3 cases we can say that B and C can never be together.

To determine the possible team strength when A and C are always part of the team, we need to consider the given conditions:

(i) If the size of the team is less than 4, then D and F cannot be selected together. (ii) If B is selected, then D should also be selected, while E should be rejected. (iii) If A is selected, then exactly one from B and C should also be selected. (iv) If C is selected, then E should also be selected, while F should be rejected.

Given that A and C are always part of the team, let's evaluate:

1. From condition (iv):

   • If C is selected, then E must be selected and F must be rejected.
   • Therefore, E must be in the team, and F cannot be in the team.

2. From condition (iii):

   • If A is selected, then exactly one from B and C should also be selected.
   • Since C is already selected, B cannot be selected.

So, with A and C in the team, E must also be in the team, and B and F cannot be in the team.

The remaining candidate to consider is D.

• If D is selected, the team consists of A, C, E, and D. This makes the team strength 4.
• If D is not selected, the team consists of A, C, and E. This makes the team strength 3.

So, the possible strengths of the team, with A and C always part of it, are 3 or 4.

The correct answer is: 

       4. 3 or 4

Lets consider the different cases here
Case (i) Teams with 2 members :
A cannot be a member of any such team as otherwise at least one of B and C must be selected ( From condition (ii) and if B is selected then D also and if C is selected then E also hence in this case number of teams would be more than Possible teams are:
(B, D), (C, E), (D, E ) AND (E, F)
Case (ii) Teams with 3 members : Possible teams with 3 members are (A, C, E), (A, B, D), (C, E, D)
Case (iii) Teams with 4 members : Possible teams with 4 members are (A, B, D, F), (A, C, E, D)
Team with 5 or 6 members is not possible.
Possible teams without B and F are:
From Case (i) (C, E), (D, E)
From Case (ii) (A, C, E), (C, E, D)
From Case (iii) A, C, E, D

On the basis of above given question , we can say that
A team of size 3 has to have one of the M and Q and one of the P & R. The only other member that can be selected all alone is N
L cannot be selected as K has to be selected with him and then the total member will increase to 4.

Form the above answer M is the one of the options given in question. Hence, M is the member of a team of size 5 .

As per the given above question ,
Since S, U and W come together but there is no restriction with S hence if S is include the team will have S, U, W, M or Q, N.
This is the above largest possible team with 5 members.

Given in the question ,
If the team includes N, then it does not include L and K.
One out of M and Q can be include and one out of P,S and R can be included. If S is a member, so are U and W will also be member.
So we can select one out of M and Q in 2 ways
And we can select one out of P, S and R in 3 ways
Hence total number of ways = 2 x 3 = 6 ways.

Refer to the given information and eliminate the options, David and Peter cannot be in the same team so option (4) must be eliminated. If Rahim is selected then Shyam must be selected so option (1) must be eliminated.
David and Faza must be in the same team so option (2) must be eliminated.

Refer to the given information and eliminate the options we will get only option (2) satisfies all the given conditions.Hence , Peter, Shayam, Rahim is a feasible group of three .