Team Formation Test

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Team Formation Test - 2

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Question 1
3 / -1

Direction: At Pioneer Career Kolkata six students A, B, C, D, E and F aspire to be a member of organizing team of New Year Party The team should have at least two people with following 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.
Q. If team size is 3 then which one of the following can not be a part of the team?

A
B

B
A

C
F

D
None of these

Solution

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.
Question 2
3 / -1

Direction: At Pioneer Career Kolkata six students A, B, C, D, E and F aspire to be a member of organizing team of New Year Party The team should have at least two people with following 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.
Q. Which of the following could never be part of same team

A
A & D

B
B & C

C
D & F

D
None of these

Solution

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.
Question 3
3 / -1

Direction: At Pioneer Career Kolkata six students A, B, C, D, E and F aspire to be a member of organizing team of New Year Party The team should have at least two people with following 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.
Q. What could be the strength of team if C and E are always part of the team?

A
2

B
3 or 4

C
2 or 3

D
None of these

Solution

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 all the three available cases A and C can be a member of the team that has strength 2 or 3 or 4
Question 4
3 / -1

Direction: At Pioneer Career Kolkata six students A, B, C, D, E and F aspire to be a member of organizing team of New Year Party The team should have at least two people with following 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.
Q. If B and F are not selected in the team then who should definitely be selected?

A
C

B
E

C
D

D
A

Solution

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
Question 5
3 / -1

Direction: K, L, M, N, P, Q, R, S, U and W are the only ten members in a department. There is a proposal to form a team from within the members of the department, subject to the following conditions :
(i) A team must include exactly one among P, R and S.
(ii) A team must include either M or Q but not both.
(iii) If a team include K, then it must also include L, and vice versa.
(iv) If a team include one among S, U and W then it must also include the other two.
(v) L and N cannot be members of the same team. L and U cannot be members of the same team
(vi) The size of a team is defined as the number of members in the team.
Q. Who cannot be a member of a team of size 3?

A
L

B
M

C
P

D
N

Solution

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.
Question 6
3 / -1

Direction: K, L, M, N, P, Q, R, S, U and W are the only ten members in a department. There is a proposal to form a team from within the members of the department, subject to the following conditions:
(i) A team must include exactly one among P, R and S.
(ii) A team must include either M or Q but not both.
(iii) If a team include K, then it must also include L, and vice versa.
(iv) If a team include one among S, U and W then it must also include the other two.
(v) L and N cannot be members of the same team. L and U cannot be members of the same team
(vi) The size of a team is defined as the number of members in the team.
Q. Who can be a member of a team of size 5?

A
K

B
L

C
M

D
P

Solution

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 .
Question 7
3 / -1

Direction: K, L, M, N, P, Q, R, S, U and W are the only ten members in a department. There is a proposal to form a team from within the members of the department, subject to the following conditions:
(i) A team must include exactly one among P, R and S.
(ii) A team must include either M or Q but not both.
(iii) If a team include K, then it must also include L, and vice versa.
(iv) If a team include one among S, U and W then it must also include the other two.
(v) L and N cannot be members of the same team. L and U cannot be members of the same team
(vi) The size of a team is defined as the number of members in the team.
Q. What would be the size of the largest possible team?

A
8

B
7

C
6

D
5

Solution

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.
Question 8
3 / -1

Direction: K, L, M, N, P, Q, R, S, U and W are the only ten members in a department. There is a proposal to form a team from within the members of the department, subject to the following conditions:

(i) A team must include exactly one among P, R and S.
(ii) A team must include either M or Q but not both.
(iii) If a team include K, then it must also include L, and vice versa.
(iv) If a team include one among S, U and W then it must also include the other two.
(v) L and N cannot be members of the same team. L and U cannot be members of the same team
(vi) The size of a team is defined as the number of members in the team.

Q. In how many ways a team can be constituted so that the team includes N?

A
2

B
3

C
4

D
6

Solution

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.
Question 9
3 / -1

Direction: A group of three or four has to be selected from seven persons. Among the seven are two women: Fiza and Kavita, and five men: Ram, Shyam, David, Peter and Rahim. Ram would not like to be in the group if Shyam is also selected. Shyam and Rahim want to be selected together in the group. Kavita would like to be in group only if David is also there. David if selected, would not like Peter in the group. Ram would like to be in the group only if Peter is also there. David insists that Fiza be selected in case he is there in the group.
Q. Which of the following is a feasible group of four?

A
Ram, Peter, Fiza, Rahim

B
Shayam, Rahim, Kavita, David

C
Shayam, Rahim, Fiza, David

D
Fiza, David, Ram, Peter

Solution

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.
Question 10
3 / -1

Direction: A group of three or four has to be selected from seven persons. Among the seven are two women: Fiza and Kavita, and five men: Ram, Shyam, David, Peter and Rahim. Ram would not like to be in the group if Shyam is also selected. Shyam and Rahim want to be selected together in the group. Kavita would like to be in group only if David is also there. David if selected, would not like Peter in the group. Ram would like to be in the group only if Peter is also there. David insists that Fiza be selected in case he is there in the group.
Q. Which of the following is a feasible group of three?

A
David, Ram, Rahim

B
Peter, Shayam, Rahim

C
Kavita, David, Shayam

D
Fiza, David, Ram

Solution

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 .

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Team Formation Test - 2

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Team Formation Test - 2

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Question 1

B

A

F

None of these

Solution

Question 2

A & D

B & C

D & F

None of these

Solution

Question 3

2

3 or 4

2 or 3

None of these

Solution

Question 4

C

E

D

A

Solution

Question 5

L

M

P

N

Solution

Question 6

K

L

M

P

Solution

Question 7

8

7

6

5

Solution

Question 8

2

3

4

6

Solution

Question 9

Ram, Peter, Fiza, Rahim

Shayam, Rahim, Kavita, David

Shayam, Rahim, Fiza, David

Fiza, David, Ram, Peter

Solution

Question 10

David, Ram, Rahim

Peter, Shayam, Rahim

Kavita, David, Shayam

Fiza, David, Ram

Solution

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