Grouping and Team Formation
Direction: A team is to be selected out of the four boys  Prashant, Amit, Sood and Gupta  and the four girls  Ruchi, Neha, Deepti and Sriya  such that the team should have at least two boys and two girls. Further conditions are as follows:
(i) If Ruchi is selected, neither Amit nor Sood can be selected.
(ii) If Prashant is selected, Gupta is also selected.
(iii) Sriya will be in the team only if Sood is also in the team.
(iv) Amit, if selected would not like to have Neha in the team.
 If Sriya and Deepti are part of a team of four, then who will definitely be a part of the team ?

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Is Sriya and Deepti are part of a team of four, it means that two boys have to be selected. Since Sriya is selected therefore Sood will be definitely selected. Now , the second boy can be either Amit or Gupta. Therefore, the answer cannot be determined.
Correct Option: D
Is Sriya and Deepti are part of a team of four, it means that two boys have to be selected. Since Sriya is selected therefore Sood will be definitely selected. Now , the second boy can be either Amit or Gupta. Therefore, the answer cannot be determined.
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.
 If team size is 3 then which one of the following can not be a part of the team?

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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)Correct Option: C
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.
Direction: Nine people in a family have to go out for dinner. There are two available cars  Car 1 and Car 2  each of which can accommodate five persons. But there are certain conditions that need to be followed:
(i) Vats will always go in Car 1 and does not want Aks in the same car.
(ii) Exactly two out of the three children  Meh, Rey and Dan  will be in one car.
(iii) Chat and Nag will always be together in a car.
(iv) If Ana and Aks are in the same car, then Vij will also be in the same car.
(v) Any car cannot have more than five persons.
 If Meh and Rey are in Car 1, how many different combination are possible ?

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Vats is in Car 1 and Aks is in Car 2. Now, Meh and Rey are also in Car 1, which means that Dan is in Car 2.
Car 1 : Vats, Meh and Rey
Car 2 : Aks , Dan
The number of possible ways to arrange the remaining person is
Car 1 : Chat, Nag
Car 2 : Ana, Vij
Car 1 : Ana, Vij
Car 2 : Chat, Nag
Car 1 : Ana
Car 2 : Chat, Nag, VijCorrect Option: C
Vats is in Car 1 and Aks is in Car 2. Now, Meh and Rey are also in Car 1, which means that Dan is in Car 2.
Car 1 : Vats, Meh and Rey
Car 2 : Aks , Dan
The number of possible ways to arrange the remaining person is
Car 1 : Chat, Nag
Car 2 : Ana, Vij
Car 1 : Ana, Vij
Car 2 : Chat, Nag
Car 1 : Ana
Car 2 : Chat, Nag, Vij
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.
 What could be the strength of team if C and E are always part of the team?

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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.Correct Option: D
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
 If B and F are not selected in the team then who should definitely be selected?

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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:Correct Option: B
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