Grouping and Team Formation
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.
 Which of the following could never be part of same 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: 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.
From the available 3 cases we can say that B and C can never be together.
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 Ana and Aks are not in the same car, then which among the following cannot be the complete list of the occupants of Car 1 ?

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In option (c), all the children are in Car 2, which contradicts the basic condition.
Correct Option: C
In option (c), all the children are in Car 2, which contradicts the basic condition.
 If Ana is in Car 2 which has four persons, then which of the following is definitely true ?

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Ana is in Car 2, which has exactly four persons, Aks is already in Car 2, and since Aks and Ana both are in Car 2, therefore Vij is also in Car 2, which means that Car 2 will have exactly one child.
Correct Option: D
Ana is in Car 2, which has exactly four persons, Aks is already in Car 2, and since Aks and Ana both are in Car 2, therefore Vij is also in Car 2, which means that Car 2 will have exactly one child.
 If Chat is in Car 2, then who among the following is definitely in Car 1 ?

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If Chat is in Car 2, Nag is also in Car 2. Now, if Ana is also in Car 2, then Vij will also be Car 2. This would mean that all the three children are in Car 1, which in turn violates the basic condition.
Correct Option: C
If Chat is in Car 2, Nag is also in Car 2. Now, if Ana is also in Car 2, then Vij will also be Car 2. This would mean that all the three children are in Car 1, which in turn violates the basic condition.
Direction: Big B, the political wizard, was selecting his team for the forthcoming elections. His team was to have two speechwriters, two spokesman and two media coordinators. The available speechwriters for selection were A, B, C and D. Similarly, the available spokesmen were E, F and G and the available media coordinators were H, I, J, K. Further conditions are as follows:
(i) If A is selected, neither F nor J can be selected.
(ii) If C is selected, then J is definitely selected .
(iii) H and K will always be selected together.
(iv) I and K will never be selected together.
 Which two people cannot be a part of the same team ?

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A and C cannot be part of the same team since F has to be always selected with C but never with A.
Correct Option: D
A and C cannot be part of the same team since F has to be always selected with C but never with A.