Grouping and Team Formation
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
 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.