In how many ways can the cabinet be selected ........

Logical Reasoning(SBI-PO) Puzzle Test

Direction (): The chief minister of a state has to select 5 ministers in his cabinet: Abhishek, Bardhan, Chetan, Darshan, Edwin, Fawad, Gurdeep and Harsh. The age (in years) of each minister is different among 36, 38, 39, 45, 48, 54, 57 and 59 years. From the eight ministers, the CM has to select at least one minister who is in his thirties, at least one minister who is in his forties and at least two ministers who are in their fifties. The CM must ensure the following additional conditions are also met:
* Bardhan, who is in his thirties, will be in the cabinet only if Harsh is not in the cabinet.
* Fawad is younger than Harsh and Harsh will be in the cabinet only if Abhishek is in the cabinet.
* If Chetan is in the cabinet, Darshan must not be in the cabinet.
* Edwin is six years older than Chetan and if one of them is in the cabinet, the other must be in the cabinet.
* Gurdeep is three years younger than Abhishek.
* Darshan will be in the cabinet if and only if Fawad, who is in his fifties, is in the cabinet.
* If Edwin is in the cabinet, Harsh must be in the cabinet.

In how many ways can the cabinet be selected?

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Explanation:

If one of Edwin and Chetan is in the cabinet, the other must be in the cabinet.

Case I: Both Edwin and Chetan are in the cabinet. Since Edwin is in the cabinet, Harsh must be in the cabinet. This implies Abhishek is also in the cabinet. Since Chetan is in the cabinet, Darshan cannot be in the cabinet. This implies Fawad is also not in the cabinet. Since Harsh is in the cabinet, Bardhan cannot be in the cabinet. So, the members of the cabinet are: Abhishek, Chetan, Edwin, Gurdeep and Harsh.

Case II: Neither Edwin nor Chetan is in the cabinet. Bardhan will be in the cabinet only if Harsh is not in the cabinet. Suppose Bardhan is in the cabinet, then Harsh cannot be in the cabinet and vice versa. But both Edwin and Harsh cannot be out of the cabinet as the cabinet has at least two ministers who are in their fifties. So, the members of the cabinet are: Abhishek, Darshan, Fawad, Gurdeep and Harsh.

The cabinet can be selected in 2 ways