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.
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If B and F are not selected in the team then who should definitely be selected?
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- C
- E
- D
- A
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
