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Answer the next 3 questions based on the information given below.
Amit, Bhushan, Chetan, Dinesh, Emran and Farah meet at a startup fair. The organizers of the fair decide to form a team of 5 members from this group by allocating to each member one of the five responsibilities - Marketing, Technology, Content Development, Public Relations and Human Resources.
The team formed must satisfy the following conditions:
If Dinesh takes the Technology role and Emran is responsible for Public relations, which of the following cannot be a possible person-role combination?
Answer: C
We know that if Bhushan takes the responsibility for Marketing then Chetan should get the PR role.
But Chetan and Dinesh cannot be on the same team. Hence, Bhushan cannot get the marketing role.
Hence, option 3.
If Emran is responsible for Human Resources and Bhushan for marketing, which of the following options represent the other role allocations?
Answer: A
As Bhushan has marketing, Chetan must have PR.
As Chetan is part of the team, Dinesh cannot be part of the team.
As HR is already taken, Amit can do only Content Development.
Hence, option (a).
If Amit is responsible for HR and Chetan is responsible for Public Relations, who is responsible for Content Development?
Answer: C
As Chetan has PR, Bhushan must get marketing.
As marketing and PR are gone, Farah must do Technology and Hence, Emran must do Content Development.
Hence, option (c).
Answer the next 5 questions based on the information given below.
K, L, M, N, P, Q, R, S, U and W are the only ten members in a department. There is a proposal to form a team from within the members of the department, subject to the following conditions:
What could be the size of a team that includes K?
Answer: E
A team which has K should have L also.
Since L is there in the team, N and U should not be there in the team. Since U is not there in the team, S and W should not be there in the team.
So, the team will have K, L, one of P and R and one of M or Q.
So, the team size will be 4.
Hence, option (e).
In how many ways a team can be constituted so that the team includes N?
Answer: E
Since N is in the team, L and K cannot be in the team.
The team can have one of M and Q. So, 2 ways of selection.
If the team has S, then it should have U and W as well.
If the team has no S, then it should have one of P or R.
So, the number of ways of forming the team is 2 × (1 + 2) = 6 ways
N S U W (M or Q) ⇒ 2 ways
N P (M or Q) ⇒ 2 ways
N R (M or Q) ⇒ 2 ways
Hence, option (e).
What would be the size of the largest possible team?
Answer: D
Out of P, R and S only 1 can be in the team. If S is there, U and W will also be there. So, P and R should not be in the team for its size to be maximum.
Out of M and Q, only 1 can be there.
If L is there in the team, N and U cannot be in the team.
If L is not there in the team, then K is also not there in the team but N and U can be in the team.
So, the maximum team size is 5 consisting of S, U, W, (M or Q), N.
Hence, option (d).
Who can be a member of a team of size 5?
Answer: C
Out of P, R and S only 1 can be in the team. If S is there, U and W will also be there. So, P and R should not be in the team for its size to be maximum.
Out of M and Q, only 1 can be there.
If L is there in the team, N and U cannot be in the team.
If L is not there in the team, then K is also not there in the team but N and U can be in the team.
So, the maximum team size is 5 consisting of S, U, W, (M or Q), N.
So, M can be a member of team size 5.
Hence, option (c).
Who cannot be a member of a team of size 3?
Answer: A
If L is in the team, the team should include K also. The team should have one among P, R and S and one among M and Q.
So, the team size cannot be 3 if L is in the team.
Hence, option (a).
