CAT Questions on Grouping And Selection PDF:
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Instructions: 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:
A team must include exactly one among P,R and S.
A team must include either M or Q, but not both.
If a team includes K, then it must also include L, and vice versa.
If a team includes one among S, U and W, then it should also include the other two.
L and N cannot be members of the same team.
L and U cannot be members of the same team.
The size of a team is defined as the number of members in the team.
Question 1: What would be the size of the largest possible team?
a) 8
b) 7
c) 6
d) 5
e) Cannot be determined
Question 2: Who can be a member of a team of size 5?
a) K
b) L
c) M
d) P
e) R
Question 3: Who cannot be a member of a team of size 3?
a) L
b) M
c) N
d) P
e)Q
Question 4: In how many ways a team can be constituted so that the team includes N?
a) 2
b) 3
c) 4
d) 5
e) 6
Question 5: What could be the size of a team that includes K?
a) 2 or 3
b) 2 or 4
c) 3 or 4
d) Only 2
e) Only 4
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Answers & Solutions:
1) 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.
2) 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.
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.
4) 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
5) 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 can be 4.
