# Team Formation

Dear students,
The DI-LR section in CAT frequently features questions on team formation. So it is an important topic for all CAT aspirants. This set is from CAT 2006 Paper and will be very useful in decoding the pattern of this topic in CAT DI-LR section.

Answer questions 1 to 5 on the basis of 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:
• 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 must 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.

1. 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

2. 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

3. What would be the size of the largest possible team?
a.8
b.7
c.6
d.5
e.Cannot be determined

4. Who can be a member of a team of size 5?
a.K
b.L
c.M
d.P
e.R

5. Who cannot be a member of a team of size 3?
a.L
b.M
c.N
d.P
e.Q

Solution –
1. A team which has K should have L also. So, N and U cannot be included. As U is not included, S and W are not included. One out of M and Q and one out of P and R will be included. Thus, the team will include: K, L, (M or Q) and (P or R). Hence, option e.

2. Since N is in the team, L and K cannot be in the team. One out of M and Q can be included and one out of P, S and R can be included. If S is a member, so are U and W. Thus the possible teams are:
1. N, M, P
2. N, M, R
3. N, Q, P
4. N, Q, R
5. N, M, S, U, W
6. N, Q, S, U, W
Hence, option e.

3. If S is not included, the team can have P or R, M or Q, K and L. If S is included, the team will have S, U, W, M or Q, N. This is the largest possible team. Hence, option d.

4. If K and L are included, N, U, S and W are excluded. One out of P and R and one out of M and Q are included. Thus the team has only 4 members. If P or R are included, the team can have M or Q, K and L. This team also has 4 members. A team having M can have S, U, W and N i.e., 5 members. Hence, option c.

5. A team sized 3 has to have M or Q and P or R. The only other member that can be selected all alone is N. L cannot be selected as K has to be selected with him. Hence, option a.

Set analysis:-

Level of difficulty:- Easy to moderate
Expected time to solve:- 8 to 10 minutes.

Hope you learnt!

See you with the next one tomorrow!

Happy learning!
Gajendra sir
CAT Coach